Introduction:  Urbino

          The name of a new and unexpected centre of building and design has now appeared in the history of early keyboard instruments as a result of the work carried out here.  The name of Urbino can also now be associated with the following:

1. the two earliest and probably the most important stringed-keyboard instruments ever made

2. a very fine polygonal Italian virginal made in 1540

3. a very fine and spectacularly beautiful  harpsichord made in about 1710. 

Taken together, the construction of the instruments studied here, all made in Urbino, stretches over a period of some 250 years.  But what is intriguing (and mystifying) to the author is that the last of these instruments (c.1710) is both elegant and beautiful in its appearance, but also that it has important design features that are identical to those of the previous instruments which originated and were built 240 years earlier at the Court of Federico da Montefeltro in Urbino. 

          But what is, to me, the most astounding contribution made by the author to modern organology is that, despite the fact that the RCM clavicytherium and the Urbino studiolo intarsia clavichord can be shown both to have been made for the Ducal Court of Federico da Montefeltro, the town of Urbino is not at all known today as a centre of early stringed-keyboard-instrument design and building.  Donald Boalch[17], in his comprehensive list of historical keyboard makers, did not list a single keyboard instrument in his book which was made in Urbino, nor are any keyboard-instrument makers listed by Boalch in his 1995 publication, who are known to have lived, worked, and been active as stringed-keyboard-instrument makers, in Urbino.  Urbino is also not mentioned in either of the two early ‘standard-works’ on the history of the harpsichord by Raymond Russell[18] and Frank Hubbard[19].  This seems to imply that Urbino was never an important centre of keyboard-instrument design, to the extent that not a single surviving instrument is presently described in the standard printed literature as having originated there.  It was therefore a delightful surprise for the author to find that not only the oldest surviving harpsichord in the world, but also one of the earliest representations of a clavichord, both originated in Urbino – and – that both of them were very old, having been designed for Federico’s Ducal Court in Urbino during the middle of the fifteenth century well over 500 years ago now.  No other fifteenth-century stringed-keyboard instrument from anywhere in the world is known to have survived, and certainly no other fifteenth-century keyboard instrument is known to survive which was designed and made in Urbino.  But the ‘made in Urbino story’ does not end there.  Indeed there are two further extant instruments of the highest level of workmanship, of elegant design, and each with a stunning decoration, which have survived from the historical period, and these instruments also originated through strong connections with the later successors to the Montefeltro Court in Urbino. 

          The oldest surviving harpsichord in the world – a clavicytherium now in the Royal College of Music in London (New Catalogue No. RCM0001) – will be shown here to have been made in Urbino at a date sometime shortly after 1461[20] (probably in about 1471[21], based on the work of Stewart Pollens[22]).  Pollens has found that Guarnieri seasoned his woods for only about 3 years after the trees used to make the violins were cut down and before using them in his violins.  Stradivari was more cautious, and made his violins after a period of 10 to 15 years after the wood was first cut and prepared.

          The second instrument described here is a highly-accurate intarsia ‘drawing’ of a clavichord in the studiolo (study room), 1473 – 1476) of the Palazzo Ducale in Urbino.  And although the latter instrument is simply a drawing in wood.  But unlike most extant instruments of such a considerable age which have been subjected to alterations and ‘improvements’ during their long history, this is a representation of a clavichord that has not suffered a single alteration to its case, string lengths nor fretting pattern in the subsequent 550 years.  Therefore all of its features, measurements, construction details, etc. are represented without having to unravel its past history and without having to disentangle the later alterations from its original state.  But what is truly remarkable about this ‘drawing in wood’ is the amazing accuracy with which it was actually carried out as will be seen in Chapter 4 below. 

          The RCM clavicytherium and the intarsia clavichord, just by virtue of their remarkable old age, are incredibly rare (there are no other extant keyboard instruments earlier than these which are known to the author) and so, having survived for at least 550 years, they are of the highest level of interest.  What has been attempted in this book is, as well, to show that these two instruments are of the highest importance because of their superb design features.  Indeed, it is my contention that no other stringed-keyboard instruments from any period are known to the author that have a more sophisticated design than these two instruments.  Additionally, the findings presented here can contribute greatly to our understanding of the musical transition from the Gothic period to the period of the High Renaissance.  There is now no surviving harpsichord older than RCM0001[23].  The date of the studiolo intarsia clavichord drawing can, however, be reliably restricted to the period somewhere between 1473-1476 from the evidence provided by the archives that deal with the construction of the studiolo itself.  There is otherwise not a single stringed-keyboard instrument that survives from the fifteenth century.[24] 

          My study here will show that the designer and builder of these two instruments – one a real tangible instrument, and one a ‘drawing’ of an instrument in wood – may even have originated from designs produced in the same workshop, and even, perhaps, from one-and-the-same person.  It seems to me that the designs of these two instruments are so idiosyncratic that I simply cannot imagine that they were designed by different people.  The possibility that both instruments are by the same person arises because of the clear similarities between some of the most intimate and, as just mentioned, idiosyncratic details of their design  But unfortunately the name of this brilliant designer is no longer known.  And although much of the library of the Ducal Court from this period has survived, all traces of the part of the archival documentation containing the day-to-day activity of the Ducal Court during Federico’s time was destroyed in the period between 1482 and 1613, mostly at the hands of the powerful and corrupt popes active then.[25] 

          There is therefore now no irrefutable, archival proof that either of these two priceless instruments was made by or for the Court of Federico da Montefeltro.  Neither is there any irrefutable proof that they were made by the same designer.  However, there is irrefutable scientific evidence that both were made in the Duchy of Urbino during the time of Federico’s enlightened rule of the Principality.  So, although there is probably no written evidence to contradict this because of the lack of archival documents, it is at least extremely likely that these two instruments were commissioned by, and built for, Federico da Montefeltro, along with a large number of other instruments that he is known to have commissioned and even to have played himself.

          But, like the intarsia clavichord in the Palazzo Ducale in Urbino, not all of the instruments studied here were made within the walls of the fortress surrounding the town of Urbino itself.  Having used the unit of measurement to show that it is almost a certainty that the RCM clavicytherium was made in Urbino, it will also be demonstrated here in Chapter 3 that the intarsias now in the studiolo in the Palazzo Ducale in Urbino itself used the unit of measurement, not of Urbino, but of Fossombrone or of Castel Durante which are two small towns both less than 20km from Urbino (see Figure 4 on page 17 below).  However, although both towns are now outwith the administrative precincts of Urbino itself, both Fossombrone and Castel Durante were then a central part of the Duchy of Urbino itself, and so the intarsia made there could even be thought of as having been “Made in Urbino”.  The later course of this discussion will go on to show that a stunning polygonal virginal, commissioned by Eleonora, Duchessa of Urbino (1493 – 1570) in 1540 (see Figure 52 on page 131), and so about a century later than the clavicytherium, was also designed and built in either Fossombrone or in Castel Durante.  But both of these centres were (and are still) in the Duchy of Urbino, and both used the same size for their standard units of measurement, although both units of measurement were notably distinctly different from the size of the unit that was actually used in Urbino itself.  In addition, it has also been discovered here that a superb single-manual harpsichord, now in the Ca’ Rezzonico in Venice and dating to about 1710, was designed and built in the Duchy of Urbino, surprisingly since it was made some 270 years later but with many of the same design features used in the two earliest fifteenth-century instruments which were also designed and made in Urbino. 

          This recent research shows that, although previously unrecognised as such, Urbino was a centre of the highest excellence in the field of the design and construction of keyboard instruments for a period of at least 260 years from about 1471 until at least 1710.  Indeed the sophistication of the design of the first two instruments discussed here (and the first two made in the entire history of early stringed-keyboard instruments) has, in the author’s opinion, never been superseded. 

          Only superlatives can be used to describe this period of stringed-keyboard instrument design in Urbino.  Urbino is already known as a leader in the field of painting, architecture, and the fine arts.  But a prominent feature of the work carried out here is that it shows that Urbino was a hotbed of activity in all of the mathematical arts as well, and this included the design of stringed-keyboard instruments.  My work also recognises the importance of the stringed-keyboard instruments’ designers to the history of late medieval and early Renaissance keyboard building in general, and to the process of the transition between these two highly-interesting musical periods.  The two are in fact, and not surprisingly, intimately intertwined.  This work shows that Urbino was pivotal in the history of music, it was pivotal to the history of performance practice, to the understanding of fifteenth-century music in general, and particularly to our understanding of the design, construction, and the practical day-to-day use of the earliest surviving stringed-keyboard instruments. 

 

Chapter 1 – The importance of the Ducal Court of Federico da Montefeltro of Urbino in the period around the middle of the fifteenth-century, and the relationship of his Corte matematica to two of the earliest known stringed-keyboard instruments in the world.[26]

 

Section 0‑19 - Who was Federico da Montefeltro?

 

 

Figure 3 – A portrait of Federico da Montefeltro, Duke of Urbino (right) and of his second wife Battista Sforza (1446 – 1472) (left).

Piero della Francesca, c.1470.  Le Gallerie degli Uffizi, Florence, Inv. 1890 and Inv. No. 1615, 3342.

 

          Federico da Montefeltro, Duke of Urbino and his wife Battista Sforza have, until now, been unrecognised figures in the history of the earliest period of stringed-keyboard instrument making.  What will be shown below is that the clavicytherium in the Royal College of Music, the oldest known harpsichord in the world, was made in Urbino, and that it was made during the period of the rule of Federico da Montefeltro there.  This conclusion is based on two factors: 

1.      The centre of construction of the instrument:  it is clear that all aspects of the clavicytherium’s construction and design are Italianate in concept, and not in Ulm as previously held to be the case.  It is also clear that the design itself is based in a fundamental way on the use of the Urbino oncia (inch), the normal unit of measurement used in Urbino in the fifteenth century.  No other centre in Italy, nor elsewhere in Europe, is known to have used this particular size of the unit of measurement, making it a virtual certainty that the clavicytherium was made and designed there.  The mathematical determination of the size of the unit of measurement used to space the guide pins for the jacks in the main part of the instrument can be seen in Figure 32 on page 57.

2.      The dating of the instrument:  a strip of parchment glued to the back inside of the instrument and behind one of the soundboard rosettes refers to one Bartlome Abeille[27], who is known from the archives to have been a citizen of Ulm in South-central Germany during the period around the end of the fifteenth century.  The parchment is undated but, from the (highly-uncertain) date and style of the handwriting, it has been unreliably dated to the period around 1480.  So, the argument goes, the instrument must therefore have been made at some time before 1480.  However, none of the literature published so far indicates Urbino as the place in which this instrument was designed and built.

          But there are many problems and inconsistencies inherent in the arguments put forward by the RCM catalogue regarding the dating of the parchment strips onto which the German inscriptions have been written.  Some of these are listed below:

·         The chief problem seems, to the author of the present work, to lie in the supposed sequence of events preceding the gluing of the parchment strips to the baseboard inside the instrument.  The arguments put forward by Elizabeth Wells[28] to date the instrument do not take into account how these parchment strips were actually placed inside the instrument and glued to the baseboard.  The only way of gaining access to the baseboard was through the hole for the soundboard rosette through which the writing on the parchment strips can now be seen.  There seems to the author to be no doubt that the soundboard rosette was not in place because of a simple size disparity when these strips were glued to the baseboard, and this suggests, in turn, that the soundboard rosette had been broken and that it had been missing, probably for some time, when the strips were glued in place.  The parchment strips could have been added 50 – or 100 years – or more – after the instrument was first built.  To the author there is no correlations whatsoever between the date of the construction of the instrument and the date of the handwriting on the strips.  The parchment strip was taken from an old document, and could therefore date to any previous time before or after the instrument was first made.

·         Similarly there seems to the author to be no reliable correlation between the date of the inscription on the parchment strips and the date of the words “Vorders” and “Hinders” written on what is obviously the later stand now supporting the instrument.  No logical connection can be seen between the date of the writing of these two words on the stand, the date of the inscription on the parchment strips, and the date of construction of the instrument itself.  These 3 could equally all be totally unrelated in time and in the place where they were added.  The stand, at least, is recognised as being much later than the date of the instrument itself.

·         In the author’s view, all that can be said is that the inscriptions and the stand were added at some totally indeterminate date(s) after the basic instrument was first built.  To the author they tell us nothing about the date or the place in which they were added – except, obviously, that they must have been added somewhere in Germany – and they tell us nothing about the date of the original construction of the instrument.

          The author’s arguments would mean that, well after its initial construction, the instrument was exported to Ulm (across the Alps!), possibly by or for Bartlome Abeille.  Inexplicably no dendrochronological dating of the growth rings of the needle-woods of the soundboard wood nor of the wood of the rear side of the instrument was carried out until 2025.  This seems very strange since both of these locations on the instrument are in unobstructed view from the outside of the instrument, and therefore in an ideal position for carrying out such a dendrochronological analysis.  This could take place either by a direct measurement of the spacing of the ring of the wood of the instrument itself.  Or it could be carried out in a completely non-interactive way by taking a normal photograph of the soundboard, and of the back of the instrument.  A photograph would not pose any danger at all to this precious old and delicate old instrument.[29]  But such an analysis would, scientifically and with a high degree of accuracy, almost certainly be able to tie down both the region of origin of the instrument as well as a date of its construction.  It would therefore provide a satisfactory back-up analysis to confirm what has been shown here, independently of the dendrochronological analysis. 

          Dendrochronology is a science with simple principles which can be carried out using simple methods and analysed against an enormous background of databases of relevant reference material consisting of dendrochronological sequences.  These reference databases can be used to date any piece of spruce, fir or oak for which the databases exist.  The instrument and its importance have been known since it first became a part of the Royal College of Music Collection in 1894 but, inexplicably, no proper dendrochronological analysis has been carried out by any of those in charge of the Collection until it finally happened earlier this year (2025).  

          This year, the last visible growth ring was dated to 1461.  However, inexplicably no location has yet been found for the region in which the tree making up the wood of the instrument.[30]  What is exciting about this (even with the uncertainties placed on this by not being able to fix the location) is that the date 1461 is very important to the history of the instrument in the context of the other things that were happening in Urbino.  This will be discussed later.

 

 

A further connection of the Urbino intarsia clavichord to Urbino and to the RCM clavicytherium

          An additional Urbino connection with the very early history of keyboard-instrument-making is provided by the intarsia clavichord studied in detail in Chapter 3 of this work.  This clavichord is represented with astounding accuracy in the wood-inlay intarsia in the small studiolo (study room) in the Palazzo Ducale in Urbino.  The Palazzo Ducale is an enormous building that was commissioned by Federico da Montefeltro, under whose direction the RCM clavicytherium discussed above, must have been made.  The image of the intarsia clavichord in the Palazzo Ducale is positioned in the walls of the small studiolo, along with many other images including those of a number of musical instruments.  The intarsia of the clavichord is drawn with such accuracy, and in such detail, that even the tuning of the instrument in Pythagorean intonation[31] can be reconstructed from the accurate positioning of the tangents and the slots in the keyboard rack.

          Although the RCM clavicytherium and the intarsia clavichord were probably designed at least 20 years apart, it is demonstrated here that they have a number of intrinsic, and highly idiosyncratic design features in common, which immediately then suggest that both instruments originated from the same workshop tradition.  Indeed these characteristics, despite being small in number, are so uncommon and idiosyncratic that their similarities imply that the two instruments may even have been designed by one-and-the-same person. 

          But clearly, without Federico’s support and patronage resulting from his immense wealth, it is unlikely that the two instruments discussed here would even have existed in the first place.  And this would mean that their contribution to our knowledge of the design features of the two earliest surviving keyboard instruments would also be unknown.  It would mean further that our understanding of the contemporary keyboard music would also be notably poorer.  Now, as a result of the knowledge of the two instruments studied here, the understanding of the music of the period will certainly be enriched even further after a re-appraisal of the instruments that played this music, in the light of what is shown in the chapters below.

 

 

Section 0‑1 - Where is Urbino?

          Urbino is a late medieval walled town in the hilly countryside in the foothills of the Northern Apennines.  It lies at the heart of the old feudal territory in the northern part of the present Italian province known as Le Marche[32] in a position roughly straight north of Rome and straight east of Florence[33].  The land belonging to the Duchy of Montefeltro had Urbino roughly in the middle of its territory as its capital and headquarters, with Rimini, Pesaro and Senigallia on the Adriatic coast along its eastern flank.   

Figure 4 – Extract of a map showing Le Marche with some of the centres studied here.  Urbania, at the time of Federico da Montefeltro, was known as Castel Durante.  Gubbio, the birthplace of Federico da Montefeltro and seen at the lower left, is now outwith the modern boundaries of Le Marche. 

          Federico da Montefeltro was Duke of Urbino and was one of the most successful condottieri[34] (mercenary general) of the Italian High Renaissance.  The role of condottiero carried with it a very high danger of injury or even death during the commissions he was expected to carry out.  Because of the risks involved both to the condottiero himself and to his troops, and because it required a large number of men to carry out these exploits, a condottiero would normally have been hired out for a very, very large sum of money.  As result of his many exploits, ventures and adventures as a soldier of fortune, Federico became immensely wealthy as Lord of Urbino from 1444, and as Duke of Urbino from 1474 until his death in 1482.  Federico was involved in battles against the Kingdom of France, the Kingdom of Naples, the Venetian Republic, as well as with the rulers of numerous Duchies and Earldoms within the present modern-day borders of Italy.  All of these were high-return exploits that brought Federico vast sums of money and wealth.  This huge capital was used by Federico to secure his own position in his Dukedom, but also to finance huge building schemes, and also to finance a long and sustained advancement of the Arts in Urbino in all of its aspects.

          Federico was born in Gubbio, a small town about 60km south of Urbino.  He was the illegitimate son of Guidantonio da Montefeltro, but was legitimised by the then Pope Martin V in 1422, two years after Federico’s birth, by virtue of Guidantonio’s wife, Catherina Colonna, being Pope Martin V’s cousin.  As a youth Federico was extremely fortunate in acquiring a good, solid, humanist education (see footnotes 36 and 46 below) which was much superior to that of his elder half-brother Oddantonio.  Federico, aged only 15, was sent in 1437 to train in the art and craft of war with one of the then greatest Milanese condottieri of all time, Bartolomeo Colleoni (1400 – 2 November 1475).  Also in 1437 he was knighted by Emperor Sigismund, Emperor of the Holy Roman Empire.  In the same year he married the 21-year-old Gentile Brancaleone, his father’s ward, in Gubbio.  His marriage to Gentile brought a highly important dowry with it, including a number of centres (14 castles) formerly ruled by the Brancaleone family.  As a result, these centres then also became a part of Federico’s dominion and therefore of his Dukedom.  Gentile was infertile, however, and was unable to bear Federico any children.  Gentile died in 1457 and so, 20 years after her marriage to Federico in 1437, he was left without an heir.

          But as a result of his fine education, Federico was of a thoroughly humanistic disposition and followed his humanist principles to the letter.  Following these ideals, he was unusually (for the time) kind to the men whom he commanded, and also to the wives and the families of those of his troops who died under his command.  This kindness and sympathy towards his soldiers had a positive feed-back effect, as a result of which he had a very faithful military following, which then supported him totally.  This led, of course, to his further successes as a condottiero and to his increasing wealth and importance. 

          Federico’s father died in 1443 and was succeeded by Federico’s older brother Oddantonio.  But Oddantonio was inefficient, cruel and dissolute, and was murdered in a conspiracy led by his enemies[35] in July 1444.  As a result Federico took on a new role as Lord of Urbino from that date onwards.  Because Gentile, his first wife, died in 1457, he then married Battista Sforza (see Figure 3 above) with whom he had been carrying on an affair for some years prior to the death of Gentile.  After their marriage in 1460, Battista Sforza took on the responsibility for much of Federico’s administrative chores, and seems to have bee a great help to Federico.  Battista eventually bore Federico 7 girls before giving birth to Federico’s male heir Guidantonio II.  Battista, the great love of Federico’s life and his right-hand companion during times of both peace and war, died shortly after the birth of his male heir in 1472 and Federico, by then 50 years old, never again re-married.

          Federico was also one of the truly great ‘characters’ of the time.  He was badly disfigured and blinded in his right eye in a jousting accident in 1451 when he was 29 years old.[36] As a result of this disfigurement his portraits were always painted showing his ‘good side’ (see Figure 3 above and Figure 13 below).

 

 

 Section 0‑2 – Federico da Montefeltro and the Corte matematica (Court of the Mathematical Arts) in Urbino.

          Why was Federico da Montefeltro and his court so important to Renaissance history in general and to the history of early keyboard-instrument building in particular, and why is it necessary to understand what happened under the rule of Federico, to his Court in Urbino?  Coinciding with Federico’s rule and influence in Urbino, a number of further components of Federico’s life came together there – many at his instigation – at the beginning of the second half of the fifteenth century.  It can be confidently asserted that this all happened in a way that was truly unique in Europe, and which gave rise to the intellectual climate that was active in this period in Urbino. 

          Having spent an initial period of time during his youth as a hostage in Venice, Federico had to be moved to Mantua because of a severe plague which over-ran La Serenissima when he was aged about 12.  Fortunately Federico then ended up in the famous enlightened school – La Ca’ Zoiosa (the House of Joy) – under the tutelage of Vittorino da Feltre.[37]  In La Ca’ Zoiosa he received the foundations of one of the purest forms of humanist education based on the quadrivum – the four ways.  This taught him the basics of the mathematical arts under the titles of the four subjects: arithmetic, geometry, astronomy and music performance.  It was here, at the very beginnings of the great humanist movement, which coincided perfectly with the beginnings of his studies, that his education brought to the forefront his great humanist ideals.  These included the mathematical arts, and these four subjects were later to play such an important part in his life.  They were also to contribute so much to the study carried out in the present work.  

          As a condottiero Federico was remarkably successful.  The devotion of his troops to him and to his leadership, and the fact that he never betrayed any of his patrons by ‘changing sides’ as a result of a more lucrative offer from the opponent with whom he was doing battle, meant that he was trusted not only by his troops, but also totally trusted by his employers.  As a result of his many successes in battle, he encouraged others to employ him, and with such a large number of ‘clients’ hiring him on, he became hugely wealthy. 

          Federico used this wealth to build palaces and fortifications for himself throughout the whole of the Duchy of Urbino.  But his investment in ‘bricks and mortar’ was also matched by his investment in the arts, sciences, literature, philosophy, music and musicians and, it would seem, in musical-instrument design and building.  The two instruments discussed below in Chapter 2 and Chapter 3 are both good examples of the kinds of things being produced in Federico’ Court. 

          Federico went on to assemble a huge group of the most important figures of the artistic, scientific and humanist movement around him.  His court was filled with some of the greatest minds of all times including artists, scientists, philosophers, writers and, especially important to this study, he assembled some great musicians and mathematicians who were able to solve some of the most difficult problems encountered in the string-scaling design of musical instruments.  This will be illustrated using the design of the RCM clavicytherium (studied here in Chapter 2) and in the design of the intarsia clavichord drawn in wood into the walls of the studiolo of Federico’s Palazzo Ducale in Urbino, studied in Chapter 3.  Among the many other marvels of Federico’s Palazzo Ducale in Urbino are the two staircases inside the ‘torricini’ (towers) of the Palazzo Ducale with the famous studiolo worked into the fabric of the building between them.

Figure 5 – The spiral staircase in the south-east ‘Torricino’ (little tower) of the Palazzo Ducale in Urbino, showing the skill of the mathematicians, architects and stonemasons who erected this circular, spiral staircase in a rectangular stairwell.

          But this staircase is only a taster-demonstration of the skills of those working for Federico!  His sponsorship led, for example, to the publication of the fundamental work on perspective during the Renaissance – The Science of Perspective - that was formulated in his ground-breaking work by one of Federico’s personal friends Leon Battista Alberti, (1404 – 1472) (see Figure 6 on page 20 below).  Alberti was an Italian humanist in the widest sense of the word, and one of the truly great Renaissance polymaths.  He was the principal initiator of Renaissance art theory and is, indeed, considered to be the father of Early Renaissance art theory.  Alberti was the first to propose a set of principles by which artists could give 3-dimensional depth and perspective to their 2-dimensional art works.  This was laid out by Alberti according to a highly logical set of compositional rules.  But he was not only an exceptionally prodigious mathematician, but he applied his skills in many different aspects of art and architecture.  Indeed he was, even during his lifetime, a renowned architect – he designed the façade of the Churches of Santa Maria Novella in Florence (see Figure 7 below) and also the Basilica of Sant’ Andrea in Mantua, for example.  He was also a cryptographer and, as well, he wrote the first Italian grammar.  But he also wrote about astronomy and the science of geography. 

 

Figure 6 – Portrait of the great Renaissance polymath, Leon Battista Alberti, 1404 – 1472.

Alberti was the polymath who invented the mathematics and science of drawing a 2-dimensional representation of a 3-dimensional object.

The painter and the present location of this painting are unknown.

 

          The above painting somehow gives an insight into the depth and breadth of Alberti’s character and knowledge.  In his book De pictura (On Painting, 1435 - 1450), Alberti laid down a secure mathematical foundation and scientific approach to the drawing and painting of perspective that was fundamentally and mathematically thorough and enduring.  In this work he laid the mathematical foundations for the representation of perspective, which has been found to be valid right up to the present day.  Alberti’s ideas were, for example, incorporated into the intarsia perspective drawings of Federico’s studiolo 20 years later, in the latter’s Palazzo Ducale in Urbino, as well as in an unlimited number of artistic works by contemporary and by later artists. 

          His design of the great façade of the Basilia of Santa Maria Novella in Florence is universally recognised as one of his greatest and most important works (see Figure 7 below). 

Figure 7 – The white marble façade of The Basilica of Santa Maria Novella, Florence.

Designed by Leon Battista Alberti, 1456-70

 

          Perhaps most importantly, his ideas on perspective provided the basic foundations for two of the greatest Renaissance artists of the next-generation, Piero della Francesca and Leonardo da Vinci.  He was, incidentally, a great personal friend of Federico da Montefeltro with whom he shared many ideas and new concepts. 

          Although Alberti is best known for his treatises on perspective and on architectural design, he is also credited with being the first artist in the world to produce a self-portrait.  He did this in the form of a bronze cast medallion (not illustrated here) of which many versions have survived.[38]

          As well as the person of Alberti, Federico collected together a whole group of extremely capable scholars, artists and musicians most of whom were also competent mathematicians and scientists.  For Federico, there was to be no separation of the arts and the sciences that is unfortunately now, in many ways, characteristic of the modern period.  Those scholars and scientists who he assembled in his Court were to set the scene for what has become known as the true ‘Renaissance Man’.  The concept of ‘The Renaissance Man’ was formulated by Leon Battista Alberti who said that “a man can do all things if he will.”  The ideal of ‘The Renaissance Man’ embodied the basic tenets of Renaissance humanism, which considered man to be the centre of the universe, limitless in his capacities for development.  This philosophy led to the notion that men should try to embrace all knowledge and develop their own capacities as fully as possible.  These men[39] had a very strong interest in mathematics and the sciences.  They included contemporaries like the astrologer Paolo da Middelburg, Piero della Francesca (see Figure 3 on page 14 above), Luca Pacioli and Francesco di Giorgio Martini (see Figure 8 below) all of whom were directly involved in Federico’s Court and in the activities surrounding it. 

          Of these was Francesco di Giorgio Martini, who was probably the greatest of Federico’s architects.  He is notable for the length of time he spent in Federico’s Court, and for the multitude of works he carried out there for Federico.  Martini was born in Siena, where he apprenticed as a painter with Lorenzo di Pietro, usually known as ‘Il Vecchietta’.  Francesco was also a true ‘Renaissance Man’ and, as such, was active as an architect, engineer, painter, sculptor, and writer – in other words he was a good example of a Renaissance polymath.  He was considered a visionary architectural theorist.  And as a military engineer, he executed many structural and building designs as well as sculptural projects for Federico.  He built almost seventy fortifications for Federico, each with heavy defensive walls, and early examples of unusual star-shaped fortifications (see Figure 9 on page 23 below), referred to by some as being ‘turtle-shaped’!

Figure 8 – FRANCESCO GIORGIO SCUL.(TORE) E ARCHIT.[ETTO] SANESE

A charming portrait of Francesco di Giorgio Martini (Sculptor and Architect from Sienna).

Giorgio Vasari, Lives of the Most Excellent Painters, Sculptors, and Architects, Giunti, Florence, 1568 [slightly enlarged version].

 

          Francesco di Giorgio’s most important written work was an architectural treatise in 3 volumes, Trattato di architettura, ingegneria e arte militare,[40] (A Treatise on architecture, engineering and the military arts) which he worked on for decades, and which he finally brought to completion sometime after 1482.  But this was only after the death of Federico, his great patron.  The architectural projects listed in this work were conceptually well in advance of any other works completed at the time.  For example, in staircase planning, Francesco di Giorgio Martini made staircases run in flights and landings around an open centre – or they were divided at a landing to turn symmetrically to the sides and to each side wall.  These then became a part of standard architectural vocabulary in the following centuries and are almost taken as standard by modern architects.  Martini’s third book is preoccupied with the ‘ideal’ city (see Figure 10 on page 24), or with fortifications or bastions, often constrained within star-shaped polygonal geometries reminiscent of the star fort, whose wedge-shaped bastions are generally accepted to have been one of Francesco’s many great innovations (see Figure 9 below).

          The author has a strong suspicion (but without any proof) that Francesco di Giorgio Martini may have been responsible for the design of the superb clavichord drawn in Federico’s studiolo in his Palazzo Ducale in Urbino!  This will be discussed further in Chapter 3 below. 

Figure 9 – The Fortezza of Palmanova, in the Province of Friuli-Venezia Giulia, Italy, designed in 1593.  It is a typical ‘star shaped’ fortress and one of the few of this design that has survived almost intact to the present day.  It was designed according to the principles laid down by Francesco di Giorgio Martini about one hundred years earlier in 1482.

 

          The principles of perspective laid down by di Leon Battista Alberti, at about the same time as the ‘star fortresses’ of Francesco di Giorgio Martini, led to many works of art showing perspective images such as that seen in Figure 10 below, which is only one of a whole series of similar works.  

Figure 10 – The ideal city (1480-1490?) once attributed to Melozzo da Forlì , but which is now unattributed (but see Appendix 18 on page 236).  This scene is drawn with a mathematical precision and accuracy typical of the intarsia images in the studiolo of the Ducal Palace in Urbino.  Both the image above, and many of the images in the studiolo, betray an obsession with the science and mathematics of perspective.

Galleria Nazionale delle Marche, Urbino.

 

          The new sense of awareness created in Urbino by Federico became the fertile ground in which many of the greatest figures of the Italian High Renaissance took root.  Their curiosity spread like wildfire throughout Italy and the flames created an uncontrollable blaze that then raged across the whole of Europe.  In the process Urbino became a virtual cauldron, attracting intellectuals from across Europe that further fanned the fire created in Urbino.  Urbino, incontrovertibly in the author’s opinion, was the birthplace of the Renaissance, although routinely the credit for the rise of the Italian Renaissance is given inexplicably to Venice, Florence and Rome despite the fact that much of the revolutionary work of the Renaissance scholars dates to roughly 50 years before these same subjects were treated in the latter three centres.[41]

       Federico, even during his lifetime, was known as “The Light of Italy”.  This is no exaggeration!  Federico brought to his Court some of the greatest names and leading lights of the late Gothic and High Renaissance periods.  And Federico was himself a great man of science, an illustrious philosopher and was one of the most cultivated and greatest Italian patrons of the arts and sciences during the earliest stages of the High Renaissance.  Federico surrounded himself with the greatest names in the fields of Renaissance painting, sculpture, architecture, philosophy, science, and mathematics.  Federico’s Court was host to, among others, Bramante (born 1444 in Fermignano, just 9km from Urbino), Piero della Francesca, Raphael (also born in Urbino), Justus van Ghent (Joos van Wassenhove), Leon Battista Alberti, the gifted architect Francesco di Giorgio Martini (see Figure 8 on page 22 above), Paolo Ucello, the Spaniard Pedro Berruguete and the artist, sculptor and architect Benedetto da Maiano.   

 

 

The importance of Federico as a condottiero

          Federico’s military accomplishments were also highly regarded in this own time.  Within a short period during 1474, Federico was nominated as Duke, and as a Knight of the Order of St. Peter.  He almost immediately became a General of the New Vatican League and a Standard-bearer of Pope Sixtus IV.  He was invested in the Order of the Ermine by Ferdinand of Aragon, and then firstly, in the Order of Garter by Edward IV of England and then, secondly, also by Edward IV as the Duke of York.  Federico was, understandably, very proud of these honours and made sure that posterity would be aware of them by making frequent references to them in, for example, the images and paintings he commissioned for his various palazzi throughout his Duchy and particularly for his studiolo in the Palazzo Ducale in Urbino which is discussed below in Chapter 3.

          As suggested above, Federico commissioned many works by some of the finest painters, writers, sculptors and architects of his time.  His various palazzi and fortresses that he had built throughout the part of the province of Le Marche that he controlled were all exceptional centres of artistic activity, and his influence was felt, not just in Urbino, but extended well beyond the boundaries of Le Marche .  The first studiolo (1473 – 1476) was commissioned for Federico’s palazzo in Urbino.  This huge palazzo, seen above in Figure 43, is situated high up along the West side of the town’s old fortified wall.  Built as part of this huge complex is the loggia between the two towers of the palace with the studiolo opening out towards the sunny southwest side onto the splendid countryside of Le Marche.  The second intarsia studiolo was part of a separate commission (1478 – 1482) for another of Federico’s palaces in the town of Gubbio[42] where Federico was born, and which was the favourite residence of Federico’s second wife Battista Sforza.  The studiolo in Gubbio was still not totally complete at the time of Federico’s death in 1482. 

          Both of the studioli made for Federico make frequent use of symbolism.  Even the doors of the Urbino studiolo make it clear how important the use of symbolism was to Federico and to the artists around him.  These doors are covered in densely-packed images, with symbols and intellectual games all in praise of mathematics.  The intarsia images inside the studiolo are contained, not in ‘flat’ drawings or paintings, but within carefully conceived and constructed perspective representations in wood, which are, of course ‘drawn’ in perspective, and are full of depth and realism.  The walls of the studioli in both Urbino and Gubbio (now transferred to the Metropolitan Museum of Art, New York) are lined with wood intarsias that are both very beautiful and are also extremely skilfully and accurately cut. 

          Made by carving the desired shapes out of a flat piece of wood called the ground, intarsia is made by then filling the removed spaces in the ground with perfectly-fitting replacement woods of different textures and colours to imitate a (more-or-less) monochrome image in darker- and lighter-coloured woods.  Taken as a whole, the images in the two studioli imitate rooms drawn up in perspective with shelves, drawers, niches and doors, into which contemporary objects including books, geometrical instruments, lamps, armour, musical instruments, etc are piled.  The objects depicted in the two studioli reflect Federico’s own interests and accomplishments, and his intense love of music, the graphic arts, architecture and of the mathematics of perspective and of the study of mathematics itself. 

          The use of perspective in art is, even today, a relatively new feature , at least in relation to the long history of the art of mankind, but even in relation to the discovery of the principles of incorporating perspective into art.  The first known picture to make use of linear perspective in art was that by the Florentine architect Fillipo Brunelleschi[43] (1377-1446).  Brunelleschi’s early works using the principles of perspective have unfortunately long since been lost, although a good example of a painting in which the perspective has been carefully worked out is The Ideal City attributed (but with a great deal of uncertainty) to Melozzo da Forlì (see Figure 10 above).  The linear perspective system used in this painting, like those of the studioli in Urbino and Gubbio, projected the illusion of depth onto a two dimensional plane by the use of ‘vanishing points’ to which all lines converged on the horizon at eye level. 

   

Figure 11 – A Mazzocchio depicted in intarsia, clearly one of the most difficult images to represent in three dimensions.  But this image is a triumph, not only of the art of the intarsiatore[44], but also of the actual calculation of the perspective drawing of the object (see: Figure 12 below) .  The figure has a ‘donut’ shape with 8 rings of wood running around the ‘donut’ in alternating dark and light colours, drawn in perfect perspective, shaded – even with shadows – to give a completely realistic image in 3-dimensions of an object that perhaps may never even have existed in the real world.

Francesco di Giorgio Martini, 1478 – 1482, Urbino and Gubbio

Studiolo from the Palazzo Ducale, Gubbio

Metropolitan Museum of Art, New York, Acc. No. 39.153

 

Figure 12 – A seventeenth-century rendering of Martini’s mazzocchio.

La perspective curieuse (Paris, 1638)

Jean François Niceron, Paris, (1613-1646)

 

           One of the most striking things about the intarsias found in Federico’s studioli in Urbino and (originally in) Gubbio is the use of Alberti’s rules of perspective.  Although the discovery of the mathematics and geometry of perspective in art had already been enunciated for the first time in the 1430’s, the perspectives used in the intarsias in Urbino and Gubbio, and later in Savona, Genova, Mantua and Rome during this period, was a new and exciting development typical of the humanist movement prevalent at the time.[45]  It was also a typical feature of the high standard of the patronage that Federico extended to the artists and scientists of the time in his Court.  This is just one of the many developments that did a great deal to foster the exciting advancements made during his time in Urbino, and these of course have all elevated the prestige and importance of Federico.

          The studiolo in Urbino is located on the first floor (piano nobile) of the Ducal Palace, and was Federico’s private room for study and contemplation.  The stunning ceiling of the studiolo is coffered in gilt octagonal shapes with the arms of the Duke worked into the central part of each octagon.  Lining the walls above the wooden intarsia decorations, Federico commissioned a large number of paintings of illustrious figures from history, philosophy, literature, the sciences, mathematics and the arts, all of which were important to the humanist thinkers of the time, and to Federico in particular.  Unfortunately roughly one-half of these paintings was stolen by the French troops during the Napoleonic invasions of the Italian peninsula about 250 years after they were first created.  These have now, mostly, found their way to The Louvre in Paris.  But even so, the intarsia images on their own give rise to a constant play in both the studiolo in Urbino and the one (tragically sold) from Gubbio, between the actual solid architecture and some ethereal fantastical world intended to create an effect of great marvel in the observer.  In order to achieve this, Federico employed some of the greatest artists, architects and intarsia cutters in these projects.  Just how great these artists were will be revealed in the discussion of the intarsia clavichord image in Chapter 3 below where the extraordinary achievements of these truly great masters are revealed. 

          The Urbino and Gubbio intarsias are much better known and have received much more attention and study than those in Savona, Genova, Mantua and Rome, although the latter are all equally beautifully and professionally carried out.[46] They are all of extreme importance to organology and to our study and knowledge of the stringed-keyboard instruments of the late Medieval and the early High Renaissance periods, although it has not been possible to deal with them all here.  But, to me, they deserve a great deal of further examination, measurement, analysis and study.

 

 Section 0‑3 – Federico and his relationship to music at his Court in Urbino.

          It is clear that Federico loved music and that he loved music being performed in his Court.  Although there is actually very little in the way of music manuscripts, instrumental arrangements, or even keyboard music surviving from his Library, his interest shines through from the references made in many of his books and from the decorations in his palazzi.  Perhaps the earliest evidence of Federico’s interest in music is provided by his initial education at the Ca’ Zoiosa run by Vittorino da Feltre (see footnote 36 on page 18 above).  Vittorino, in addition to instilling a life-long interest in music in Federico, was also responsible for the Renaissance idea of the complete man, or l'uomo universale – the health of body, the strength of character and the wealth of the mind.  Federico spent about two years of his education at Vittorino’s school, beginning when he was about 14.  In a short treatise by Iohannes Gallicus, De ritu canandi vetustissimo et novo (1458-1464), he writes that Federico was ‘a fine man – a good musician, a fine listener, and an excellent practitioner of music’.  Vittorino, Federico’s teacher, also reports that Federico sang with a sweet voice and that he was a good player of the ‘lira’ or ‘lyra’ – probably some type of stringed instrument (possibly an early version of a viola da gamba (see Figure 15 on page 33 below).  But although the total number of references to Federico are somewhat sparse, those that do, write about Federico’s musical abilities with unrestrained praise.[47]

          An excellent picture of the music scene in Federico’s Court can be found in the book by Nicoletta Guidobaldi.[48]  Guidobaldi relates that one of the clearest testimonies of the musical activity at Federico’s Court is that provided by Vespasiano da Bisticci[49] (see Figure 13 above) who writes:

“ – that he (Federico) was an avid dilettante who understood both vocal and instrumental music perfectly.  He had an enviable musical chapel filled with musicians who had a total understanding [of their craft] with numerous young musicians (musicisti = male musicians?) who performed as choristers and soloists[50].  There wasn’t [a single] instrument that he didn’t have in his house.  He enjoyed the sound [and character] of them all.  He had [at his command] excellent players of many instruments.  But he particularly loved quiet instruments (istrumenti sottili) in preference to those that were loud, like trumpets which he liked much less.  But he loved the organ and [other] quiet instruments very much.”[51]

          Clearly Federico was a man of excellent musical taste and refinement.  Many others praised Federico for his military and diplomatic skills and as a cultivated humanist, but few others seem to have understood what Federico was really like as well as Vespasiano, who was both his librarian and his great friend of many years.

          Federico employed two full-time organisti (keyboard players), which, among the otherwise rather small number of musicians at court, indicates the importance that Federico placed on music for the keyboard.  His interest also seems to be reflected in the choice of the musical instruments depicted in images in the intarsias in the studioli in Gubbio and Urbino.  Among the images in the intarsias there are altogether three particularly interesting keyboard instruments:

1.    the famous clavichord in the Urbino studiolo, which has a forward-looking compass of F,G,A to f3 (see Chapter 3 below), rather than the more restricted and limited compass of the RCM clavicytherium (see the top diagram in Figure 35 on page 65 below).

2.     a less-well known intarsia also in the Urbino studiolo depicting a small portative organ which also has a compass of F,G,A to f3.  

3.     a small organetto in the Gubbio studiolo which has an even smaller 3 octave compass of G to f2,g2 (seemingly with a GT and a BI in the bass).

          However, as well as the intarsia images along the lower walls of the two studioli, Federico also commissioned a number of important paintings to be hung above the intarsia walls.  One of these paintings includes a small portative organ in the image of La musica (London, National Gallery, NG756) painted by Justus of Ghent for Federico’s Urbino studiolo.  [include an image??]Copyright applicable

          But in addition to the keyboard instruments, the intarsias include images of lutes, vielles, violas da gamba, flutes, recorders, cornetti, tambourines, harps, rebecs, lyres, fiddles, citterns, drums, horns, etc.  There are also at least two images of music scores written on a (for the time, modern) 5-line stave now familiar to all contemporary musicians.

 

 

Section 0‑4 – Federico da Montefeltro’s library in his Palazzo Ducale.

          In addition to his many other accomplishments, Federico collected one of the most comprehensive libraries of all time.[52]  This library was very much a part of Federico’s Corte matematica and employed as many as 30 to 40 full-time scribes at times, in a specially constructed scriptorium, in which the books that he bought or borrowed were copied and where these were illustrated and decorated.  Federico avidly collected ALL of the books then known to Western civilzation on the sciences and the arts, and kept his scribes constantly busy copying these works into volumes for his own private library.  Federico’s library thus became the most comprehensive in its content, and larger in the number of volumes it contained than either the Medici Laurentian Library in Florence, or the Papal Vatican Library in Rome.  Federico’s library was particularly rich in Greek platonic and hermetic[53] texts, with many texts in ancient Arabic, Greek and Latin, on geometry and mathematics.  Among the authors represented in Federico’s library were Euclid, Archimedes and the mathematician, astronomer and astrologer Regiomontano.[54]  But Federico also collected all of the available works in these topics to ensure the overall completeness of his library.

          Suffice it to say that, with two librarians at its helm, one of whom was Vespasiano da Bisticci, no other library in the Western World at the time compared with that of Federico da Montefeltro for the depth of content, for the range of material, nor for the sheer size and number of the volumes it contained.

          The main inspiration, the character and the finance of the library in Urbino was clearly provided by Federico.  And when Federico died in 1482, the primary incentive to continue to build the library died with him.  After Federico’s death, the line of the Montefeltros then passed on to his son Guidobaldo (or Guido Ubaldo) who, as explained above, was probably gay and left no heirs.  But Guidobaldo did pass on the title of the Duchy of Urbino to his nephew Francesco Maria I della Rovere (see Figure 14 below).  However, Federico’s heirs, although not in direct line, seem to have inherited Federico’s humanist passion for books, works of art, for sculpture and architecture and, perhaps most importantly, for the sciences and mathematics. 

 

 

Section 0‑5 – The successors to Federico da Montefeltro in the Duchy of Urbino.

          The passing of the Montefeltro line from Federico to his son Guidobaldo, began a whole new line of succession to the Montefeltro family.  Guidobaldo was childless and was possibly gay, and so he formally passed on his line of succession to his nephew Francesco Maria delle Rovere (see Figure 14 below).

 

Figure 14 – Young man with an apple, Raffaello Sanzio di Urbino (Rafael),  c.1504.

Portrait, thought to be of Francesco Maria I della Rovere as a teenager,
 Le Gallerie degli Uffizi, Florence; Inv. 1890, no.  8760

 

          The image below is of the same Francesco Maria I della Rovere, and shows  him at a stage only about 4 years later in his life than the image in Figure 14 above, and only slightly more mature, is very interesting.  It is one of the very few images of any of the members of the Montefeltro/della Rovere family, who ruled in Urbino, who is depicted actively engaged in music. 

Figure 15 – Portrait of Francesco Maria I della Rovere in his youth (1490 – 1538), but  aged slightly older than in the portrait seen in Figure 14, above.

Bartolomeo Veneto, Ca’ Rezzonico, Venice

 

           In the painting by Bartolomeo Veneto above, the sitter’s left hand holds what is known as a ‘lira da braccio’ (or interchangeably ‘lyra da braccio’) or in English as “lyra, [to be played] on the arm”, a Renaissance version of a viol played in the arms of the musician, and not between his/her legs.  It is, indeed, an ancestor of the modern violin, although the violin, in its earliest form, was a contemporary of the lyra.  The lyra da braccio is an instrument that has a flat peg-box, an arched bridge, and six strings like a viol.  It is an instrument that seems to have been relatively common during the period of the Early Renaissance.  However, no reference to Francesco Maria’s ability in playing the lyra – nor, for than matter that he actually owned such an instrument - is known to the author.  However, the painting is proof enough, and such a serene image betrays a confidence and self-assurance of someone totally in charge of his own abilities. 

          We know that Francesco Maria I was also an avid bibliophile.  He collected some 13,000 more books to add to the family library.  These volumes he added to the library in his new Palazzo Ducale, which he built for himself in Castel Durante.  Unlike Federico’s original library which consisted, almost without exception, of hand-written and hand-decorated volumes on parchment and vellum, Francesco Maria I’s library was of printed books produced using a mechanical moveable-type printing press which was made especially for him.  These books, as now, were printed onto paper and not onto parchment or vellum.  The Montefeltros were not to be left in the background by anyone, and the important purchases that they made, such as their enormous wealth of books, were left as evidence to prove their rank and position in society, and in the world of their contemporary owners, as well as those of future generations.

          Francesco Maria’s son Guidobaldo II della Rovere (1514 – 1574)[56] also took a great interest in books, and also inherited the combined riches of Federico’s library of manuscript books, as well as the printed books of his father Francesco Maria I.[57]  As well as sponsoring the work of Tiziano Vecellio (Titian in English), Guidobaldo II even purchased Titian’s famous and controversial Venus of Urbino in 1538 (see Figure 17 below). 

 

Figure 16 – Guidobaldo II della Rovere (1514-1574), and his young son Francesco Maria II della Rovere (1540 – 1631) (see Figure 56 below).

Tiziano da Vecellio, sold, 19 April, 2018, but the present location is unknown.

 

 

Figure 17 – The Venus of Urbino, Tiziano Vecellio (Titian), Venice, finished in 1534, and sold to Guidobaldo II della Rovere in 1538.

Le Gallerie degli Uffizi, Florence

 

          After the death of Francesco Maria I della Rovere, the great, combined libraries of Federico, Guidobaldo da Montefeltro, and Francesco Maria I della Rovere, passed on to Guidobaldo della Rovere, Francesco Maria’s son, and, in turn, on to Francesco Maria II della Rovere (1574-1631) (see Figure 56 on page 136 below).  Franco Peperino’s exhaustive study[58] (see footnote 57 below) shows that Guidobaldo della Rovere’s Court, carrying on a tradition founded by Federico da Montefeltro several generations earlier, held reign over an amazingly splendid Court marking a second outstanding period of musical and artistic patronage in Urbino.  It would seem that Guidobaldo wanted to hold Court over the richest and most lavish Court in the whole of Italy.  Indeed, it is likely that, if Guidobaldo had had sufficient resources, he would have reigned over the finest, most intellectual, most talented and most celebrated court in Italy at the beginning of the High Renaissance.  But Guidobaldo was in almost constant financial difficulties and his earnings as a condottiero, his principal source of wealth, were at constant risk.  However, it is necessary to take into account the fact that the extensive archives of the musical life of Guidobaldo did survive, whereas those of Federico did not, so that any comparison of the achievements of these two great men, particularly in the field of music, is fraught with uncertainties.  Although Francesco Maria II did have an avid interest in his huge library, the Duchy of Urbino found itself, at the beginning of the seventeenth century, both at the periphery of the culture, politics and power in the Italian peninsula, and also found itself in some serious financial difficulty as well.  Still there can be little doubt that the musical life at the Court of Federico exceeded that of Guidobaldo by an order of magnitude.  Unfortunately there are now no archival documents surviving either to allay or to confirm the doubts about the Court of Federico in comparison to that of Guidobaldo.

          On the death in 1631of Francesco Maria II, the combined libraries of Federico, of Francesco Maria I, of Guidobaldo and of Francesco Maria II then passed, according to the will and testament of Francesco Maria II, to the Community of Urbino (Commune di Urbino) under the condition that the two parts of the great libraries would never be separated and would be kept together in perpetuity.  Through a series of coincidences and chance meetings of those involved, the two libraries came to the attention of Pope Alexander VII (1599-1667) who was persuaded to purchase them from the Commune di Urbino for 10,000 scudi.  It is not clear exactly what the equivalent value of the books in these two superb libraries would be in today’s money, but it has to be said that it was a vast sum that kept the many centres in Le Marche, which were under the control of Urbino, funded for many years to come.  The two libraries were moved in 1657 from Urbino and from Castel Durante (Urbania) to the Vatican in Rome.  They have subsequently remained there intact to the present day, and now form part of the Biblioteca Apostolica Vaticana in Rome, where they constitute the major part of the so-called Fondi Urbinati or ‘The Urbino Foundations’. 

 

The Duchy of Urbino and Federico’s influence there. 

          Although the Palazzo Ducale in Urbino was Federico da Montefeltro’s principal residence, he kept very busy building further palaces – which are all, in fact, better to be considered substantial fortifications – throughout the province of Le Marche.  It seems clear that Federico – Il condottiero – wanted to ensure that all of the centres under his control should remain so in the future, and not be threatened by rival aristocrats nor their families.  So he spared no expense in fortifying all of the major and minor towns in the Region he ruled.  Some of the forts, palazzi and strongholds he constructed were begun from scratch, but most were alterations or additions to previous palaces or castles that already existed.  Many of these, both new-builds and alterations, were designed by some of Italy’s greatest Renaissance architects working under Federico:  Luciano Laurana, Girolamo Genga and notably Francesco di Giorgio Martini (see Figure 8 on page 22 above) all worked for Federico on these strongly fortified buildings. 

          One of the many fortezze (fortifications) built for Federico da Montefeltro throughout Le Marche was the impressive fort (now in the Province of Rimini well north of Urbino) which was designed by Francesco di Giorgio Martini is La Fortezza di San Leo (see Figure 18 below).  In 1441 the young Federico, then aged only 21, scaled the walls of the old fort and immediately recognised its weaknesses.  So he commissioned Francesco di Giorgio Martini to build him a new, impenetrable castle over the top of the ancient Roman fortress.  The result can be seen below in Figure 18:

 

Figure 18 – The Fortezza San Leo, San Leo, comissioned by Federico da Montefeltro

Francesco di Giorgio Martini, 1441.

 

Having completed the Fortezza di San Leo for Federico, Francesco di Giorgio Martini (see Figure 8 above) then spent most of his remaining career working for Federico on his palaces and fortresses in the centres throughout much of the rest of the Province of Le Marche.  Some of the locations of these fortresses were built for Federico, are the following:

1.         Gubbio – Federico’s birthplace about 60km south of Urbino, where Federico also commissioned a second studiolo adorned with intarsias on the walls (now unfortunately removed to the Metropolitan Museum in New York).  His palace in Gubbio was the favourite residence of Federico’s second wife Battista Sforza, and the birthplace of his son-and-heir Guidobaldo II. 

2.         Fossombrone where, as will be shown below, the intarsias were actually designed and made for the sublime studiolo in Federico’s palace, only about 18km east of Urbino.  (Fossombrone used the same size of unit of measurement as Castel Durante, and so the latter could also be where the Urbino studiolo intarsias were designed and made.)

3.         Castel Durante – now called Urbania and less than 15km from Urbino.[59]  The size of the unit of measurement is indistinguishable from that used in Fossombrone (above).  One of Federico’s many titles was ‘Lord of Castel Durante’.  He was nominated ‘Monk Commandant’ of the monastery of Castel Durante as early as 1445 when he was only 25 years old.

4.         Fermignano – about 7km south of Urbino.

5.         Federico also held the title of ‘Signore’ of all of the major, important centres of Le Marche, and most of the minor centres as well.  Although not all of these were the sites of fortifications built for Federico, and not all were even residences of Federico, they were all important to Federico and to the defence of his dominions.

6.         Federico’s heritage of fortresses served duty right up to and through the course of the entire first half of the twentieth century.  During the Second World War the then Superintendent of the Galleries and Works of Art in Urbino placed around 10,000 priceless works of art (including those of Giorgione, Piero della Francesca, Paolo Uccello, Titian, Mantegna, Raphael and many others), into the Rocca [Fortress] Ubaldinesca or into the Rocca Sassocorvaro.  These works of high art were moved to these locations, all within the confines of Le Marche, for the duration of the Second Great War, and were gathered from all of the major museums and galleries in Italy that were then under threat of being stolen by the Nazis or, indeed, by the Italian Fascists.  Clearly Federico’s palaces where still thought to be strong enough, and resistant to attack even at the time of WWII, some 500 years later than their construction by Federico da Montefeltro.

 

 

Figure 19 – The Rocca [Fortress] Sassocorvaro, designed for Federico da Montefeltro, by Francesco di Giorgio Martini, c.1474, clearly one of the greatest minds who ever worked for Federico.  This fortress is clearly a symbol of strength and impenetrability, and is typical of the many fortresses of unconventional design made for Federico throughout the province of Le Marche.  It is clearly not the usual rectangular structure with fortified corners, but has a form with a clearly mathematical shape, designed to increase the overall defensive security of the building. 

 

 

          Because Federico spread his influence so widely, so solidly and so forcibly (he was a condottiero!) throughout the Region, that any work created, made for, or built in any of the above centres, can creditably be considered to have been ‘Made in Urbino’.  For example, the author’s work carried out here shows that the famous intarsias in the studiolo made for Federico’s Palazzo Ducale in Urbino, used the unit of measurement in their design not of Urbino itself, but of Fossombrone or of Castel Durante, which both used the same unit as one another, but a unit that was not the same as that used in Urbino.  This therefore suggests that they were, in fact, actually made in Fossombrone and Castel Durante, only a few kilometres from Urbino.  This attribution to an origin outwith Urbino itself is based on the calculation of the size of the unit of measurement used to design and construct the intarsias (see Section 0‑29 on page 96 below).  But these intarsias are, of course, to be considered to have been ‘Made in Urbino’ where they have found their home for almost 550 years even though they were not physically designed and constructed there. 

          But what we can all take away from the photographs of Figure 18 and Figure 19 is that Federico was a condottiero, both offensively and defensively.  He was capable of an important element of surprise when engaging in battle against his enemies, and he himself made every effort not to be taken by surprise particularly anywhere under his dominion.  This he did by constructing some of the strongest and most innovative fortifications made anywhere in the Italian peninsula during the period of Federico’s rule in Urbino.

 Section 0‑6 – Who made and designed the superb instruments studied here, all of which were made in Urbino (or at least for the Ducal Court in Urbino).

          Perhaps the greatest personal disappointment that the author has had to endure during the course of this extensive (and sometimes exhausting) study is that, for all of the superb and excellent instruments examined in the course of this research, no trace has been found on a single one of them of the name(s) of their designer(s) and maker(s).  This means that, of all of these superbly-designed and beautifully-made works, by perhaps the greatest keyboard-instrument makers who have ever lived, there remains no evidence of who they actually were, nor of what their names were.  The records of Federico’s Court were all destroyed at the hands of Pope Alexander VII when they were all moved to the Vatican in Rome.  So it seems unlikely that the maker(s) of the RCM0001 clavicytherium and the intarsia clavichord from the studiolo of the Palazzo Ducale in Urbino will ever be known.  Although the later Urbino archives have survived from the time of the Duchessa d’Urbino’s virginal (1540) and the time of the single-manual harpsichord now in the Ca’ Rezzonico (c.1710) in Venice (both will be shown below to have been made in Urbino), no hint of who the makers of these two later instruments were has survived either. 

          The lack of any information about the makers of any of the instruments studied here is extremely disappointing and to me, having spent a great deal of time and much effort on this project, is also extremely frustrating.[60]  And this is particularly so in the light of the outstanding brilliance of the design and execution of all of these Urbino instruments.  What is clear is that all of the instruments studied here were either made within the walls of Urbino itself, since they all use the unit(s) of measurement of Urbino, or they were made within the Province of Le Marche, all of which were under the domination of Federico di Montefeltro.

          By way of analogy with two of the most famous painters to have lived and worked in Urbino, and two of the most brilliant artists in their technique and execution, it might be said that the RCM0001 clavicytherium can be attributed to the Raffaello Sanzio of the harpsichord and the studiolo intarsia clavichord to the Piero della Francesca of the clavichord![61]

 

 

  

 

 

 

Chapter 3 – The Anonymous Clavicytherium, Urbino, c.1471, in the Royal College of Music, London, Cat. No. RCM0001.[62]

 

Figure 20 – A front view of the RCM0001 instrument.

Anonymous clavicytherium, Urbino, c. 1471.

Royal College of Music, London, Cat. No. RCM0001.

 

          As mentioned above, the oldest surviving stringed-keyboard instrument in the world[63] is the clavicytherium in the Royal College of Music in London, pictured above.[64]  An important point about this instrument is that, although it is very old, it is still about 80 years younger than what remains of the Norrlanda organ in the Swedish History Museum in Stockholm.[65]  In other words, there are older keyboard instruments which have survived, but no stringed-keyboard instruments earlier than the RCM0001 clavicytherium.  That it is not the oldest keyboard instrument does not, however, in any way diminish the interest nor the importance of the RCM clavicytherium as a document that contributes an enormous amount to our understanding, not only of the earliest period of stringed-keyboard making and design, but also to our understanding of music history and music practice in the mid-fifteenth century.  Unfortunately descriptions of the instrument in the past have made no attempt to analyse its scientific and mathematical design and construction, both of which are of the highest interest, and are among the prime objectives of the present study.  And what the present study shows is that, without any doubt, the RCM clavicytherium was designed and built in Urbino.

          What will also be shown below is that RCM0001 is an instrument designed and built during a narrow, crucial period of music and instrument-making history.  The clavicytherium, and the clavichord represented in the intarsia in Federico da Montefeltro’s studiolo in Urbino (discussed in Chapter 3 below) have numerous idiosyncratic features in common with one another that suggest that they were both designed by the same maker (or at least in the same workshop).  Although we will probably never know who this brilliant designer was, it was someone in total command of his craft, who had a profound understanding of the music that it was to play, and was someone who even had an excellent grasp of the physical and metallurgical properties of the strings he planned to use to string it. 

          The RCM0001 clavicytherium and the intarsia clavichord taken together with a number of small organetti and portative organs also depicted in the intarsia walls and paintings in the studioli in Urbino and Gubbio, were all designed in a period at the cusp of the transition from what we recognise today as Medieval music to what we call Renaissance music.  The instruments seen and studied in the intarsias are unique examples of what were probably the perfectly normal instruments from a period which is now about 5 centuries ago.  Because the instruments drawn in the intarsias could never have been altered musically, they are depicted in their original state, and so are free of any of the ambiguities of most surviving early instruments that have suffered alterations during various periods after they were first built.  Where else in the field of early keyboard organology do we have the opportunity to study totally unaltered instruments of this age? It is clear from this study that the intarsia images are representations of real instruments that can be measured and analysed.  Such a study is what has been carried out here in this restricted body of research.

And we must not forget that the RCM0001 clavicytherium is still the oldest known surviving stringed-keyboard instrument in the world.  And although it is very old, an analysis of the design of its string scalings shows that it is extremely elegant and sophisticated in ways that have not hitherto been recognised for this instrument.  Indeed this features have not been found in any other instruments made during the following 5 centuries.  What the author wants to try to show here is that this instrument is designed with superb skill and sophistication in both its structure and action, but particularly in its string-scaling design.  What will be shown here is that it has one of the most interesting and inventive stringing-design concepts in the world, and it is of particular interest because of this fact, quite aside from the instrument’s extreme old age.  It sheds a great deal of light onto our understanding of the musics and instruments made and used during the short time between the Medieval period and the High Renaissance, and thence further on into the modern period, and the music of today.

Many of the physical details and some of the measurements of this instrument are described in the catalogue of “The Musical Instrument Collection of the Royal College of Music, London” (see footnote 63 above), and the reader is encouraged to read and study this to gain a basic understanding of this amazing instrument.  However, the description of the clavicytherium in the RCM catalogue is certainly one of the least informative and most confusing descriptions of any instrument discussed in any publication known to me.  It is confusingly written, it is lacking in clarity and precision, and is very misleading in most of its descriptions.  It seems a great shame that it was not written with more accuracy, with more scientific understanding, and a great deal more editorial intervention.  The description certainly requires a greater definition of many of the missing characteristics.  This is especially so because of its importance to the history of music, to the history of organology, and to our understanding of instrument design and building at the pivotal time of its construction.  Because of the high level of interest in this instrument as a result of its age and importance to music history and to the history of musical-instrument construction, it has also been described and discussed in a great many earlier publications, although unfortunately also never with any great insight.  There is a somewhat incomplete list of these publications in the ‘References’ section on p. 25 in the RCM catalogue[66].  But it is the great hope of the present author that the current work will go some way to correcting this unfortunate situation, and that it will contribute some new information and insight into the design and construction of this fine instrument.

The RCM has published some associated data sheets and a full-sized drawing of the clavicytherium that have been extremely useful in the study and analysis of this instrument.  This drawing, by William Debenham, was made in 1983 and is in total contrast to the catalogue of the RCM collection in its clarity and precision.  The author began his study of this instrument in the early days, from a highly-distorted paper copy of a drawing provided by the RCM.  However, laterally it has been possible to use a digital copy of the drawing, kindly supplied by Richard Martin of the RCM.  This digital version is totally lacking in any of the distortions and inaccuracies of the earlier paper drawing, and is what has been used in the present study.  No problems were encountered in the analysis of the instrument from the use of the drawing, rather than the instrument itself, in the discussion of the instrument when using the measurements taken directly from the Debenham drawing. 

          A partial section of the RCM0001 drawing showing only its essential parts can be seen in Figure 21 below in a modified and somewhat simplified form.

 

` 

Figure 21 – A portion of the drawing by William Debenham of RCM0001 published by the RCM, but here greatly simplified.  Not to scale.

Anonymous clavicytherium, Urbino, c. 1471.

Royal College of Music, London, Cat. No. RCM0001.

 

 

Section 0‑7 - Problems surrounding the published catalogue description of the RCM0001 clavicytherium.

          The RCM catalogue suggests that the instrument was made in Ulm in Southern Germany, and that it should be dated about 1480.  These suggestions have been made because, glued over what might be a crack inside the case at the rear of the instrument[67], there is a piece of parchment which is written in German dialect, in a late fifteenth-century hand.  This parchment mentions the name of Bartlome Abeille[68], who is known to have practiced viticulture (he declares himself to be a ‘Weingartner’ or wine grower)s and who, as is known from the archives in Ulm, was once a citizen of that city.  There is no date on the parchment itself, but it has been dated vaguely to the period around 1480 from the style of the handwriting.  But any dating based on the style of handwriting is a very subjective and highly unreliable method.  And even if it were possible to date the actual piece of parchment, there is now no way of knowing how old the parchment was when it was glued inside the instrument.  It therefore tells us nothing, really, about the date of construction of the instrument.  That will have to await a dendrochronological dating of the wood(s) used to make the instrument. 

Abeille’s name is also mentioned in a separate, unrelated, archival document found in Ulm and dated 1471.  However, even if the parchment glued to the instrument could be dated, it seems likely that the parchment repair would have been added at a time long after the instrument was first built, so that any date obtained from it is extremely inaccurate and unreliable.  It is common for old, used pieces of parchment to be found serving a menial purpose such a repairing or strengthening a crack by holding the two side of the crack in place.  This repair could only have been carried out through the (now missing) top soundboard rosette.  The location of the parchment is in a very difficult location, which would have to have been accessed through the rosette hole itself. 

          This means that there is very little basis for dating the construction of the whole instrument to the period around 1471 since we are dealing here only with a scrap of parchment that was used simpley to carry out a minor repair.  So there is no reliable indication that this parchment has a date that is, in any way, related to the period of the construction of the instrument.  However, the assumption has been made in the catalogue description of RCM0001, that the existence of these two parchment documents, one with Abeille’s name, means that the instrument itself is German, and that it is from Ulm.  It is further assumed in the catalogue description that, because of its association with Abeille and of his known dates, that the clavicytherium must date to about 1470-1480 as well. 

          However, there are two reasons for not associating the presumed date of construction of the instrument with the date of the parchment.  There is no logic or evidence to relate the two to one another.  In any case, from the variability in the style of handwriting in any period or region, the sceptic would immediately question the accuracy of dating the parchment (and the instrument) only on the basis of this handwriting style.  Additionally, the parchment strip may have been, say, 50 years old at the time that it was used to make this repair.  And this simple fact points out that these parchment strips are completely useless in assigning any precise date to this clavicytherium.

Figure 22 – A photograph of a small section of the parchment strip on the rear inside surface of the baseboard taken through the top left soundboard rosette hole with the writing and signature of Bart[o]lome Abelle on its top surface.

Anonymous clavicytherium, Urbino, c. 1471.

Royal College of Music, London, Cat. No. RCM0001.

 

          To the author it seems very unlikely that such a well-made, beautifully-crafted instrument would be in need of repair and in need of this piece of glued parchment almost immediately after it was initially made, and then to have survived almost intact for more than 500 years without the need for any further similar repairs.  It seems much more likely that the instrument was repaired quite some time after it was first made and obviously, perhaps even in a centre some distance away from its original place of manufacture.  Also, the parchment document itself would have to have been old enough when it was glued to the back of the clavicytherium that it was no longer current in a way that it was when it was first written.  It is impossible now to know the time lag between the construction of the instrument, the writing of the document on the parchment, and the time when the parchment was used for such a menial task as repairing a crack in the back of the case of this instrument.  This suggests that the date of the instrument simply cannot be based on the dating of this parchment.  It is simply a left-over piece of parchment that could have been used to repair the crack in the rear of the instrument at any time after the instrument was initially made, and after the parchment had been inscribed.  The parchmenttells us nothing at all about the date of the instrument nor does it tell us anything about where the instrument was originally made.  It seems therefore to be very important to dispel the notion (for it is nothing more) that the instrument was constructed at the same time that the parchment used for the repair to the rear of the instrument was written, and that the parchment is from the same centre as that of the construction of the instrument itself.  The questionability of both of these assumptions cannot be stressed strongly enough.

On the other hand, the German origin of the instrument seems, initially at least, to be supported further in the arguments given in the RCM catalogue, which records two inscriptions on the front and rear boards attached to the inside of the base support of the instrument.  These boards have the words Hinders and Vorders written on them.[69]  However, according to the RCM catalogue[70] and clearly visible among the photographs in the catalogue, these boards are additions to the base support of the instrument, and were clearly not actually an original part of the instrument’s construction.  This therefore greatly weakens the argument that the instrument as a whole was made in Germany for the simple reason that the base support of the instrument was a later addition made perhaps many years after the initial construction of the instrument itself.  The German origin of the instrument is further discredited by the ink inscriptions on the bottom keyboard sticker ‘primo basso’ (first bass) and ‘ultimo sopran’ (last soprano = high pitched) on the top sticker.  These words would have been written on the stickers during the initial construction of the instrument when it was in Urbino, and therefore these words clearly point to an Italian origin of the instrument, and not a German one.

          So neither the parchment repair on the inside of the back of the instrument, nor the pair of inscriptions on the base structure of the instrument is an original part of the clavicytherium and, at best, indicate only that the instrument was repaired at some time totally indeterminate later period, in Germany when it was given the base support and the parchment repair.  Also, like the parchment repair, the addition to the base of the two battens may have happened quite some time after the instrument’s original construction.  Ulm reached a high point in its economic and cultural history after the Protestant Reformation from about 1525.  So there would have been the money in Ulm at that time for the instrument to have been bought by a wealthy merchant or trader in Ulm, and then exported North across the Alps and into Ulm.[71]  Musically RCM0001 may perhaps still have been current in Ulm in about 1525, although already out-of-date in Urbino.  We know far too little about the music performed in either Ulm nor in Urbino to draw any conclusions.  The date chosen for the original construction of the RCM0001 clavicytherium is to about 1471, and its arrival in Ulm might be dated to about 1520. 

          Although this dating also has its uncertainties, what can be added to this – and what is very clear – is the fact that even the most cursory analysis of the measurements of the instrument indicates that it was not made in Ulm.  Historically, the unit of measurement in Ulm is well known[72] and was 1 Fuß (foot) = 286.5mm so that 1 Zoll (inch) =  = 23.875mm.[73]  Not a single one of the primary design-measurements of the clavicytherium can be expressed in simple, convenient, whole- or half-integral units of the Zoll used in Ulm.  My conclusions from this is that the instrument was therefore certainly not made in Ulm.  More will be said about the original centre of construction of the instrument in Urbino in Section 0‑11 below. 

 

 

 Section 0‑8 - A brief physical description of the RCM0001 clavicytherium

          The instrument itself, like many other early keyboard instruments made in Italy, is contained in a protective outer case.[74]  One of the most obvious and unusual features of RCM0001 is the shape of the case (see the title page of this book and Figure 20 above).  Unlike a ‘normal’ harpsichord or clavicytherium which has a bentside and a tail, here the bentside consists of only a single curve starting as usual at the far end of the cheek.  But here the bentside reaches all the way to the straight side or spine, without finishing with the usual extra side or tail.  It has an upright stature as is normal for a clavicytherium, with the keyboard lying along the front, lower edge.  Both the nut and the bridge reach across the whole width of the instrument right to the case sides leaving no space at the ends of the bridge and nut to facilitate the free vibration of the ends of the bridge.  There is the usual cutoff bar running almost parallel to the bridge underneath the soundboard and this is placed, in turn, underneath a further decorative ‘cutoff bar’ for most of its length.  The unusual feature of the physical cutoff bar and the decorative bar is that they delineate a kind of step in the soundboard with an absence of soundboard below the step so that, in the area below the ‘cutoff bar’, the baseboard is visible although partly covered by a decorative scene.

 

 

Section 0‑9 – The Italianate features of the clavicytherium and the size of the unit of measurement used in the construction of RCM0001.

          As seen above both the paper[75] written by Elizabeth Wells, and her catalogue with a description of the instrument, imply that the instrument was made in Ulm on the basis the inscriptions on the instrument.  But before beginning the analysis of the size of the unit used in the design and construction of the case dimensions, and in the design of the string-lengths, the following Italianate characteristics of RCM0001 need to be noted by the reader:

1.         The case sides are wrapped around the back (equivalent to the baseboard) of the instrument in a manner similar to that found incorporated into the construction of virtually all Italian harpsichords, virginals, spinets and clavichords made throughout the Italian peninsula during the whole of the historical period.  This is one of the most basic characteristics of Italian stringed-keyboard construction.  Despite this, the RCM0001 catalogue maintains that the instrument was made in Ulm in Southern Germany.  On the other hand, harpsichords from the German-speaking part of Europe, and indeed from the whole of the area north of the Alps, normally have case sides that sit on top of the baseboard and are not wrapped around the outside edges of the baseboard.  Even the early 1537 harpsichord by Hans Müller, Leipzig, now in the Museo nazionale degli strumenti musicali in Rome,[76] which is superficially similar to many Italian harpsichords, has the case sides sitting on top of the baseboard as is usual for North-European keyboard instruments.  The Müller harpsichord is a German instrument and of an early date and it does not at all resemble the usual Italian harpsichord construction in this respect. 

2.         In the clavicytherium the front mouldings (what would be the top mouldings in a harpsichord case in its normal position and orientation) are added to the inside and outside edges of the case sides, as well as being placed on top of these added mouldings, and are not moulded into the actual wood of the edges of the case sides themselves.  Unlike RCM0001, virtually all harpsichords made north of the Alps have the latter feature, their mouldings being cut into the case sides rather than being applied as in the usual type of Italian construction.  So RCM0001 appears to be of Italian origin also on the basis of this construction feature. 

3.         The soundboard rosettes of RCM0001 are made of layered parchment and/or vellum and are neither carved from the wood of the soundboard nor are they made of cast metal fitted into a hole in the soundboard.  The soundboard rosettes of RCM0001 are, however, very similar in style to most soundboard rosettes of Italian harpsichords made all the way from Venice and Milan in the north right down to Naples and Palermo in the south (see the photographs of Figure 23 and Figure 25).  They do not at all resemble the usual North-European soundboard rosettes in this respect, and this aspect also points to an Italian origin.

4.         The edges of the soundboard and the cover in front of the jacks are also decorated with strips of layered, incised and punched parchment or vellum.  These are similar in style to the decorations found on many of the earliest Neapolitan and Sicilian harpsichords.  This does not, however, signify that the instrument was made in either of these two centres, but only that it is a very simple, very old Italianate design and tradition.

          Therefore, in the light of these Italianate characterises of this harpsichord, the possibility that it was made somewhere in Italy has to be considered in its assessment, without excluding the small likelihood that it also may have been made in a German-speaking country.  Compared to the instruments which have been analysed in the author’s previous publications and discussed in the papers listed in footnote 89 (check this) below, it was necessary to change the author’s approach slightly to be able to determine the unit of measurement for this particular instrument.  Here it is not at all obvious how the back – equivalent to the baseboard in a ‘normal’ harpsichord – was designed (it does not, for example, reach right down to the bottom of the back of the instrument), and also there is no tail nor tail angle from which to get a first estimate of the size of the unit of measurement, as has been done in order to be able to assign a unit of measurement to the other harpsichords, virginals and spinets discussed in the papers listed in footnote 89 above.  However, as will be seen below, the linear-regression analysis of the lateral pin and register spacings tie the unit of measurement used in the instrument’s construction very firmly to Urbino with an extremely high level of confidence and accuracy.

 

 Section 0‑10 – The decoration of the RCM clavicytherium.

          Although it may not, at first, be noticed because of its other strange features, the RCM clavicytherium is very highly decorated, suggesting that it was made for and owned by a person of wealth and importance.  This would, of course, accord perfectly with it having been made at the Court of Federico da Montefeltro in Urbino.  As part of its elaborate decoration, the instrument has a most unusual carved and painted scene at the front of the instrument below the diagonal edge of the cutoff bar underlining the soundboard.  Space for this scene has been cleared by constructing a step at the edge of the soundboard as described above, and attaching the ‘scene’ to the back (baseboard) of the instrument.  This ‘scene’ is constructed of carved, painted and composite pieces, sometimes of plant materials like moss and lichen, in a kind of landscape setting.  Unfortunately much of this composite decoration was too fragile to withstand the vicissitudes of the instrument’s long life and is now missing, so making it difficult to determine what exactly it was originally meant to represent.  But the effect of this elaborate scene only highlights that this clavicytherium was a highly-extravagant instrument built for a person who was extremely wealthy, and who had a very good taste in decoration.

 

 

The soundboard borders

          As just mentioned above, and seen in a number of the photographs in this work, there is a large ‘landscape scene’ set into the lower bass area of the soundboard against the back of the instrument, and at a level behind the soundboard.  As just explained above, the exact nature of this ‘scene’ is now not clear from what little remains of it.  The whole of the scene is surrounded by a decorative border, very Gothic in nature[77], which is made up of a strip of carved and pierced parchment thickened behind it by a thin layer of wood (lime? = tilia sp.[78]).  Much of this decoration is similar to that of the soundboard rosettes of many later Italian (and a small number of North European) keyboard instruments.  Examples of this pierced decoration can be seen below in Figure 23 and Figure 24 below.  The parchment and wood border in Figure 23 is gilded whereas in Figure 24 it can be seen to have been painted, possibly with vermillion, ultramarine and lead white.  The wide section with the pierced parchment and wood pattern in Figure 24 has a blue background, that is painted probably using the highly-prized ultramarine pigment which came from Afghanistan during this period.   

 

Figure 23 – The position of the lowest of the 3 soundboard rosettes showing a small section of the bridge, two of the soundboard ivory buttons, and the incised, gilt parchment-and-wood border along the edge of the soundboard.

Anonymous clavicytherium, Urbino, c. 1471.

Royal College of Music, London, Cat. No. RCM0001.

 

          The grain of the wood of the soundboard and baseboard (through the hole for the old rosette) can be seen clearly in Figure 23 above.  The wood of both the soundboard and baseboard has very sharp, distinctive growth rings which are typical of spruce (sp.  picea).[79]  The soundboard wood seems, after more than 573 years, to have lost very little of the ‘sparkle’ typical of spruce cut accurately on the quarter.  However, the grain, and the cut of the soundboard wood can be seen clearly at the edges of the top and bottom soundboard rosettes, indicating that the soundboard wood was, indeed, cut very accurately on the quarter as is typical of any good soundboard wood.  The turned ivory beads, used in various places on the instrument, can be seen in Figure 23 and also in Figure 25 below. 

 

Figure 24 – The decoration along the lower edge of the soundboard showing the painted squares with dots at the top, a pierced, carved and gilt Gothic pattern with the background, possibly of ultramarine, and a white strip possibly with added blue ultramarine dots along its lower edge.

Anonymous clavicytherium, Urbino, c. 1471.

Royal College of Music, London, Cat. No. RCM0001.

 

 

The soundboard rosettes

          The instrument originally had 3 soundboard rosettes (only one of which is now wholly complete), the usual case mouldings typical of most Italian instruments made South of the Alps, a number of ivory beads decorating various parts – again in the style of many instruments made in the Italian peninsula – and a delicately-carved thin bridge in the shape of the limb of a tree with branches leading off it at regular intervals. 

 

Figure 25 – The middle soundboard rosette with a number of other decorative details.

Anonymous clavicytherium, Urbino, c. 1471.

Royal College of Music, London, Cat. No. RCM0001.

          The only remaining (more-or-less) complete soundboard rosette can be see in Figure 25 above.  It is clearly missing some of the background colouration in the top and top right of the rosette.  The front of the rosette consists of delicately-cut parchment with a wood (lime?) underlay.  Behind the carved front part of the rosette there are small panels of parchment decorated in ultramarine and gold as a background.  Normally one would otherwise describe this as being in a neo-Gothic style, but, in fact, the Gothic period did not end until about 100 years after this instrument was built.  So it is actually a true Gothic rosette in both style and period.[80]  What is clear is that this small rosette was made, like all aspects of this instrument, with consummate skill and accuracy to give this delicate, symmetrical Gothic design.   

 

 

The keywell scrolls

          One of the many exceptional and rare features of the RCM0001 clavicytherium is the ‘decoration’ of the keywell scrolls.  Normally the keywell scrolls are of plain wood or they are sometimes made up of a sandwich of differently-coloured woods, - or sometimes they have a carved figure or shape.  The scrolls are, at any rate, usually of a shape that is described perfectly by their name, ‘keywell scroll’. 

Figure 26 – The bass keys of the present-state compass showing the bass keywell scroll covered by a strip of scarlet velvet as decoration.  The unusual decoration of the parchment key arcades can also be seen, although these are probably not an original part of the decoration. 

Anonymous clavicytherium, Urbino, c. 1471.

Royal College of Music, London, Cat. No. RCM0001.

 

           The author has never seen a strip of velvet used for this kind of decoration on any keyboard instrument, whether it was made North or South of the Alps.

 

 

The bridge

          The bridge also has an unusual type of decoration that may also be unique to this instrument.  The actual bridge bearing the bridge pins is of a basically rectangular shape, but with a carefully rounded top surface (see Figure 27 below).  What is unusual about this bridge is the carving of branches or twigs branching out of the main bridge giving the impression that bridge is made from the limb of a tree with the branches coming off it.

 

Figure 27 – A view of a section of the bridge.  The limbs are spaced regularly along the bridge with a separation of about 2½ Urbino once between successive limbs (see Figure 36 below).

Anonymous clavicytherium, Urbino, c. 1471.

Royal College of Music, London, Cat. No. RCM0001.

 

          Figure 27 above shows a photograph of a short section of the bridge.  Clearly this is meant to represent the limb of a tree, with portions of short branches or twigs leading off it at regular intervals.  Figure 27 also shows small diamond shapes, in alternating ultramarine or gold, painted at regular intervals between the hitchpins.  The bridge is beautifully and carefully made, and hardly seems to be anything but the natural branch of a small tree.  Both the main part of the bridge and the branches growiing away from it are smoothly finished, and each branch is accurately cut to resemble its neighbour.  The severed ends of the branches are painted alternately red and blue, probably using the precious pigments vermillion and ultramarine[81].  Some of the measurements of the case and bridge are shown in the drawing of Figure 28 below.  This shows that the spacings of the branches the bridge are all close to about 74mm.  The calculated spacing of these limbs has been found to be 75.229mm or 2.551 Urbino once.  This result has an difference of only 2% from exactly 2½ Urbino once = 73.7mm, and seems to indicate that the ‘limbs’ may have been intentionally spaced regularly with a distance along the ‘branch’ of 2½ Urbino once.[82]

Figure 28 – A drawing based on part of the bass endk of the bridge, which also shows the spine side, the spine liner, the bentside, the bentside liner, and the hole for the, missing, lowest Gothic soundboard rosette which has the inscribed strip of parchment with writing on it and placed behind it.

Anonymous clavicytherium, Urbino, c. 1471.

Royal College of Music, London, Cat. No. RCM0001.

 

 

The wrestplank rosette

          Another of the unusual decorative features of this instrument is the turned and partly carved rosette decorating the middle of the wrestplank (see Figure 29 below). 

 

Figure 29 – The small turned and carved rosette found near the middle of the wrestplank, one of the many unusual features of this instrument.  The near ends of the jacks can be seen at the top of the photograph, and the nut and nut pins at the bottom.  The nut pins are clearly small nails each with its own small head.

 

          The wooden wrestplank rosette appears to be made of a fine-grained fruitwood (possibly pear?).  It is composed of a small disc of wood that has first of all been turned to give the external ridges in the ‘petals’, with a raised bump and circle in the middle.  The outer part of the rosette has then been carved awat at regular intervals to give the impression of petals to the overall rosette.  It seems to have no structural or acoustical purpose, and the only reason for its presence seems therefore to be purely decorative.

 

Figure 30 – Detail of the bass section of bridge, including additional features.

Anonymous clavicytherium, Urbino, c.1471.

Royal College of Music, London, Cat. No. RCM0001.

 

          A section of the bridge can be seen in Figure 30 above.  A unique feature of this bridge is that it is clearly meant to represent a branch, with twigs coming out the of the branch on alternate sides.  The ends of the twigs are painted alternately red and black, and there are small diamond shapes alternately white and black painted between the hitchpins.  Like so many aspects of the construction of this instrument, the representation of this bridge section has been carried out with great care and attention to detail and, in addition, the carving has been carefully finished and polished.

 

 Section 0‑11 – The jack mechanism of the RCM 1 clavicytherium.

          The plucking mechanism of this extremely early clavicytherium is similar to that of the jack mechanism of most of the later clavicytheria, and is essentially the same as that found in instruments dating right on into the 18th century.  Some 18th-century clavicytheria have a detached sticker mechanism (in many ways similar to the sticker mechanism in an organ action), but here the jack is fixed to the sticker which, in turn, is fixed to the keylever.  This is, in fact, also the case with most of the later clavicytheria.  This strongly points out the ingenuity of the methods used by the instrument makers at the Court of Federico da Montefeltro and, indeed, seems already to point to a relatively long-standing tradition of early keyboard instrument building from well before 1471, the estimated date of the RCM0001 clavicytherium.  The jack/sticker/keylever mechanism of RCM0001 is shown below in Figure 31 at a scale of 80%. 

 

Figure 31 – The jack/sticker/keylever mechanism found in the RCM0001 clavicytherium, seen from the treble side.  Note the round, cylindrical hole in the tongue for the plectrum.  Scale:  80%.  ©RCM, London.

Author’s drawing extracted from the full-sized drawing made for the RCM by William Debenham in 1983. 

 

          The drawing shown in Figure 31 above has been accurately scaled by a factor of 80%.  So it can be used to scale up to the actual size the components involved simply by multiplying each of the measurements as printed here by a factor of 1.250.  Clearly the maker of the RCM clavicytherium has designed this mechanism so that the balance point is roughly mid-point between the position of the sticker in the mechanism and the point at which the finger touches the natural touchplate.  This means, further, that the movement of the jack and tongue closely mirrors the movement of the finger and touchplate further down the lever mechanism.  There are several other features of the action diagram shown in Figure 31 that should be noted carefully:

1.       The instrument is clearly not now in its original state.  There must have been an earlier state in which the tongues, and the tongue axle-pin, were in a different position further toward the left-hand end of the jack.  In this position, the spring behind the tongue would not have been ideally placed to return the tongue to its desired position because of its disadvantageous lever ratio.  It seems highly unlikely that the original maker(s) of the clavicytherium would have placed the balance pin in this position, as they would have been fully aware of the disadvantages of positioning it there, given the sophistication of their design in the other aspects of the instrument.  However, the present axle-pin position is roughly ‘normal’ for a jack of this design as found in much later instruments.

2.       Notably, the ‘quill’ slot in the jack is round, and not flat as it is in the instruments of later designs which actually used (flat) quill as a plectrum material.  The fact that the plectrum slot is round strongly suggests that the plectrum was also round, and the obvious candidate for a plectrum material would therefore seem to be a thorn, an animal quill, or some type of plant material.  There is a number of thorn trees/bushes which are native to Europe any one of which may have been used here.  It is, however, pointless to speculate about the exact species that might have been used in this instrument as there seems to be nothing to base the choice of the plant (or animal) that might have been used here .  However, it should be noted that there is an often-quoted supposition that the name ‘spinetta’ comes from the Latin ‘spina’ = thorn, and may indeed indicate the origin of the word.  But other thin, round materials such as porcupine and hedge-hog quills might also have been used as plectra in this instrument.  Whatever was used, the curved cut-out at the back of tongue would seem, at first, to be an inconvenient shape for trimming off the end of the plectrum.  One possible explanation for this recess is that the plectrum, of whatever material, was cut off flush with the rear surface of the tongue, and the excess length at the back was used to move the plectrum back and forth to adjust the amount that the plectrum projected under the string.  It would, therefore, be used as a partial measure to regulate the voicing of the instrument.  

3.       The tongue-axle pin appears to be of boxwood.  Box is very hard and would be resistant to wear with long-term use.  However, it would be rather difficult to manufacture such a small item out of such a hard, intractable material.  However, it seems unlikely that the very careful, precise William Debenham might mis-identify this material when making his drawing.

4.       The RCM catalogue states that the arrangement of the jack fixed to the keylever would result in a magnified movement of the jack.  This is simply not true because the jack would move the same amount as the sticker since the length of the rear part of the keylever, the sticker, and the distance of the quill from the top of the sticker are all closely the same.

 Section 0‑12 - The lateral jack-guide pin spacings.

          The following analysis uses a standard mathematical method called a linear-regression analysis by the method of least squares[83], and gives results with a precision that cannot be achieved by any other means known to me.  It is based on simple but strict mathematical principles, some of which, just as with the calculation of the regular spacing of any other series of pins, keys, jacks, register slots, etc are based on the calculation of the average spacing of the objects involved

          The lateral spacing of the bridge-pins, nut-pins and register jackslots (or jack-guide pins for the RCM clavicytherium) of stringed-keyboard instruments has not been the subject of any published keyboard organological study known to me.[84] And yet the lateral spacings of the various elements of an instrument is an aspect of early-keyboard construction that is just as much a part of the design process of the instrument as are the string scalings.  Although the past obsession with string lengths is extremely important and fruitful to our knowledge of stringed-keyboard instrument acoustics and design, the string lengths are often the only features of a stringed-keyboard instrument that have received any attention in the literature published up to this time.  In the author’s opinion the lateral spacing of the bridge- and nut-pins, of the register slots and of the keytails is of paramount importance to the design of a stringed-keyboard instrument, and should be among the first of an instrument’s features that should be studied in the analysis of any early stringed-keyboard instrument.

 

 

 The action mechanism of the RCM clavicytherium.

          Because this instrument is a clavicytherium, its mechanism requires some method to convert the up-and-down motion of the tail of the keylever into a back-and-forward movement of the jacks.  As with many later clavicytheria, this is achieved, as it must be even with such an early instrument, with a simple pivoted tracker mechanism attached to the tails of the keylevers.  The jacks and the top part of the tracker mechanism are held in position with a series of pins placed comb-like in a batten along the lower edge of the gap, and these are positioned at the top edge of the wrestplank.  These guide pins are not all drawn in Figure 20, but the tracker guide-pins for the treble jacks are clearly visible at the right-hand end protruding up into the gap space.  Figure 32 below shows a side-view section of the action mechanism.  One of the jack guide-pins can be seen in this figure and is indicated by the dark arrow and the added text. 

 

Figure 32 – A drawing of a section of the action of the RCM0001 clavicytherium, extracted from the RCM drawing made by William Debenham (not to scale).  ©RCM, London.

Royal College of Music, London, Cat. No. RCM0001.

 

          Because there is a large number of jack guide pins, and because they seem to be equally spaced, the application of the usual linear-regression analysis to the measurement of their lateral spacing should result in a value that has a very high accuracy and a small error.  The measurements of the positions of the jack-guide pins consist simply of recording the distance from the left side of each of the jack guide-pins to the inside of the spine (i.e.  the long, case side standing vertically on the left-hand side of the instrument), always taking care that each of the measurements is recorded in a direction accurately perpendicular to the spine.[85]  These measurements are given in Table 1 below taken by estimating each measurement to the nearest  of a millimetre.

Table 1 – The lateral spacing of the tracker-guide slots measured in mm from the inside of the spine to the left side of each of the guide slots.  These are plotted below in Figure 33.

Anonymous clavicytherium, Urbino, c.1471.

Royal College of Music, London, Cat. No. RCM0001.

 

          The measurement from Table 1 are plotted in the graph of Figure 33 below and show clearly that the points all lie on a single straight line.  They were therefore analysed by carrying out a linear-regression analysis on them.  This graph plots a very good straight line with very little scatter of the points on either side of the calculated line.  The result of this analysis gives the slope (= the averaged lateral spacing of the pins), which can be seen in the graph shown in Figure 33 on page 59 below. 

Figure 33 – A graph of the lateral position of the same side of each jack guide-pin, measured relative to the spine of the instrument.

Anonymous clavicytherium, Urbino, c.1471.

Royal College of Music, London, Cat. No. RCM0001.

 

           Clearly the graph of the measured positions of the register guide-pins seen in Figure 33 above does, indeed, plot a curve that is a very good straight line with very little scatter in the points used to calculate it.  This indicates that the spacing of these guide pins is very regular and, simply because the plot is a straight line, that it doesn’t change in its regular spacing across the whole of the compass of the instrument.  In order to determine what the averaged spacing of these pins is, the measurements from Table 1 were subjected to a normal linear-regression analysis.  Part of the ‘Summary Output’ table generated by the Excel spreadsheet is shown as Table 2 below.

 

Table 2 – A part of the output table of the Excel spreadsheet giving the linear-regression analysis results for the data given in Table 1 above.

Anonymous clavicytherium, Urbino, c.1471.

Royal College of Music, London, Cat. No. RCM0001.

 

          Although many of the results of the linear-regression analysis found in Table 2 above are of use in certain applications, only a small number of these is of importance to the analysis carried out here.  Among those that are relevant are the regression coefficient ‘Multiple R’ = 0.999997, indicated in a dashed-line box near the top of the table.  This value is very close to 1 and this therefore indicates, in turn, that the errors in the results are very small.  This indicates both that the calculated output is a VERY good fit of a straight line to the data, and that the results of the regression analysis are both accurate and are ones in which we can have a high level of confidence.  Of particular interest and importance is the standard error which has been highlighted in blue in this table.  This number tells us how accurately the data fit to a straight line, and what the deviation of the data is to the straight line.  The ‘X Variable’, or the slope, is indicated in this table in a box with a double-line border at the bottom of the table.  This value is 14.7388, and corresponds to the averaged lateral spacing of the tracker-guide slots.  The standard error of this value is given by the value highlighted in blue = 0.447205 with an error of only 0.006126mm.  Expressed to the correct number of figures of accuracy, the averaged lateral spacing of the tracker-guide slots is therefore:

                                                                     14.74mm ± 0.45mm                                         Equation 1

or, expressing the error as a percentage instead:

                                                                         14.74mm ± 3%                                             Equation 2

          Because of the high accuracy of this result, it will be used below as a critical element during the analyses of the size of the unit of measurement used in the design and execution of many other aspects of the RCM clavicytherium.  The importance to the analysis carried out here is that, with such a low error, the calculation of the average lateral tracker-slot spacing can be considered as an accurate result on which a great deal of confidence can be based.  The accurate calculation of the size of this unit turns out to be crucial to the determination of the centre in which this instrument was built.

          This kind of analysis shows the importance of the use of some of the standard scientific and mathematical tools used throughout this discussion.  Without the certainty provided by the errors calculated by these standard mathematical/statistical procedures resulting from the linear-regression method of analysis, it would have been impossible to say with any conviction that this instrument was made in Urbino.  In addition, we would also not have any idea of the skill of the instrument builders working for Federico da Montefeltro, nor of the accuracy with which RCM0001 was made.

 Section 0‑13 – The determination of the unit of measurement used in the design and construction of this instrument.  Where was RCM0001 originally made?

          That the makers of almost any object in historical times used the local, pre-metric unit of measurement in common use in their centre, to design and build almost any item that they were working on, makes perfect sense.  In Italy and Germany there wasn’t a single unit used universally across the whole country as there was in France and England, for example.  Instead, each city or city-state had its own local unit of measurement that was standard for that particular area, but was not in general use elsewhere.  The author has made a large database of the units of measurement used in the different areas in Germany and, particularly, in Italy[86].  The use of a calculation of the size of the unit of measurement to identify the city of origin of an historical keyboard instrument has been used by the author in a number of papers published in the past.[87]  Indeed, the non-metric system is the same traditional system still in use today in the ultra-conservative United States[88] and, up until a few years ago, also in the United Kingdom. 

          The primary reason that each centre in Italy used its own unit of measurement was that it was a requirement of the regulations of the local guilds to do so.  The use of the same unit of measurement by everyone in a centre was imposed in order to ensure that a measurement of one braccio (arm) was the same for all of the merchants in that centre.  This meant simply that the length of the subdivisions of the braccio into one piede or oncia or palmo, etc was the same for everyone in that centre or region, thus ensuring that no client would be cheated through being sold an item measured according to a unit of measurement different from that which was the accepted standard for that centre.  From our point of view as modern organologists, it is very fortunate that, in countries like Italy and Germany, for example, the size of the unit varied from place to place, from city-state to city-state and from region to region.  The variability in the sizes of the units of measurement used across a country means that, if we can first of all just determine the size of the unit of measurement used in the construction of an object, we can then, through a knowledge of the sizes of the units used from place to place in historical times, determine its location of origin.[89] 

          The relevance of the size of the unit of measurement in the design of keyboard instruments was first pointed out by Herbert Heyde in the literature.[90]  Heyde noted that, because the size of the unit of measurement varied from place to place, a determination of the size of the unit of measurement could then be used to find the original centre of construction of stringed-keyboard instruments.  But unfortunately he, and a number of other writers on the subject, perhaps through the lack of any practical experience of actually building instruments, failed to begin their analyses by using the dimensions of the baseboard. 

          The historical Italian makers seem universally to have begun the construction of their instruments by measuring out the raw dimensions of the baseboard, without the additional thickness added by the case sides.  They therefore measured out the baseboard in simple numbers of the local unit of measurement.  It therefore remained for the author to provide a reliable table of the sizes of the units of measurement used in the various Italian centres for comparison with the calculated size of the unit of measurement used in historical Italian keyboard instruments.[91] 

          In the particular case of the RCM clavicytherium, the extreme age and fragility of the instrument make the re-measurement of the instrument in order to determine the unit of measurement used to design and build it, a particularly delicate and – because it has already been measured and drawn – unethical procedure.  Therefore only the drawing and the data sheets supplied by the RCM have been used to carry out the analyses here.[92]  Needless to say all of the measurements taken from the drawing were based on the linear scales in both the x and y directions.  They are therefore felt to be accurate representations of the actual dimensions of the clavicytherium.

          Normally the determination of the size of the unit of measurement used to design and build an instrument relies on accurate measurements of a few of its critical case parts – normally, for a harpsichord, virginal or clavichord – of the baseboard.  It is therefore the ‘naked’ baseboard without the additional thicknesses added to the case dimensions by the case sides and by the outer mouldings, that were measured out by the maker in his workshop, and it is these ‘naked’ baseboard measurements that need to be analysed in order to determine an initial size for the unit of measurement. 

          For harpsichords, the components of the tail side are normally used to give an initial ‘hint’ as to the size of the unit of measurement which was used to construct it.  And for Italian polygonal virginals, the components of the short left-hand angled side of the baseboard were used for the same purpose.  This process quickly leads to an estimate of the size of the unit of measurement being used.  Using this, the other baseboard measurements can then be calculated in the size of the local unit of measurement, and these are all, normally, simple integral or half-integral measurements of whatever unit was used in the maker’s workshop.  But the RCM0001 clavicytherium does not have a ‘tail’ from which the components of the sides of the tail can be measured and used in this initial ‘guesstimate’.  So, clearly, a different approach needs to be taken here.  Because the lateral spacing of the jack-guide slots has been determined with a high accuracy, it was decided to start with this measurement instead, and to use this to make an educated guess as to the size of the unit of measurement used throughout the rest of the instrument. 

          The size of the lateral spacing of the jack-guide slots measured here and used to determine their averaged spacing using the linear-regression analysis give a value for their spacing of 14.739mm ± 0.006mm.  Using the results of these analyses it was possible to obtain a good estimate of at least some of the dimensions of RCM0001 with the extremely high degree of accuracy obtained when using the linear regression analysis when a large number of data points is being analysed.  The chief advantage of using the linear-regression analyses is that the results are then known to have been determined very accurately, and we can therefore have a high level of confidence in their use here.  Looking at a table of the lengths of the oncia used throughout Italy in the historical period (see also Appendix 17 on page 233), it appears that this dimension must represent exactly ½ of an oncia in whichever centre the instrument was constructed.  This would mean that:  

                                                   1 oncia = 2 x 14.74mm ± 3% = 29.48 ± 3%                       Equation 3

and this is the value of the oncia that will be tried here initially to express the other measurements of the instrument in once rather than in modern units of the millimetre.

          So using a value of the oncia = 29.48mm ± 3% as an initial trial for some of the other measurements of the clavicytherium gives the results seen in Table 3 below.

 

Table 3 – Trial of some of the measurements used in the construction of RCM0001 using the size of the oncia calculated using a linear-regression analysis of the jack-guide pin-spacings from Table 1 on page 58 above.

Anonymous clavicytherium, Urbino, c.1471.

Royal College of Music, London, Cat. No. RCM0001.

 

          The figures in Table 3 above represent a kind of ‘skeleton’ table where values of the weighting of the averages have not been calculated.  The main reason for this lack of refinement at this stage is that any kind of weighting or averaging for this table involves only 8 measurements, whereas the linear-regression analysis used above in Table 1 to calculate the size of a half oncia involves altogether 40 measurements and adds the refinement of the averaging process of the linear-regression analysis of these 40 measurements to give a result that is very accurate indeed.  This yields a calculation giving a small error as has been seen above.  So the 8 measurements calculating the size of the oncia in Table 3 must, because of the small number of measurements taken, and because the results in Table 3 cannot be subjected to a linear-regression analysis process in the same way, have a larger error and a much lower accuracy.  It was felt that no other calculation of the size of the Urbino oncia using measurements taken from the drawing of the instrument could approach the accuracy of the result already obtained using the linear-regression analysis which was carried out above (see Table 2 on page 60 above).

 

Section 0‑14 – Some comments about the measurements found in Table 3 above.

          The measurements in Table 3 were all measured out from the RCM drawing using a made-up ruler marked out in once, quarter-once and twelfths of an oncia of the sizes of the oncia found above from the lateral spacing of the jack-guides.  To make this ruler, the value of the oncia that was found using the linear-regression analysis of the jack-guide pins was used because of its calculated high accuracy and consequent low error.  What was surprising is that, using a ruler made up to conform to the size of this unit of measurement, many of the other dimensions of the parts and pieces making up the RCM0001 clavicytherium involved halves, thirds, sixths and even twelfths of an oncia.  At first it seems counter-intuitive that so many of the measurements involved these smaller sub-divisions of the oncia when most of the later makers tended to use only whole or half-units of the fundamental unit of measurement when measuring out the dimensions of the components of their instruments.  However, it soon became clear that the elegant and sophisticated design of the RCM0001 clavicytherium was a fact of life, and one that had to be accepted – and that these smaller divisions were meaningful.  So the use of these smaller divisions of the unit of measurement (the oncia) had to be accepted, and, they had to be seen as an intrinsic part of the refined, urbane and perfected designs typical of the polymaths working in Federico’s Court.

          Unlike the later stringed-keyboard instruments of the subsequent generations, RCM0001 is a product of the complex design principles of the remarkable polymaths working at the Court of Federico da Montefeltro around the middle of the fifteenth century.  More details of the elegance and sophistication of the design of this instrument will be seen in the later discussions and analyses in the sections below.

 

Section 0‑15 – The keyboard of RCM0001.

          As with so many aspects of the clavicytherium RCM0001, the design of the keyboard is particularly fine (see Figure 34 below).  The keyboard, although it has survived in a somewhat incomplete and mostly non-original form, seems to be based on the usual Italian traditional methods of construction.  For example, there are the usual (for Italy) nail holes near the middle of the original top and bottom keylevers which match exactly with corresponding holes below the keylevers at the extreme ends of the balance rail.  These holes in the top and bottom keylevers, with corresponding holes in the balance rail, can only be the result of nailing the keyplank to the balance rail before it was cut apart into keylevers.  This was done in the process of marking out the rear ends of the keylevers in situ so that there is a perfect correspondence between the position of the ends of the keylever tails and the spacing of the jacks.  This was done by placing a dummy jack, sometimes dipped in ink to mark the keyplank in each register slot in succession, to mark the future positions of the jacks.  These were then used to mark out the ends of the keylevers on the keyplank.  The holes for the balance pins were also drilled at this stage, thus ensuring a perfect correspondence between the balance-pin positions and the balance pin holes.  The holes for the balance pins, marked out and then drilled in the keyplank in this way, were then at the exact centres of what, eventually, would become the new keylevers. 

          From the evidence provided by the keylevers and the balance rail, it is clear that the keys belong to the balance rail, and that there is no sign that the balance rail has been replaced, moved or altered.  However, some of the keys in the middle of the compass appear now not to be in their original order (see Figure 35 on page 65 below).  The use of the positioning pins to hold the keyboard in place on the balance rail while it was being drilled for the balance pins, surprisingly to me at least, uses exactly the same system as that used for the next generations of keyboard-instrument makers during the subsequent period covering a time span of about 570 years!

          But much of the details of the key balance points and the touchplates appears not to be the original.  The naturals have embossed keyfronts that have been gilded, and the actual natural-key touch plates are of bone, with two scribed lines running parallel to one another along the top of the natural touchplates just in front of the sharps.  The sharps are decorated with differently-coloured wood parquetry laid out in various geometrical lozenge patterns (see Figure 34 below).  However, it is clear from the earlier scribed lines and marks now found underneath both the naturals and sharps touchplates, and on the keylevers themselves, that the present natural touchplates and the sharp tops are not the originals. 

Figure 34 – A general view of the present non-original key coverings.  The lower edge of the wrestplank is just visible at the top of the photograph with some tuning pins and some fragments of old stringing wire.

Anonymous clavicytherium, Urbino, c.1471.

Royal College of Music, London, Cat. No. RCM0001. 

 

 

          The present clavicytherium keyboard as a whole has a layout that can be represented schematically by the lower part of Figure 35 below.  No attention has been paid in this diagram to the exact original lengths of either the natural touchplates, nor of the sharps.  Although many of the keylevers in the lower part of this diagram are still in their original positions today, several have been moved, and some are now missing altogether.  This aspect of the study of the instrument will not be touched on further here as it is dealt with competently in the RCM Catalogue, and it contributes nothing further to the discussion of the origins of the instrument, which is the principal aim of this study. 

There are two important points to note about Figure 35, however.  Firstly, it will be noted that, although some of the millimetre measurements of the instrument have been expressed in Urbino once, many of the other measurements, including those of the keyboard, can also be expressed in simple whole and half units of the Urbino oncia where 1 Urbino oncia = 29.48mm.  These are indicated as such on the top diagram.  The top diagram is of particular importance to the discussions made here, and the reader is encouraged to study this figure carefully.

Figure 35 – The presumed layout of the original keyboard (above) and of the present keyboard (below).  The measurements are given in both millimetres and in units of the Urbino oncia, which will be discussed below.  The width of the keytails (14.74mm) in the top diagram was determined, like that of the register-guide pins, using a linear-regression analysis of the their lateral spacings.  The two keylevers shown in the lower diagram are now missing. 

Anonymous clavicytherium, Urbino, c.1471.

Royal College of Music, London, Cat. No. RCM0001.

 

          As can be seen from the diagrams of the keyboard above, virtually all of the measurements can be expressed as a simple number of Urbino once.  The total width of the keyboard with 40 keytails is 19.97 once exactly, but this is only 0.15% different from 20 once and so, nominally, must have been designed to be 20 once in width before a small amount of wood was cut away, perhaps when sawing out the keyplank.  This means that the ends of the keylevers, with 40 keylevers occupying a space of 20 Urbino once, is just ½ once per keylever.  This is obviously the same value as the spacing of the guide pins for the trackers cut out in the instrument just below the ‘gap’, and analysed in Table 2 on page 60 above. 

          The use of the Greek letter Ψ (psi) as a note name has been introduced here.  It will be shown  in the course of this discussion that the use of the letter Ψ is a very useful concept in this connection.  In many fields of the physical sciences, Ψ is used as a symbol that can represent any number, abstract or otherwise - or it can even represent another letter of the Greek or Roman alphabet.[93]  So the use here of the Greek letter Ψ is used here to represent any note of the musical scale.  Basically, in the case of this particular keyboard, it means that the lowest three keylevers, although they appear to look something like E, ET and F, are represented here by Ψ1, Ψ2 and Ψ3, where these symbols are used to mean that these bottom three keylevers can operate jacks plucking strings tuned to any useful pitch depending upon the tonality and pitch of the piece currently being played by the musician.  The importance of this concept of tuning the bass notes of an instrument to any useful desired note, will be seen numerous times in this discussion.  All that is required of the reader at this stage of the discussion, is that he or she should forget, at least for the bottom notes of a Medieval keyboard, that these notes should be tuned to specific, named notes as they are in the more familiar C/E short octave.  Although it occurred much later, a good analogy to this is the variable tuning of the diapason bass strings of the large Renaissance lutes, which also had a variable tuning and were simply tuned and re-tuned by the player to notes according the to current musical context and need.

          As well as making a drawing of the instrument, a great deal of work was carried out by William Debenham to determine the original compass of the RCM clavicytherium.  In his careful analysis of the keys, both by using X-ray analysis and by looking at and matching up the woodgrain of the various key levers and the end-grain of the natural keylevers across the whole compass, Debenham has shown that the original layout of the keylevers is that given by the upper part of Figure 35 above.  This extremely useful determination indicates that the original compass began with what appears to be an E followed by a raised ‘accidental’, and then an apparent F, followed by the notes (in the Helmholz system) of a compass from G to g2 including a top fT2 (this is not what is shown here, but is explained below).  The treble part of this compass is not surprising.  The arrangement of both the original and the present keyboard layouts had the same number of keylevers and natural notes.  The bottom part of Figure 35 above shows the present state of the keyboard and has a layout with the familiar C/E short octave. 

Seen in this light, the original keyboard of this instrument (shown in the top diagram) has a 3 octave compass and begins at Γ-ut[94], but then with three additional keylevers below Γ-ut that are tuned ad-libitum to any notes needed by the requirements of the music and the musician.  The presence of these three lowest keylevers means that this instrument is of fundamental importance to the history of music and to the history of early keyboard-instrument making – and to our understanding of Medieval performance practice. 

 

Although it has suffered a later change in it’s compass, in the author’s view this instrument, as well as being the oldest extant keyboard instrument, can therefore also be seen as the earliest extant short-octave keyboard instrument as well.

 

The difference between the short octave of this instrument and the later C/E short-octave instruments is only that the note names and the notes of the strings to which they were tuned in the RCM clavicytherium were variable depending on the bass accompaniment needed by the composer or the musician who was playing the composer’s music.  No significance should be associated with the apparent ET: it would no more have been thought of by the contemporary musician as an ET ‘accidental’ in this context, than the apparent FT and GT of the conventional short-octave are thought of today as accidentals.  It certainly would never have been thought of by the contemporary musicians as an ET in 1445, any more so than it would be today.

          The use of the Greek letter Χ (chi), the letter in the Greek alphabet that precedes the letter Ψ, has been avoided here.  My hope is that the use of the symbol Ψ for the three notes below Γ-ut will avoid any confusion which might have arisen through calling it X, which would normally have stood for an unknown.

_______________

 

          As explained above, the strings operated by the bottom 3 keylevers in the bass part in the top of the diagram of Figure 35, giving the original compass, might have been tuned to any desired notes.  The important thing about this keyboard arrangement is that, at the time that RCM0001 was being built, musical composition and performance were going through a period of rapid and profound changes.  Music during this period should probably better be described as ‘transitional’ rather than as either ‘late’ or ‘early’ or ‘Medieval’ or ‘Renaissance’.  Before this period, and at least up to the period around 1455 to 1465, music was almost certainly played with keyboards using notes tuned to pitches in Pythagorean intonation[95] with pure fifths.  This music was characterised by a very limited ability to modulate away from the home key in either the sharp or the flat direction.  To modulate by more than 2 degrees in either the sharp or the flat direction, when using Pythagorean intonation, results in some major thirds that are unbearably out of tune (21½ cents = the syntonic comma – almost a quarter of a semitone worse than pure-meantone thirds).  Any chord played on an instrument with pure fifths and with major thirds that are out of tune by this amount would sound very discordant and very unpleasant indeed.  But what is truly surprising about this situation is that Pythagorean intonation does result in beautifully concordant harmonies in 5 playable tonalities, all of which have major thirds that are very close to being pure intervals and, obviously, and are tuned with pure fourths and fifths.  Which tonalities these are depends upon where the ‘wolf fifth’ is placed when the instrument is initially tuned.  These tonalities are - namely, in the ‘home’ key and the tonalities on either side of this going 2 sharps in one direction or 2 flats in the other.  The result of combining these sounds, all five of them essentially with pure harmonics, would be wonderfully concordant (see Table 20 on page 191 below), and would result in beautifully-tuned chords and harmonies.  These chords are exaggerated in their beauty by the almost-perfect tuning of the harmonics created in the strings themselves, held at a pitch very close to their breaking point at R + 5, a fifth higher than ‘normal’.

          However it also needs to be added here that it was impossible to play octaves on the keyboard of the clavicytherium (or of the clavichord studied in the next chapter) simply because the octave span of the keyboards of these two early keyboard instruments was far too great to be stretched by the human hand.  For the keyboard of RCM0001, the 3-octave span is close to 530½mm,[96] compared to a modern piano keyboard with a 3-octave span of about 500mm, or of a typical eighteenth-century French harpsichord or piano with a 3-octave span of only 475mm – about 55mm less that that of the RCM clavicytherium.  One octave of keys on RCM0001 amounts to 177mm, whereas on a French harpsichord it amounts to only 158mm, or about 20mm (= 13%) less in just one octave.  Effectively it would be impossible, even for a player with very large hands, to stretch their hand wide enough to play an octave when also playing the other required notes sounded in rapid succession on the RCM clavicytherium.  However, the inability to play a normal 1-3-5-8 chord does not detract from the beauty of the sound of this instrument when playing a simple 1-3-5 major triad – a chord that is fundamental to all post-Renaissance music.

 

 

Section 0‑16 – What does the design of RCM0001 tell us about the transition from Late Gothic music to that of the High Renaissance?

          In order to try to make sense of the bass part of the compass of the clavicytherium, the 3 keylevers below the Gamma-ut have been labelled in such a way that there is at least some connection with the later music of the High Renaissance, and with the later bass-compass keyboard layout.  Note that in the suggested configuration of the original keyboard compass, no allowance has been made for a low F.  The reason for this is simply that the lowest note of the Guidonian keyboard compass is Γ, the so-called Guidonian GAMMA-UT.  In medieval music theory there was no note lower than the Gamma-ut, and so F, as a note lower than Guido’s Gamma-ut, was outwith the range of the music, outwith the normal range of the human voice, and so would be thought to be useless when found in an instrument used for the music of the period.  This was, of course, all to change totally from about 1470 to 1500 as we will see with the Urbino intarsia clavichord later on in the next chapter.

          It needs to be added here that, although this compass seems strange to us now, the evidence provided by the X-ray and end-grain analyses carried out by William Debenham is clear and unambiguous.  It shows that the lowest notes appear superficially to be E, ET, F, G, GT, A, BI, B, c, etc.  An ET, whether found as here in the lowest part of the compass, or even higher up in the compass, makes no sense in the context of the music of any historical period, and can be disregarded as the note to which this ‘accidental’ was actually tuned during the period contemporary with the instrument’s construction.  It would no more have been tuned to a hypothetical ET, than the ‘accidentals’ of the normal short-octave were tuned to FT and GT during the following period.  Unfortunately there is no additional information provided by the clavicytherium instrument itself as to the actual pitches sounded by the strings of the three lowest keylevers below Γ-ut and labelled Ψ1, Ψ2 and Ψ3 here.  It is the author’s view that the strings on these three bottom notes could have been tuned to any desired pitch intrinsic in the Medieval system.  To see the compass in this way makes sense musically, and it ties the instrument both to the old Guidonian system, and also to the later Renaissance and Early Baroque musical climate.  To the author it makes clear the connection of these 3 lowest notes particularly to the later short-octave, and is clearly analogous to the normal C/E short-octave.  Unfortunately the ‘replica’ of this instrument commissioned by the Royal College of Music was given a ‘modern’ compass of C/E to g2, so that it is difficult now to try out the possible tunings or bass fingerings that might have been used at a time contemporary with its construction.  It is indeed sad and unfortunate that the significance and importance of the notes of the bass compass was not realised during the period when the drawing of the instrument was made, and when the ‘replica’ of the instrument was commissioned and built.  All we can learn from the ‘replica’ now is that, with a 3-octave span of 528mm it is impossible to play octaves with the instrument as has been discussed above.   This does not, however, detract in any way from what we could learn from the instrument, nor from the beauty and musicality of what could be played on it!  Personally, the author would dearly love to hear a replica instrument strung with ‘normal’ yellow-brass wire, and tuned to a pitch of R+5, a fifth higher than normal Baroque pitch.  It seems beyond comprehension that the RCM, as a centre with a world-wide reputation in the field, seem determined to leave the replica instrument as it is, tuned a fifth below its design pitch, with strings of the wrong material (modern phosphor bronze instead of soft yellow brass) producing harmonics that clash in a very unmusical way with the fundamental harmonic of each and every one of it’s strings.

 

 

Section 0‑17 – The construction of the bridge and the spacing of the branches on both sides of the bridge.

          As more and more work was done on the many aspects of the components of the RCM clavicytherium, it soon became obvious that all of the features of the RCM0001 clavicytherium are based on the length of the Urbino oncia.  But what is unusual about the design of this instrument is that many of the dimensions, instead of being dimensioned in lengths of integral or half-integral numbers, are in units of small multiples of  of an oncia.  In the author’s view the use of whole- or half-integral numbers of the units of measurement in the design and construction of an instrument, reflects a kind of laziness or devil-may-care attitude.  The design of the RCM0001 clavicytherium, on the other hand, seems to the author to display a complete and total attention to detail, where integral units could have been used, but where smaller divisions of the oncia were preferred because they gave structural strength and rigidity where it was needed most and, perhaps more importantly, they resulted in numbers that were in an almost exact proportion to other numbers being used in the design of the instrument.  The designer of the RCM clavicytherium therefore maintained proportionality exactly in balance to what was needed.  To the author this reflects an attention to detail and to a sophistication virtually never found in the design of most later stringed-keyboard instruments. 

          There is perhaps one of the most surprising uses of the Urbino oncia in the design of the bridge of the clavichord that will be confirmed from the measurements of the studiolo intarsia studied in the next chapter (see Figure 48 and Figure 49 on pages 113 and 115 below) as well as in the spacings the branches leading off from the clavicytherium bridge on either side of it (see Figure 36 below).

          The drawing seen in Figure 36 below shows a front view of the part of the instrument around the bass end of it’s bridge.  This figure was drawn using AutoCAD by pasting this part of the image from a .jpg image of the drawing of the clavicytherium supplied by the RCM museum into an AutoCAD template.  It therefore represents a full-sized section of the original drawing of RCM0001 that was supplied by them to me.  Here the spacings of the branches on either side of the bridge has been measured out by the AutoCAD programme and these are indicated in Figure 36 below.  There are, in all, 14 measurements from which an average can be made.  Indeed the main reason for making this drawing of the branch spacing was to get a large number of measurements, all of the same feature, which could then be used to calculate an average spacing of the branches, and, by using a large number of measurements of the same feature, of increasing the accuracy by a factor of the square-root of the number of measurements that have been made of this feature.[97] 

 

Figure 36 – A schematic drawing of the bass section of the soundboard and bridge showing the spacing of lowest branches coming off the sides of the bridge.

Anonymous clavicytherium, Urbino, c.1471.

Royal College of Music, London, Cat. No. RCM0001. 

 

          The average spacing of the branches in Figure 36 is therefore equal to the sum of the individual spacings divided by 14 (= the total number of spacing measurements).  The sum of all of the spacing measurements is 1053.2mm, so that the average is 1053.2mm/14 = 75.229mm or 2.552 once.  However, this result is very close to 2.5 once = 2½ once, and this has been calculated directly from the measurements taken from the drawing itself.  All of these features help to confirm that the Urbino oncia was also used in the construction of this facet of the instrument and this, in turn, again points to Urbino being the centre in which the instrument was designed and built.

 

 

Section 0‑18 – The implications of the compass of RCM0001 to our understanding of Medieval music and to our understanding of other instruments built during this period.

          What can we learn from the features discovered above about the music that was played on this instrument in the mid-fifteenth century?  Unfortunately the author is not the best person to answer this question[98], although it is hoped, in the discussion below, that a satisfactory attempt to find a solution to this question helps us along the road to the discovery of some of the answers.  The whole discussion can, however, at least be explained partly by the excellent work done by Mark Lindley.  His most relevant paper deals in some detail with the situation between 1400 and about 1520.[99]  Lindley makes the cogent point that, in the period around 1400, Pythagorean tuning with pure fifths and with some almost-pure major thirds would have been the ‘default’ tuning system.  This means that, in a total of 5 tonalities - ie. in the ‘home’ key and in key signatures 2 whole steps on either side of ‘home’ – all of the intervals encountered when playing the music would have been, essentially, pure and totally harmonious in a way that is never encountered today when playing music of any period.  In equal temperament, with major thirds that are about 14 cents wider than pure (and therefore quite out of tune), the tuning is much worse for these intervals, at least, than Pythagorean intonation where the intervals are either pure or are only about 7 cents away from being pure.  Modulating any further than this gives rise to major thirds that are out of tune by the syntonic comma = about 21.5 cents – an interval that is harshly out of tune, and which would be recognised as such by even an ear with no musical training whatsoever.  Put simply, this interval is excruciatingly out of tune!

          But, during this early period, this tuning system was the norm:  it had pure fifths and major thirds that were only 7 cents out of tune (compared to 17 cents out of tune in ‘normal’ equal temperament).  By the time of the composition of the later music of the Renaissance, the situation had changed totally.  The major triad in meantone tuning which had pure major thirds, instead of the pure fifths of Pythagorean intonation with only 2 pure major thirds, had become the normal type of tuning.  Lindley further makes the point that it was only in the period from about 1480 to 1520, and so somewhat after the estimated date of construction of this instrument, that the playing of major triads was considered to be a useful feature of musical instruments (particularly keyboard instruments) by the theorists and musicians of the time.  This means that, for example, the early organs of the members of the famous Italian Antegnati family, and of the other Italian organ builders working in the period from about 1480 to 1520, were almost certainly still tuned in Pythagorean intonation rather than in meantone temperament.[100]  This feature is something that seems to be totally unrecognised by modern organists, organ tuners and organ builders.

          It will be shown below – based on the same conclusions reached by many others – that the clavichord seen in the intarsia (1476) of the studiolo of Federico da Montefeltro in Urbino (see Figure 46 on page 103 and Figure 47 on page 115 below) can only have been tuned in Pythagorean intonation.  So it seems equally clear that the even-earlier Lorenzo da Prato organ (1471-75) in the cathedral of San Petronio in Bologna, one of the few playable organs surviving from this period, was almost certainly tuned in Pythagorean intonation, at least at the beginning of its playing career.  This extraordinary organ still retains its original keyboard, and also has exactly the same F,G,A to f3 compass as the intarsia clavichord.[101]  Unfortunately, presumably for the practical reasons imposed by the later church liturgy and church music, it is no longer tuned in Pythagorean intonation with the many pure intervals that this tuning provides (see footnote 100 below), and which is musically pleasing when sounded by the undying note of the pipes of an organ.

 

 

Section 0‑19 – The string scalings of the RCM0001 clavicytherium. 

          The RCM catalogue lists the scalings of the lowest notes of the RCM0001 clavicytherium, and of the c and f notes higher up in the compass.  But unfortunately the lengths of none of the intermediate notes is given in the catalogue.[102]  This means, for this instrument, that its most important and characteristic features are disguised and cover up the face of the true nature of this instrument.  However, as mentioned above, a digital drawing has been published by the RCM, from which the scalings of all of the notes can be read.[103]  These have been measured and are given below in Table 4, in both millimetres and also converted into units of the Urbino oncia (the length of the Urbino oncia as used in the RCM clavicytherium will be determined below to a high accuracy).  The reason for the use of the Urbino oncia is, of course, because the instrument has been claimed here to have been made in Urbino.  If the instrument was actually made in Urbino, then its scaling design should be capable of being expressed in simple numbers of the known length of the Urbino oncia during the historical period.  The scalings of this instrument is one of the most important aspects of the design and properties of this instrument that needs to be investigated here.

 

Table 4 – The string lengths (measured from the digital version of the RCM drawing made by William Debenham) in mm and in putative units of the Urbino oncia.[104]

Anonymous clavicytherium, Urbino, c.1471.

Royal College of Music, London, Cat. No. RCM0001.

 

A semi-logarithmic graph of the measured string scalings.

          The string lengths from Table 4 above are plotted in the graph seen in Figure 37 below.  This graph has a logarithmic vertical scale (y-axis) with a normal linear horizontal (x-axis) scale.[105]  This means that any series of lengths that produces a plot that is a straight line here represents, mathematically, a logarithmic function where each point on the graph is determined by multiplying (or dividing) the value of the previous point by a constant factor.  One such common factor is  = 1.0594631…, which is just the factor that is the basis of Pythagorean scalings that double (are multiplied by 2) every 12 notes.  This is the normal factor used in the design of the treble scalings of most 16th-, 17th- and 18th-century stringed-keyboard instruments (but not as we will see below, of the instruments studied here and in Chapter 4 below).  It is also the natural progression of the lengths of the pipes in an organ tuned in normal equal temperament.  The open question, at the root of this discussion, is therefore: “What are the multiplication or reduction coefficients that were used in the stringing design of the RCM0001 clavicytherium?”.

          The graph of Figure 37 gives the arbitrarily assigned played note along the linear bottom x-axis.  But it will be shown below that the instrument must have been designed for stringing with brass wire and tuned to sound at R + 5, a fifth above ‘normal’ pitch R.  Therefore the top x-axis is also labelled according to the sounded pitch, a fifth above the pitch indicated by the played notes plotted along the bottom axis.

          The thicker lines on the graph of the string lengths of Figure 37 are those that are given by fitting the string lengths which have been subjected to a normal linear-regression analysis.  This therefore represents the fitted scalings calculated from the measured scalings.  The thin line represents Pythagorean scalings based on tenor g = 515.9mm.  Clearly, the scalings are Pythagorean in nature (ie. they double in length going from treble to bass, every 12 notes) in the restricted part of the compass from tenor g downwards towards the bass until about the note d, a fourth lower.  Above the note tenor g, the scalings follow a different straight line but, because the points representing the string scalings here form a straight line on a logarithmic scale, they are indeed logarithmic, but are not Pythagorean in nature.

          Such a design with only a small section of the scalings with Pythagorean scalings is very unusual in the field of early stringed-keyboard instruments design.

Because it is unusual to have non-Pythagorean scalings incorporated into the design of an instrument with scalings which are, on the other hand, logarithmic, the concept of the multiplication/reduction coefficient used to calculate such a scaling design has been introduced here.  In the two upper octaves of the string-scaling design, the logarithms of the values of the string lengths from g to g2 were fitted to a straight line using the usual linear-regression analysis.  The result of the linear-regression analysis then gives the best possible straight line that connects these points together, and which therefore best represents the measured points graphically.  The linear regression process, by definition, minimises the distances of all of the points, taken together, from the straight line and, in the process, calculates the best-fit value of the slope of that line.  The slope of the line plotting the logarithm of the string lengths from g to g2, calculated by the linear-regression analysis, is m = -0.02082 ± 0.3% (the slope is negative because the line follows the points whose lengths are decreasing as the pitch rises).  The ratios of the lengths of successive notes is therefore antilog(-0.02082) = 0.953185 (see Table 5 on page 88 below for some common multiplication and reduction coefficients used in the design of some of the stringed-keyboard instruments encountered during the course of the study carried out in this book).  The regression coefficient, giving the goodness-of-fit of the points to this calculated line, is 0.99987[106], a number very close to 1, and this therefore gives us a high level of confidence that the points do follow the theoretical model.  This calculated reduction coefficient Rf can be compared with a multiplication coefficient Mf corresponding to a doubling in length every 14 notes (rather than with octave doubling every 12 notes, which is characteristic of a design which has Pythagorean scalings).  The exact mathematical ratio of octave doubling every 14 notes is just Mf  =  = 1.05076[107] and the corresponding reduction coefficient Rf is 1/1.05076 = 0.951695.  The difference between this hypothetical value (= 0.951695) and the value of the slope calculated here by the linear-regression analysis (= 0.953185) amounts to only 0.15%.[108] This difference is so small that the two values can be considered to be identical with the difference explained easily by the errors introduced through the inaccuracy of the measurement process (mostly by the author!).  In other words we have a high confidence that this is the value of Rf used by the designer and maker of RCM0001 and that this is the reduction coefficient used to design the treble scalings of this instrument in the top two octaves of the compass from g to g2. 

          This is therefore a good indicator that the note-on-note reduction in the length of the top two octaves of strings used by the person who designed this instrument is, in fact, a reduction in the length by the factor 1/ = 1/1.05076 = 0.951695.[109]  Indeed, multiplying the length of a given note in this range by this factor, gives a length that is very close to the measured length of the next higher note.  This amounts to a strong suggestion that the string lengths do not follow the normal progression found in instruments with Pythagorean scalings of 1/ = 1/1.0594631 = 0.943874   , and therefore that a different multiplication/division factor was used by the designer of this instrument, namely 1/ = 1/1.05076 = 0.951695.

          The use of this unusual factor (= in this 15th-century instrument, is clearly not the normal way of designing the treble scalings of a stringed-keyboard instrument in the manner that we would usually encounter during the period from the sixteenth-century and later.  The reader is therefore asked to make careful note of the fact that here, the treble strings do not have Pythagorean scalings and therefore do not double in length with each octave drop in pitch.  In the later period the use of Pythagorean scalings with a reduction coefficient which gives string lengths that double every octave = every 12 notes, is almost universal.  The equivalent reduction coefficient is 1/ = 1/1.059463 = 0.943874.  However, the close agreement between the design values and the actual values of these features gives real assurance that the two are, effectively, the same.

Figure 37 – A graph of the measured string scalings, based on the length of oncia used in Urbino at the time = 29.48mm.

Anonymous clavicytherium, Urbino, c.1471.

Royal College of Music, London, Cat. No. RCM0001.

 

 

Section 0‑20 – Do the string scalings of the present design of the RCM0001 clavicytherium incorporate a simpler, prototype design? 

          The analysis presented below seems to make it highly likely that the design function of the lengths of the strings that we now find in the scaling pattern of RCM0001 is, in fact, of importance in an even more basic and fundamental way, that has been hinted at, but without so far discussing the implications of such a basic underlying design.  We can see that if the Pythagorean length-reduction ratio is used to calculate what the lengths of the lower strings would be assuming Pythagorean scalings from tenor g all the way down to Γ-ut, rather than only down to tenor cT, we get a startling result.  In this case such a prototype design would produce a length for Γ-ut, an octave below tenor g, of twice the length of tenor g, and so it would have a length of 2 x 17½ Urbino once = 35 Urbino once.  It cannot be only a coincidence that the length of the bottom string of the RCM clavicytherium is 1036½mm = 35.1 Urbino once, and so an amount that is very close to this value (error = 0.45%)  This value is, to within the errors of the measurements carried out here, very close to 35 Urbino once.  To try to understand this tdhe author makes the suggestion that the present scaling-design of this clavicytherium is the ‘developed’ model of an earlier prototype design that had a compass of only three octaves from Γ-ut to g2, but with no notes and keylevers below Γ-ut.  With a bottom string of length 35 Urbino once and Pythagorean scalings from Γ-ut up to tenor g, and then with scalings with a geometric design and a length reduction coefficient of 1/ above tenor g, it would have been exactly the same instrument as the one with the scalings given in the graph of Figure 38 below.[110]

          Seen from a mathematical point of view, the simplicity of such a design is remarkable!  What is also remarkable is that, in Federico’s “Court Matematica”, where classical Greek theory was held in such high esteem, the treble scalings do not follow the rule of the highly-regarded Greek mathematician Pythagoras where the string lengths halve with each octave rise in pitch (as was to be the string-scaling rule in the following centuries of string-scaling design). 

Clearly it was more important to the polymaths in Federico’s Court that the strings should be designed be tuned to within a hair’s breadth of breaking, so that they then had accurately-tuned harmonics, and a correspondingly musical sound.

 To the author’s knowledge, this principle was not followed in any stringed-keyboard instrument designed and built in the following centuries – other than that for the exceptionally fine Ca’ Rezzonico harpsichord studied below in Chapter 6 on page 150 – but which was also designed and built in Urbino.

          This is but another example of the brilliance and sophistication of the scholars, polymaths and makers working in Federico’s Court around the middle of the fifteenth century.  These brilliant design features seem somehow to have continued on in Urbino at least until 1710 at the beginning of the 18th century in at least one other Urbino plucked keyboard instrument (see Chapter 6 on page 150 below for more details).  In the author’s view the principles used in Urbino have not been surpassed by any of the countless makers active in the subsequent centuries. 

          This is but one example of the importance of the incredible design and the mathematical discipline of the scholars, artists, craftsmen, and the exceptional polymaths who inhabited the Court of Federico da Montefeltro in Urbino. 

Figure 38 – A graph of the putative design scalings of a prototype ‘ancestor’ of RCM0001, which is based on a design with Pythagorean scalings for the lowest octave of strings from Γ-ut to tenor g using a Pythagorean length reduction ratio of 1/ (ie. ), and then with a change to geometric scalings in the two top octaves which diminish note by note by a factor of 1/ .

Based on the anonymous clavicytherium, Urbino, c.1471.

Royal College of Music, London, Cat. No. RCM0001.

 

 

           Clearly the string scalings of the prototype clavicytherium must have been based on a length for Γ, the lowest note in the compass, and the lowest note in the Guidonian scale, of exactly 35 Urbino once = 1031.8mm.  This seems to be valid at least up to the note tenor g, an octave higher than the initial note Г-ut.  Here, in the bass octave from Γ-ut up to tenor g, the prototype clavicytherium was designed to use string lengths calculated on the basis of a normal Pythagorean reduction ratio of 1/ = 1.0594631, and therefore the same factor used in the subsequent centuries of stringed-keyboard-instrument design.  It is felt that it is no coincidence that this corresponds to notes encompassing the octave from Γ-ut (the fundamental note of the old Guidonian scale) up to tenor g, exactly an octave higher. 

          Following on from this in the design, the string lengths of the top two octaves of the prototype clavicytherium are designed beginning with the length of tenor g = ½ x 35 once = 17½ once.  This involved a change in the design of this upper portion of the compass based on non-Pythagorean geometric scalings for the top two octaves from tenor g to the top note g2.  These string scalings are generated by the considerably greater multiplication/division factor of 1/ = 1/1.05076 are therefore all shorter that those generated by a normal 1/ multiplication ratio.  The reader may wish to compare the scalings plotted here in Figure 38 with those of the present, extant instrument seen in Figure 37 above.  It will then be clear that the scaling design of the proposed prototype clavicytherium with the scalings seen in Figure 38 is very closely related to the scalings of the actual instrument whose scalings are given in Table 4 on page 77 above. 

          Such a prototype ‘ancestor’ of RCM0001 would be different only in lacking the three bottom keylevers and notes of the early short-octave arrangement.  The effect on the design of adding the 3 bottom keys and keylevers was to carry over the length of the bottom string from the role it played as the Γ-ut in the 3-octave prototype clavicytherium seen in Figure 38 on page 77, to becoming the bottom note Ψ1 of the new design of the present instrument still with a compass of Γ-ut to g2, but with the three additional bottom notes Ψ1, Ψ2 and Ψ3.  RCM0001 is therefore a kind of first step in the history of string-scaling design, which progresses from the simple prototype model seen in Figure 38 above, to the present design seen in Figure 37 on page 74 above.  But the important question is: “Is it just a coincidence that the numbers found for the suggested prototype instrument fit the present design so neatly?”. 

          It would be a remarkable coincidence if this were in fact true, but this possibility points to the need to try to find some other aspect of the design of RCM0001 that points to an antecedent of the original design, and which shows conclusively that the design seen in Figure 38 below is a prototype of the present state of the instrument, and not just a tidy coincidence. 

          Because the design of the lateral spacing of the bridge and nut pins, although perhaps not as obvious as the design of the string scalings, is actually as much a part of the overall design process of any harpsichord or clavicytherium builder, as are the string scalings.  Therefore the lateral spacing of the bridge- and nut-pins were recorded by taking the measurements of their distances from the spine using the digital version of the RCM0001 drawing by William Debenham.  These measurements are given in Table 24 of Appendix 12 on page 213 below.  As explained in Appendix 12, the positions of each of the bridge and nut pins of the RCM0001 were measured out from the position of the inside of the long vertical spine side of the instrument.  These measurements are shown in the appendix in Table 24 on page 213.  The row highlighted in green in Table 24 indicates the transition note from the top two octaves of the treble-scaling design with a geometric scaling progression using a reduction factor of 1/ = 1/1.05076, to the more usual Pythagorean reduction factor of Rf =  =  = 0.9438743 in the tenor/bass.  The latter scaling design could easily be calculated without the use of logarithms to a high degree of accuracy (error = 0.06%), using a simple geometric scaling-reduction factor of  = 0.944444, instead of the exact factor just calculated above of 0.9438743.  The difference between the two is only a tiny 0.060%.  This is only one possible way that the mathematicians at Federico’s Court, who lacked knowledge of logarithms, might have calculated the string scalings in the part of the compass from d to g1 that used this scaling-reduction factor.  

          In order to try to discover another element of the design of the RCM clavicytherium, the lateral positions of the bridge pins and the nut pins were measured and are given in Table 24 on page 213.  These measurements are plotted in the graph of  Figure 39 below.

 

          Several things become clear when the lateral positions of the bridge- and nut-pins from Table 24 on page 213 are plotted as shown in Figure 39 above.  The nut-pin positions plotted with the fitted black line, black points and black triangles clearly all lie on the same straight line except for the four bottom notes.  This means simply that, for the notes above Г-ut in the present design, the nut pins all have the same regular spacing relative to one another throughout the whole of the compass of the instrument except for the bottom four notes.  The bridge-pin positions, on the other hand, are somewhat more complicated in their design structure, as revealed by Figure 39 above.  Again, the four bottom notes are clearly exceptional in their spacings and do not belong to the grouping of the other bridge-pin positions higher up in the compass.  But it is very important to note that the spacings of these four bottom notes belong to a different scheme from all of the others as well.  Above the four bottom strings, the spacing of the bridge pins is then divided into two simple sections above ГT.  The notes between ГT and g1 can be all be plotted on a single straight line indicating that these notes all have the same regular spacing with the same geometric multiplication factor.  But the plot of the notes from g1 to g2 yields a different straight line with a different slope – and therefore a different lateral spacing and multiplication factor.  This indicates clearly that the note g1 was a fundamental design note since both the string-scaling design and the lateral pin-spacing design both change at this note.

          The graph of Figure 39 above indicates that there is a notable difference in the lateral positions of the bridge and nut pins across the compass of the clavicytherium.  Basically it is the difference in the horizontal positions of the bridge-pin and nut-pin positions that are plotted on this graph for the same note.  To calculate this difference, the points on the two sections of the lines for the bridge-pin position seen in Figure 39 were each fitted separately to their own straight lines, and the difference between these and the fitted nut positions was calculated.  The fitted lateral positions of the nut and bridge pins are given in Table 25 seen in Appendix 13 on page 214.  These differences are plotted below in Figure 40. 

 

Figure 40 – The difference between the lateral positions of the nut- and bridge-pins calculated using the measurements from Appendix 12 on page 213 below, which have been fitted to straight lines using the normal linear-regression analysis.

The anonymous clavicytherium, Urbino, c.1471.

Royal College of Music, London, Cat. No. RCM0001.

 

           Figure 40 above demonstrates a number of prominent features which should be noted by the reader, and which characterise the design of the nut- and bridge-pin positions of the RCM clavicytherium:

1.         In all cases the nut pins are further from the spine than the bridge pins.  This means that the calculated differences in the positions yield negative results in all cases.  It also means that none of the strings in the clavicytherium is parallel to the long vertical side of the instrument and that, in fact, the strings all lean away from the spine at their top ends when looking at the instrument from the front.  From this position of the observer, the upper ends of the strings at the bridge are all further from the spine than they are at the nut.  However, it should be noted that these differences are small and amount to differences in the positioning of the bridge and nut pins of only about 2.5mm (for g2), or to about 8mm for g1.

2.         The bottom four notes Ψ1, Ψ2, Ψ3 and Г all belong together and they all have lateral spacings that do not belong to either of the two regular patterns of the notes from ГT and above.  This will be discussed further below.

3.         Above Гut the bridge-pin position starts from a point about 6.3mm further from the vertical spine side than the nut pin, and then the difference between the bridge- and nut-pin positions gradually increases (negatively) until it reaches a value of about 7.5mm.  It would appear therefore, from the plot of the differences in the nut- and bridge-pin positions that, for g1, there are two differences between the nut and bridge positions, and that these are about 0.66mm apart!  This, physically, is clearly impossible! 

4.         The two points indicated as being 0.66mm apart are, instead, the result of the accuracy and refinement of the linear regression analyses used in this investigation.  It seems clear that, only through the use of the sophisticated and accurate linear-regression analysis, could this small difference be calculated.  The fitted points from ГT to g1 (including g1) were calculated by subjecting the measured values in this range to a linear-regression analysis.  This results in the calculation of a difference between the bridge and nut pins for g2 of close to -7.50mm.  Then, in an entirely separate linear-regression analysis, the points from g1 to g2 were fitted using a second linear-regression analysis of exactly the same type.  However, this calculation yields a different value of about 8.20mm between the measurements of the same physical quantities.  Graphically, this results in a ‘dislocation’ between these two points of -0.66mm (see Figure 40 above).  It needs to be added that the situation that has arisen here is quite common in this type of analysis.  It is a process that has been carried out by the author many times before.  This feature seems to be the result of a ‘slippage’ or misalignment of the marking-out sticks used to locate the positions the two sets of pins when the maker moved from marking out the pins below g1 to marking out the pins above g1, probably with a different marking-out stick for each section of the compass.  Having carried out this type of analysis many times in the past, what has been found particularly interesting about the ‘slippage’ between the marking out of the tenor section of the bridge and nut, and the treble section, is that the ‘slippage’ for this instrument amounts to no more than 0.66mm, and so is a very small amount indeed.  The important feature of the linear-regression analysis here is that, because of the high accuracy of the results of this analysis, it reveals even such a small discrepancy as this.  And this, in turn, points out the importance and usefulness of carrying out a linear-regression analysis on the measurements in order to determine their physical size and to establish their mathematical foundation.

Section ‑ 0‑21 – The design pitch of the RCM0001 clavicytherium.

          As was seen above, the “design note” of this instrument, which is at the root of both the Pythagorean scalings in the tenor part of the compass and of the geometric treble scalings, is the note tenor g.  The length of the string for tenor g using the linear-regression analysis is calculated to be 517.2mm.  This compares with the actual measured value (see Table 4 above) of 514.6mm with a difference of only about 0.5%.  As indicated in the graph of the scalings, this has a c2-equivalent value of 192.3mm.  But this value of the scalings can be used for pitch comparisons since scalings are usually referred to the length of pitch c2.  Compared to the treble string scalings of most harpsichords designed and built after about 1600, this is very short for an instrument at ‘normal’ pitch whether it is strung in brass or in iron strings.  Indeed, such a short scaling indicates that this instrument must therefore have been designed for a pitch considerably higher than ‘normal’ Baroque pitch.  Although the remains of old strings of yellow brass are still found on the RCM0001 clavicytherium, there is no guarantee that, using this as an indication, the instrument was, in fact, originally strung with brass wire.  However, it will be shown here that it is highly likely that brass was indeed the original stringing material. 

          N.B.:  But it is even possible that the remaining strings are in fact, original to the second altered state, and that they date from this initial alteration of the instrument.  They therefore need to be treated very carefully indeed, and to be preserved along with (and ideally left on) the instrument as survivors of the greatest rarity and antiquity.  The reason for this is that it is not just the fact that the strings have survived this extremely long period, but also important is their critical role in calculating the notes the strings actually sounded.  As organological documents these string remnants are of the highest organological importance!  Their diameter should be measured in some non-interactive way so that absolutely nothing happens to what remains of these precious strings.

          It is to be noted further here that the c2-equivalent of g2 at a pitch a fifth higher than ‘normal’ Baroque pitch would be 192.3mm x 3/2 =290.3mm.  This value would be a perfectly normal c2-equivalent scaling for a stringing scheme using ordinary yellow-brass wire tuned to ‘normal’ Baroque pitch, where a1 is about 415 Hz.  The significance of this is that it makes it very likely that the instrument was, indeed, designed to sound and play at a pitch a fifth higher than ‘normal’, and that it was designed to be strung with strings of ordinary yellow brass wire! 

          In this situation, the strings in the part of the compass from tenor g to the top note g2 all have lengths with c2-equivalents that are greater than the notes below tenor g.  Below tenor g the strings have a constant c2-equivalent scaling, with ‘normal’ Pythagorean scalings which have lengths based on the length of the string for the note tenor g.  But from tenor g up to g2, the strings would all be subject to an ‘excess’ tension that would put them closer and closer to their breaking point the further one goes into the treble part of the compass.  Therefore, because the multiplication factor in this part of the compass is greater than . = 1.0594631 (which is the normal multiplication factor for a design with Pythagorean scalings) the strings in this part of the compass, if they all had uniform properties, would all be equally close to breaking.  

          This is clearly not the case for the design of the RCM0001 clavicytherium!  However, to compensate for this and to overcome any real danger of string breakages here, a particular property of the string-drawing process was invoked and taken carefully into account in the design of the instrument by the polymath designers of the instrument.  It is well known that the work-hardening produced when wire is drawn down to smaller and smaller diameters gives the finer gauges of wire an increased strength with a corresponding decreased likelihood of breaking.  Because of this work hardening, the strings would break at a higher and higher pitch, the more the strings are drawn down to finer and finer gauges.[111]  The strings in this region are said to be stretched, with those nearer the top of the compass here being stretched more than those near the note tenor g.  These fine treble strings at the top of the compass therefore need to be physically stronger (which they are because of work-hardening), they have a slightly higher mass-density, the material itself is harder, and consequently it has a higher breaking point. 

          In order to test the author’s hypothesis that brass could, in practice, be used at this pitch, a simple wire-breaking experiment was carried out to show that the tensile pickup[112] of the small-diameter yellow brass wire that is held in the author’s workshop, could withstand this ‘extra’ tension without the string breaking.  Using wire of diameter 0.19mm[113], with a length of close to 160mm (see Figure 38 on page 77 above) it was found that, although it initially stretched repeatedly, after a time the wire stabilised and held its pitch at the equivalent of well above R + 5, without any breakages at all.  Therefore, a design of this instrument when strung in brass and tuned to a pitch a fifth high relative to ‘normal’ baroque pitch, seems both possible and useful.  The great practical advantage of this design arises because of the quality and power it gives to the sound.  The power (the energy produced per second) is greater the greater the tension is:  if the tension is doubled, the energy radiated by the string is quadrupled.  Therefore the power is increased considerably the higher is the string tension. 

          It is not clear whether the designers of RCM0001 were aiming to increase the power of the sound in the treble, but ‘stretching’ the strings for these top notes did have two clear results:

1.       by increasing the c2-equivalent scalings of the top treble strings somewhat, the power of the sound they produced was certainly greater than it would have been over the continued use of Pythagorean scalings all the way to the top note.  The stringed-keyboard instruments made during the later periods (ie. after about 1520) seem not to have appreciated the advantages of ‘stretching’ the treble scalings.  Instead they adhered rigidly to the principles of an exact doubling in length with each octave rise in pitch as first laid out in classical Greek theory by Pythagoras. 

2.       the other crucial factor that would be affected by ‘stretching’ the strings in this way is the effect it would have on the quality of the sound produced by the strings.  The overtone structure of a string is strongly affected by its stiffness and this, in turn, is affected by the material composition of the string.  The thinner and softer the material of the string, the closer the harmonics of the sound produced by the string will be to a pure harmonic series and, as a result, the more musical the note produced would sound.  Therefore the harmonics of the strings in the extreme treble of RCM0001 would have much more accurately-tuned harmonics, and would therefore produce a sound with a more musical character than if the string scalings had followed a Pythagorean progression and were subject to a lower tension.

          The top strings of RCM0001 would have to be quite thin in order to be strong enough to withstand the ‘excess’ tension of its scaling design.  However, the top notes of this clavicytherium design would produce a series of very well-tuned harmonics with a resulting pleasingly musical sound and the sound would have been more powerful than it would have been with the continued use of a regular Pythagorean brass-wire design.  As will be seen in the next section, RCM0001 would almost certainly have been tuned using Pythagorean intonation with pure fifths and almost pure major thirds in those keys that were possible to play in this tuning system.  The combination of the pure fifths and almost-pure thirds of Pythagorean intonation resulting from the accuracy of the tuning of the harmonics of the strings, would have produced a sound that was superbly musical and extremely pleasing to the Western ear.[114] 

          The purity of this sound resulting from this design cannot have been matched by any stringed-keyboard instrument designed and built during the succeeding period of some 570 years! 

The later instruments virtually all used Pythagorean scalings right up to the top note, and therefore the top strings were not subjected to the same ‘excess’ stress of the top strings in the design by the brilliant mathematicians working in Federico’s Court!  These later instruments would therefore not have produced a sound with such accurately-tuned, and therefore highly musical, harmonics.

          It is well known that the typical c2-equivalent scalings of brass wire in Flemish instruments is about 11½ Flemish duimen = 293.4mm for the instruments built in the Flemish tradition.[115]  However, the instruments of Gianfrancesco Antegnati are the subject of a new book by the author entitled Gianfrancesco Antegnati, Arpichordaro.[116]  Typical brass and iron scalings, and typical pitches are given in this work for the designs used in Gianfrancesco Antegnati’s instruments.  As an example, an instrument by Gianfrancesco Antegnati in The Smithsonian Institution in Washington, DC, was designed with a bridge divided into two sections detached from one another, clearly with different c2-equivalent scalings on either side of the split, with brass stringing below the split and iron stringing above it.  The c2-equivalent transition scaling for the top brass string (nearest to its breaking point) is 291mm, and this is almost exactly the same value that has been used in the calculations here for the brass scalings of his instruments.  It is also the same result found by the author for the instruments of the Ruckers/Couchet family working in Antwerp.

          Taken together this is therefore in agreement with the statement by Martha Goodway and Jay Scott Odell that the properties of historical wire were essentially unchanged during most of the historical period,[117] and that consequently the same principles of scalings and stringing could be used across the whole of the historical time-span going right back into the late-Gothic period.  This is illustrated clearly by the calculations of the scalings of the RCM clavicytherium.  It goes without saying that many of the results presented here rely heavily on the excellent scientific work of Goodway and Odell.

          A rough un-weighted average of the two brass c2 scalings for the Italian and Flemish instruments is about 292mm.  Comparing this to the c2-equivalent scaling of the RCM0001 clavicytherium of 192.3mm gives a ratio:

length ratio =  = 1.51 ≈ 1.500 =

          The ratio  is, of course, the ratio of the frequencies, or the inverse ratio of the lengths, struck by a monochord to give notes a pure fifth apart.  Because of this close correspondence between 1.51 and 1.50 (error = about 0.7%), there seems to be no other possible material choice or pitch level than that of stringing the RCM clavicytherium in brass wire at a pitch a fifth higher than ‘normal’.  In other words, it is at the same pitch as the R+5 quint virginals made by the Ruckers family, and their Antwerp contemporaries.[118]  The close relationship between the factors involved in the RCM0001 clavicytherium and normal-pitch stringing practice for the well-documented Flemish keyboard instruments leads to this conclusion for both the pitch and for the stringing material of the RCM0001 clavicytherium.

          So what were the factors that led the designer/maker(s) of the RCM clavicytherium to conceive of such an elegant and highly-pleasing design?  It is particularly important to the acoustical properties of a string that it should be held at maximum tension very close to its breaking point, since holding it at this tension would result in a beautifully-musical sound with accurately-tuned harmonics.  The notes of this instrument subjected to this tension, with each string producing its own perfectly-tuned individual major chord, would sound very satisfying to the Western ear.  It is a well-established physical fact that, for a string of a given diameter, the greater the tension in the string, the closer the frequencies of the harmonics making up the partial sounds of the strings are to exact integral multiples of the frequency of the fundamental note.  This means that the most prominent lowest 5 partials of each note would be almost perfectly in tune with one another and with the fundamental note being produced by the string.  They would, effectively, each form a major chord with the fundamental note as the root of the chord.  The ‘Western ear’ recognises this as a harmonious, pleasing, and as a very musical sound. 

          This therefore leads to the inevitable conclusion that brass is the only choice as a stringing material for the RCM0001 clavicytherium at a pitch of R+5, the same pitch as the Ruckers/Couchet virginals of length 4 Flemish voeten (feet).  And this, in turn, suggests that the Ruckers 4 voet virginals could be thought of as the descendants of a tradition that can trace its lineage back some 200 years earlier than the Ruckers tradition to instruments like the RCM0001 clavicytherium and to those stringed-keyboard instruments depicted in the studiolo intarsias in the Palazzo Ducale of Federico da Montefeltro in Urbino, which will be discussed here in the next chapter. 

 Note:

          I, personally, would dearly love to hear an accurately-made version of RCM0001[119], strung with ordinary ‘soft’ brass wire and tuned to a pitch of R + 5, a fifth above ‘normal’ Baroque pitch.  It would be an easy task to tune the ‘copy’ that the RCM already holds to a pitch a fifth above ‘normal’ Baroque pitch, and to string the copy in normal brass wire, and to tune it in Pythagorean intonation with pure fifths and (almost) pure major and minor thirds in 5 different tonalities.  It would then have a wonderfully pleasing and musical sound[120].  The strings would all be critically stressed and would have very pure harmonics that would all be accurately in tune with the fundamental note of each of the other strings.  And the lower harmonics of each string would form, in themselves, a major chord with accurately-tuned harmonics.  Such an instrument, tuned to this pitch would fully represent the intentions of the original Urbino polymath makers, and give the deserved credit to those instrument designers and mathematicians working in Federico’s Court in the second quarter of the fourteenth century – some 570 years ago now!

          What is utterly amazing about this design is that the makers and designers of this instrument seemed to understand all of the important principles of stringed-keyboard instrument design used by the makers of such instruments in the subsequent 570 years, and thus taking us right up to the present day.  Some of the principles found in this one instrument are the following:

1.           the designers realised that the strings sounded best when they were stretched to a point just below their breaking point.  At this tension the harmonics of the sound being produced would be accurate whole-number multiples of the fundamental frequency of the string.  Each string therefore, in addition to producing its primary fundamental note, would produce an accurately-tuned octave, octave and a fifth, double-octave, double-octave and a major third, double-octave and a fifth, etc.  So, in effect, each string had lower harmonics that were producing their own accurately-tuned major chord, which combined musically with the other strings – also each producing its own major chord – and all in perfect harmony with one another!

2.           The designers realised that the strings needed to be angled away from the case sides so that the ends of the bridge(s) would be as far away from the case sides and liners, and would therefore be as free to vibrate and to radiate the combined string vibrations, bridge vibrations and soundboard vibrations as much as possible.  This feature is seen in virtually all later instruments made during the historical period.

3.           These early designers and makers certainly seemed to have realised that the higher the tension in the strings, the greater would be the power produced by the strings, and the louder the sound of the instrument would be.  One of the easiest ways to ensure a high tension in the strings was to give them a length as long as possible, without, of course, the risk of breaking being too high.  This they did with a mathematical precision and sophistication not equalled in the subsequent period of some 570 years.

4.           Perhaps the most astounding feature of the design of this clavicytherium – and of the intarsia clavichord that will be studied in the next chapter – is that the breaking strengths of the strings in such instruments, although one instrument uses brass as the treble stringing material, and the other uses iron, all of the strings were tuned to a point just below the breaking point of the material used in their stringing.  The two stringing materials, had different ultimate breaking strengths because of the difference in the materials used in these two metals.  But for both materials, the variable amount of work-hardening introduced when the wire was drawn down to smaller and smaller diameters was utilised as a part of the design features of the instruments to produce the best possible sound quality (and quantity!) in each case.  It is clear from the geometric treble scalings that were given to these instruments that the designers/makers understood the properties of the strings to such an extent that they abandoned classical Greek theory and incorporated a design in the clavicytherium and intarsia clavichord that took into account the work-hardening contributing to the actual physical properties of the wire instead.

          All of the above factors point clearly in one direction:  for the designers of these two instruments, the strings had to be at the highest tension they could bear without breaking.  And so this was the way that they were designed in both instrument types.  It is important to note that in the centuries after that in which the RCM0001 clavicytherium was designed, the simplistic design advocated by Pythagoras was used rather than the much more sophisticated, more elegant, and much more musical design principles used by the members of Federico da Montefeltro’s Corte matematica in Urbino.  Unfortunately, the use of ‘stretched’ treble string scalings seems to have died after it was developed by the polymath scholars and builders working in Urbino, and was never used again in the design of stringed-keyboard instruments until the, almost naïve multiplication ratio  = 0.948078    was used in the design of the early fortepiano.

 Section 0‑22 – The features of the RCM0001 clavicytherium that are fundamental to its stringing design:  the concept of a geometric progression, of a reduction coefficient Rf, and of a multiplication coefficient Mf.

          There is a number of features of the design of the RCM0001 clavicytherium that point to its pivotal role in our understanding of the early history of keyboard-instrument making and, perhaps more importantly, to our understanding of some of the very early history of keyboard-instrument-making design practices.  The analyses carried out here show that RCM0001 was the product of a very clear, definite and superlative design process.  The section of the scaling graph from the tenor note g down to tenor c follows the usual Pythagorean progression and, in this part of the compass, although the instrument dates from the middle of the fifteenth century, what we find here is what we have come to know and expect of keyboard-instrument design from the sixteenth century onwards.  However, the situation was totally different in the fifteenth century, just after the dawn of keyboard-instrument making design.  As seen here, the scaling from tenor g up to the top note g2 (2 octaves higher) is clearly not a Pythagorean design and does not utilise a multiplication/division factor based on . 

          Any logarithmic string-scaling design, whether Pythagorean or not, is generated by multiplying (or dividing) the length of the string of a given note by a constant factor and then repeating the same operation for the lengths of the next notes again and again.  But rather than using the word ‘logarithmic’ to describe the scaling design from tenor g up to g2, the word ‘geometric’ has been chosen to describe the scaling design in this part of the compass, thereby calling it what it is, in an attempt to make it clear that it is not a Pythagorean design.  But chiefly, this is an attempt to avoid confusion between a logarithmic Pythagorean design and any other type of logarithmic design.  The term geometric progression means that each string length is multiplied (or divided) by a constant factor Mf when calculating the length of the next string from the length of the string of the previous note.  In fact, as might be guessed, Pythagorean scalings also follow a geometric progression, where Mf is just  = 1.0594631….  .  This is a number that is straightforward enough for us to calculate now, but in the fifteenth century, mathematicians were not equipped with the necessary tools to be able to calculate this value directly using logarithms as we do today.  In order to do this with 100% accuracy then, as now, they would have had to invoke the use of logarithms.[121]  But logarithms were not invented until their use was published by Baron John Napier of Merchiston (now a suburb of southern Edinburgh) in 1614, some 160 years after the design and construction of the RCM clavicytherium. 

Figure 41 – Merchiston Tower, former home of Baron John Napier ‘of the logarithms’. 

It was probably built by Alexander Napier, the 2nd Laird of Merchiston around 1454.  It was the birthplace (in 1550) and the home of Baron John Napier, inventor of logarithms, and of the modern use of the decimal point when representing fractions. 

 

          Hence, it was not possible in 1471 – the date estimated to be close to that of the clavicytherium – to calculate an exact value for  – although the mathematicians of the time were able to calculate a very close approximation to it.  An example of a simple way to generate a good estimate of this scaling progression is illustrated here without the need to calculate an exact value for the twelfth root of 2.  A quick calculation will show that multiplying the ratio  = 1.058823 successively by itself 12 times, gives a series of values that is remarkably close to multiplying by the factor .  Indeed multiplying 18/17 by itself 12 times gives (18/17)¹² = 1.9855...  which is very close to the exact value of 2 (error of only 0.7%).  Repeated multiplication by 18/17, although laborious, was well within the capabilities of the mathematicians at Federico’s Court in Urbino, and this would have given a design that approximated very closely to what we would now call Pythagorean scalings[122].  It is almost certain that the polymaths at Federico’s Court would have been able to derive a multiplication factor that was even more accurate than this.

 

Figure 42 - The plotted string scaling of the RCM clavicytherium.

 

What is truly remarkable about the design of RCM0001 is that the string scalings from about c# in the bass/tenor register, to the top note g2 used two different scaling multiplication coefficients Mf, one from c# to g with a ‘normal’ Pythagorean multiplication factor of  = 1.0594631.  .  .  ., and a second from g to g2 with a multiplication factor of  = 1.05078… ≈  = 1.05000 (error 0.07%) – see Figure 37 on page 74 above.  Except for the clavichord going from g2 to g and studied in Chapter 4 on page 93, and the splendid harpsichord in the Ca’ Rezzonico in Venice studied in Chapter 6 on page 150, no other historical instrument-design is known to the author that uses a string-scaling design based on both Pythagorean scalings and on a simple geometrical-progression design.  The graph of Figure 37 above shows that both the Pythagorean section and the geometrical section of the scaling curves are based on the length of tenor g.  The length of the string for this note could therefore be seen to be the most fundamental design length of the whole of the instrument’s design since the lengths of virtually all of it’s strings are based on the length of this note, both above and below it.  What this means, effectively, is that the lengths of the strings for the notes above tenor g, have been calculated by the linear-regression analysis to give the best-fit value for both the multiplication coefficient and also for the length of the string for the note tenor g itself.  The latter is found to be 515.9mm, which compares to the actual length measured from the drawing and also found in the RCM0001 clavicytherium data sheet, of 512mm, a difference of only 0.8%.[123] Importantly this length is equivalent to 17½ Urbino once (1 Urbino oncia = 29.48mm[124], and 29.48mm x 17½ once = 515.9mm – see Figure 38 on page 77 above) which is, of course, just half of the extrapolated length for the Г-ut string.  The line forming the points higher in pitch than tenor g then follow a geometric length-reduction of 1/, or roughly (and close enough to be used for string-length calculations) to a value of  = 1.05000.  Both of these are confirmed to a very high level of accuracy by the linear-regression analysis.  From tenor g downward in the bass direction, there is a sudden change to a Pythagorean length-decrease with the usual multiplication factor of  = 1.0594631.. at the note tenor g.  Turning around and going towards the treble, and extending the line beyond tenor g, projects the thin line even though the scalings do not follow this extension line.  This extended line intersects pitch c2 at a length of 192.3mm which is, therefore, the c2-equivalent scaling of all of the points on the Pythagorean line including those from tenor g down to about cT.  What is of critical importance is that the two separate linear-regression analyses give (within the normal small limits of the statistical error of the regression procedure) the same length for tenor g regardless of whether the regression calculation is based on the lengths of the strings above tenor g, or below it.  The length of tenor g can therefore be thought of as the fundamental design scaling of both the Pythagorean part of the scaling curve and also as the design scaling of the separate geometric part of the scaling curve higher in pitch than tenor g.  It is therefore a fundamental scaling coefficient at the root of the design of the string lengths of the whole of the RCM clavicytherium.

As shown in the graph here (and by calculation), the result of the 1/ reduction coefficient in the part of the compass higher up in pitch than tenor g, is that the top note has a length of 157.3mm, rather than the Pythagorean length which would have amounted to 129.0mm.  This means that the scalings have been ‘stretched’ by about 28.3mmm for the top note g2.  Thus, with geometric scalings above tenor g decreasing by 1/, the string for the top note g2 is, effectively, at a tension which amounts to an effective pitch increase of about 343 cents higher than its ‘natural’ tension would have been if the scaling design had continued on with Pythagorean scalings up to g2 (this amounts to the strings having to be able to withstand a pitch roughly half-way between a major and a minor third compared to scalings with a normal Pythagorean multiplication factor).[125] As explained above, the ‘stretching’ of the treble scalings in such a situation is possible only because the smaller treble string diameters of wire, having been deformed more by successive drawing steps through the drawing plate, have become work-hardened, and are therefore stronger. 

          From this graph it can be seen that the treble scalings are longer than those of ‘normal’ Pythagorean scalings because the strings are designed so that each of the strings of the higher two octaves are more than half the length of the note an octave below.  Most historical and modern pianos actually also have slightly ‘stretched’ treble scalings in a manner similar in nature to those seen above, but not usually with such a large length-reduction coefficient.  The most common ‘stretching’ factor in most historical and modern pianos is such that the strings double in length every 13 notes instead of every 12.  In these instruments the reduction ratio is therefore  = 0.948078, based on scalings that halve every 13 notes.  One of the most sophisticated modern scaling designs that has been encountered by the author is that of Julius Blüthner, Leipzig, in the pre-war pianos made by his firm.  These use scalings individually adapted to the strength of the wire manufactured in Leipzig especially for Blüthner’s pianos.[126]  These have shown that the design used by Blüthner resulted in a reduction coefficient R that gave scalings that reduce in length by a factor of ⅓ every 20 notes so that the reduction coefficient is  = 0.946551.

 

Table 5 – The calculation of the exact values of some common reduction and multiplication coefficients for Pythagorean, and for some ‘stretched’ string-scaling designs used in some historical keyboard instruments.

 

           Table 5 above shows some common reduction coefficients Rf, and multiplication coefficients Mf, for some of the most interesting treble string-scaling designs used in various historical stringed-keyboard instruments.  The multiplication coefficients Mf are just the reciprocal of the reductions factors Rf, and their values decrease slightly for every step down the table.  This shows that, as the reduction coefficient increases, (or the multiplication coefficient decreases) the more intense is the reduction in the string lengths for the top treble strings.  Clearly of those given here, the Pythagorean reduction is the smallest, and the reduction coefficient of the treble notes in RCM0001, which double every 14 notes, is the greatest of all.  This unusual reduction coefficient will be seen again in the analysis of the intarsia clavichord in the studiolo of the Palazzo Ducale of Federico da Montefeltro in Urbino (see Chapter 4 beginning on page 93 below), as well as in the string-scaling design of the single-manual harpsichord in the Ca’ Rezzonico in Venice which is the subject of study in Chapter 6 starting on page 150.  The fact that these factors are used in the unusual designs of these two very early keyboard instruments is one of the factors that suggests that they were both designed by the same person.

 

 Section 0‑23 – Some features of the design of RCM0001 that are also found in the designs of instruments made in the later history of stringed-keyboard instrument manufacture.

          We have seen above that RCM0001 has a number of features of its stringing design that are unique to the instrument, but that it also has some features found in stringed-keyboard instruments made in the later period of keyboard history from about 1500 to 1800.  These features are fundamental to the design of the later instruments and require that they are also studied here to get an idea of the design characteristics of RCM0001 against a background of ‘normal’ stringed-keyboard instrument design.

          The string-scaling design of RCM0001, for example, uses a scaling-design multi-plication/reduction factor to produce string scalings that we recognise as Pythagorean in nature, at least in a small part of the compass from cT to g1.  But there are also some very pragmatic features of the design of RCM0001 that are found in the later instruments as well, but that have nothing to do with the theory of string-scaling design.  One of the features of almost all later stringed-keyboard instruments of the harpsichord, virginal, spinet and clavichord type is the way the bridge-pins and nut-pins are positioned relative to the case sides at the extremes of the compass in the lowest basses and in the top treble notes.  All of the stringed-keyboard instruments seen in the long career of the author in this field, have one – usually not very obvious – feature in common in the way the bridge and nut pins are placed in the bridge and nut of the RCM clavicytherium.  It is obvious that the proximity of the ends of the bridges to the spine and cheek is detrimental to the sound of the notes at either end of the compass, as this would tend to stiffen the bridge-soundboard combination with a resulting degradation of the sound there.  The closer the bridge pins are to the spine and cheek, the closer the ends of the (very solid) bridges are to the case sides and liners, and the less soundboard space there is to allow for its free vibration in the small area between the end of the bridge(s) and the soundboard liners.  The ‘tighter’ the bridge/soundboard combination, the weaker is the amount of sound that can be radiated from the soundboard because its vibrations will be limited by the stiffness of the soundboard between the ends of the bridge and the case sides and liners.  In the instruments built in the Renaissance and Baroque period, this problem was usually resolved – at least in part – by angling the strings away from the case sides in both the extreme treble and in the lowest basses so that as much flexible soundboard could be left to vibrate freely and produce a good sound at the ends of the compass.  An obvious further improvement could be achieved by cutting away the liner near the end of the bridge so that the vibration of the soundboard would not be limited by the proximity of the end of the bridge to the cut-away soundboard liner. 

 

Section 0‑24 – The position of RCM0001 in the history of stringed-keyboard instrument manufacture.

          In the author’s view the RCM0001 clavicytherium demonstrates – in a remarkable way – the move from the old Medieval-Guidonian system that influenced both music theory, musical composition and music performance from the time of Guido d’Arezzo (991/992 – c.1033) right up to the time in which the RCM0001 instrument was built in about 1471.  This covers a period of almost 450 years.  In accordance with the Guidonian system, what would, for us, be a low G in the usual Helmholtz notation system, has been notated here as a Γ – the gamma ut. 

Clearly the RCM0001 clavicytherium can be viewed as a crucial bridge, and as a transitional instrument between medieval music and that of the Early Renaissance.  This is now, for us in a period so long after the music was composed and performed, no longer very easy to understand because it is generally difficult for us now to comprehend and appreciate medieval music.  The internet is full of ‘the oldest extant piece of keyboard music’ – played on a modern grand piano tuned in equal temperament!  These recordings tuned in this way are grossly out of tune compared to Pythagorean intonation which had musical intervals that are absolutely pure – or very close to being pure intervals.  We hear no trace in these ‘authentic’ recordings of Pythagorean intonation based on pure fifths.  Neither do we hear the occasional jarring dissonance of a Pythagorean major third in one of the tonalities that is 21½ cents out of tune and very sharp relative to a pure major third.  And it is very difficult to find a recording of medieval music without the introduction of anachronistic Baroque ornamentation.  Our understanding of medieval music is seriously hampered by these historically un-informed interpretations. 

It is therefore now very difficult for us to imagine any very early music played on an instrument like the RCM clavicytherium without re-interpreting it in the light of the later music.[128]  We don’t even hear a recording of an instrument based on RCM0001 at quint pitch, R + 5, which has been shown mathematically and scientifically to be it’s correct pitch level.  The instruments chosen for these recordings are virtually all at a pitch which results in slack strings, usually tuned a fifth lower than the design pitch intended by the designers of the instrument.  How can an instrument with the strings made of the wrong material and tuned a fifth slack, give any idea of the musical properties of this instrument?  And how would the satisfying sound of strings tuned to a pitch with strings that were within a hair’s breadth of breaking compare with what is presented as being the ‘authentic’ sound of this ‘copy’?  To the author it brings to mind the sixteenth-century statement regarding slack strings in a ‘virginall’:

The strings are slack and they ‘soundeth not aright, they are so louse and light’!

 

Section 0‑25 - The outstanding features of the design of the RCM clavicytherium

          What is most striking about the RCM clavicytherium is the incredible sophistication of its design. The separate Pythagorean 1/and the geometric 1/ sections, are interpreted here as both being parts of a logarithmic design of the scaling curve, but in a very specific way.  The maker of the instrument seems already to have grasped – probably from his experience with  the design of the postulated earlier prototype instrument suggested in Section 0‑20 on page 75 above – the fact that the large diameters of wire below the note tenor g were physically weaker, and had a lower breaking strength than those above g.  They therefore could not be put under any excess stress through a ‘stretching’ of the scale without string breakages resulting.  But the very lowest notes are even further foreshortened and are therefore well below the ‘critical tensions’ of the strings just above them in the Pythagorean section of the graph.  This is indeed the same situation that we find in the foreshortened scalings in the bass part of the compasses of most later Renaissance and Baroque instruments.  The ‘extreme’ stretching of the scale in the part of the compass of the RCM0001 clavicytherium from g to g2 implies a disregard for the theories of Pythagoras that were, however, held in such elevated regard in the later period during the Renaissance and Baroque times. 

          The criticism that the later designers could face is that they actually abandoned musicality in the form of the purity of the upper harmonics in ‘stretched’ scalings, in favour of the strict adherence to the Pythagorean principles of classical Greek theory.  The problem is that strict adherence to Pythagoras, applies only to instruments with strings all of zero stiffness.  Pythagorean scalings are found generally on virtually all of the instruments of the sixteenth, seventeenth, eighteenth, and even the early part of the nineteenth centuries.  But at the end of the eighteenth century and up to modern times, most piano makers also abandoned the octave-doubling principles of Pythagorean scaling design in favour of a design that gave both more space around the treble end of the bridge through stretching the scalings there, and it produced a sound with partials that were more accurately tuned and were therefore more musical than they would have been without the ‘stretching’ of the string scalings.  In this respect (and in a number of others as well), the design of the treble scalings in the RCM0001 clavicytherium was therefore 400 years ahead of its time although it was more than 500 years ago now.[130]

          As mentioned above, the analysis and dating of RCM0001 awaits a dendrochronological analysis of the wood of its soundboard and back that includes a determination of the centre where the wood of the instrument grew.  Until this is done, little can be said with complete security, about the place and date of its origin – even despite the reliability of the unit of measurement method.  The early history of keyboard instruments therefore awaits the results of this analysis for a definitive result.  It is now 55 years since Elizabeth Wells first published her article on this instrument, in which it was suggested that a dendrochronological analysis of it should be done (see footnote 63 on page 40) and yet a satisfactory dendrochronological analysis which includes a determination of both the area in which the wood of the instrument grew as well as a dating of the wood.  The author can see no reason for not using the three wide planks of spruce at the back of the instrument (see the image of part of the back surface of the instrument that is visible through the hole for the rosette in Figure 23 on page 48 above)[131]. 

          One of the most outstanding features of the construction of the RCM clavicytherium is the incredible accuracy with which it was made.  The linear-regression analysis carried out in Table 2 on page 60 above shows that the averaged spacing of the rack-guide pins placed along the lower edge of the ‘gap’ for the trackers to guide the jacks has a value calculated by the linear-regression method of 14.739mm ± 0.006mm.  This has an r.m.s.  error of only 0.04% - an astonishingly low error!  It is suspected that the source of most of this error is that incurred from the author’s own measurements of the positions of the guide pins.  It needs to be remembered here that this error is a combination of the contributions of both the original maker in marking out and cutting the slots, and of the error of William Debenham in making the drawing, plus the errors of the author which were incurred when measuring Debenham’s drawing.  But the exact proportion that each of these three contributed to the final overall error can neither be measured nor calculated.  However, if the error contributed by the author and by William Debenham in the drawing and measurement of the positions of the tracker jack-guide pins is subtracted from the total error, then obviously the maker’s error is even smaller. 

          As seen from Table 1 and Figure 33 above it is clear that the lateral spacing of the jack-guide pins = 14.739mm ± 0.006mm = 14.739mm ± 0.04% was chosen by the maker to be ½ of an Urbino oncia.  Therefore, ½ Urbino oncia = 14.739mm ± 0.04%, and so the Urbino oncia would therefore have a length of twice this amount, with exactly the same error:

                          1 Urbino oncia = 2 x 14.739mm ± 0.04% = 29.48mm ± 0.01mm

Expressed as above to the correct number of figures of accuracy, the value of the Urbino oncia determined from the measurements of the lateral spacing of the tracker jack-guide pins which have then been subjected to a linear regression analysis, is therefore 1 oncia = 29.48mm ± 0.01mm.  Comparison of this value with the value found in a number of authoritative and reliable textbooks of metrology indicates that this is exactly the same size as the accepted value of the Urbino oncia to within the error limits of the measurements.[133]  There can be no doubt, therefore, that the RCM0001 clavicytherium was made in Urbino!

These factors all indicate, along with the clever design of the reduction/multiplication ratios of the string scalings, that the maker of RCM0001 was capable of an extremely sophisticated design AND that it was made by a master who was capable of carrying out this design to an astonishingly high level of accuracy, with the lowest possible error.  This would have required the highest manual dexterity almost certainly aided by some clever mechanical means of setting out and executing his design.

          What is also evident, particularly from the intarsias commissioned by Federico da Montefeltro for his studioli in Urbino and Gubbio, is that RCM0001, which seems to have been designed by the same person who designed the clavichord depicted in the Urbino intarsia images and discussed in the next sections, is a product of some of the most sophisticated minds of the past.  The present book has been written in a rather unusual and idiosyncratic way, that gives a great deal of credit for the brilliant design of these instruments to Federico da Montefeltro and his Corte mathematica.  This contradicts the usual convention enunciated by Claudio Annibaldi[134] who feels strongly that credit should always go to the artist, and not to the artist’s sponsor.  Annibaldi’s point of view can be fully understood but, in compiling this book, it has been felt that, without drawing some degree of attention to the background of the artist(s) who designed this instrument, it was simply not possible to understand the brilliance and elegance of its design.  So the author has therefore felt it necessary to come back again and again to the rich (in both ideas and finances) backdrop of the work that was taking place in the stringed-keyboard instrument workshops in Urbino in the period around 1471.  This could only have happened in Federico’s Court as a result, not of Federico’s own intellectual brilliance, but because of his immense wealth which provided the circumstances and atmosphere for Eleonora d’Este, Duchess of Urbino, and for those around those working for him.

 

This instrument is not to be taken lightly.  It is not only the oldest surviving stringed-keyboard instrument in the world, but it is also an instrument with a design and execution that matches or exceeds that of virtually all later stringed-keyboard instruments. 

But it does need a bit of science and mathematics to arrive at this conclusion. 

However, it is also true that:

ARS SINE SCIENTIA NIHIL EST!

____________________________________________

 

N.B.:  All of the material on this web-page is copyrighted by Grant O'Brien, and may not be reproduced or published in any form without written permission from him:  grant.obrien@claviantica.com