URBINO. A new centre of the highest significance to Italian stringed-keyboard instrument design and construction.

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N.B.:  Grant O'Brien holds the copyright on all of the material on this web-page, none of which may not be copied, reproduced, or published in any form without his written permission:  grant.obrien@claviantica.com

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Second Part:  The studiolo intarsia clavichord in the Palazzo Ducale in Urbino.

©Grant O’Brien, Edinburgh, July 2025

A photograph of the part of the studiolo intarsias showing the famous clavichord.

            It is extremely important to note here that there are two things happening simultaneously in the design of the instrument that can be seen in the graph of the scalings in Figure 5 above.  These two things have both to be understood and analysed separately in order to grasp the brilliance of the design of this instrument.  What is unusual here is that the position of the frets in each fretting group produces semitones and minor thirds that are of the correct calculated size for Pythagorean intonation.  At the same time, by a strict calculation of the separation of each fretting group in the bass part of the compass, and by a strict calculation of the separations and sizes of the ends of the keylevers in the treble part of the compass, there is an over-riding regularity in the scaling design that is not Pythagorean.  It may take a bit of reflection to realise what this means and how it was achieved physically.  This is obviously not the case for the short design group of less than an octave in the middle of the compass from f¹ to d^T1 (drawn here in magenta) which does, as usual correspond to Pythagorean scalings with a Pythagorean multiplication factor.

           What is truly amazing and absolutely brilliant about this design is that the person who calculated the positions of the tangents of this clavichord was able to amalgamate the correct and accurate tuning of each fretting group to give the correct pitches for Pythagorean intonation with pure fifths, but with 3 different overall multiplication and reduction factors, two of which have nothing to do with Pythagorean scalings nor with the Pythagorean scaling coefficient.  The sophistication of this design is something that has taken the author some time to get to grips with and to understand mathematically and intellectually . 

          It has, however, expanded the author’s appreciation of and respect for the designer(s) of this clavichord exponentially!

          What this means in practice is that this clavichord was designed by a master capable of the absolute highest level of sophistication, who had superb mathematical abilities and thought processes.  To make it even more impressive to us living now with the advantages of calculators and computers, is that this was all done without even the use of logarithms, let alone pocket calculators or desk-top computers.  The methods used rely on the simplest mathematical principles of multiplication and division, but produce a design of unexcelled sophistication!

Section 6 – An interpretation of the string scalings of the intarsia clavichord in the studiolo of the Duke of Montefeltro in Urbino.

            What is truly surprising and unusual about the scaling graph of Figure 5 is that the designs of sections 2 and 4 are not Pythagorean in nature, but rather that they have a design with scalings which, overall, double every 14 notes and every 11 notes, respectively.  Therefore, although the overall scalings are not Pythagorean throughout the whole of the treble and tenor parts of the compass as they are for the instruments made after about 1500, they are all geometric and therefore all logarithmic in each of the 3 separate sections indicated, since they each plot a graph that is a straight line on a graph with one logarithmic axis.  This is true for the top 3 sections, but not for the lowest foreshortened bass section.  Therefore the lengths in each of the middle and top sections can, generally but not exactly, be calculated by multiplying each of the lengths in a given straight-line section by a constant factor, a fact that is a simple property of any logarithmic function.[16]  This multiplication coefficient is just the factor introduced in Section 1.10 above and which is called the multiplication coefficient M_f and its reciprocal, the reduction coefficient R_f. 

          In order to confirm these conclusions which have been ‘eyeballed’, but not yet subjected to a rigorous analysis, each group of points in each of the separate parts of the compass was analysed individually by taking the logarithm of the individual measurements of the lengths, and fitting the logarithms for each section to individual straight lines using the usual linear-regression analysis separately for each of the different sections.  Fitting each section in this way gives the ‘best fit’ line for each section of points in order to represent the string lengths calculated by Pierre Verbeek as accurately as possible and in a mathematically rigorous way.  The actual fitted scalings are those shown with heavy lines in the graph of Figure 5.  Each of these heavy lines follows the measured string lengths very closely ignoring, for the time being, the positioning of the tangents in each of the fretted sections in order that the tuning should result in Pythagorean intonation.  These three lines seem to be a good mathematical representation of what was intended by the person who designed the clavichord depicted in the intarsia drawing.  The errors in the three fitted sections, calculated using the linear-regression analyses, are given below in column 3 of Table 4. 

Table 4 – Showing the use of the linear-regression analyses to calculate the differences between the theoretical and calculated values of each straight-line section of the graph shown in Figure 5 above.

The clavichord depicted in the perspective intarsia in the Duke of Montefeltro’s studiolo in the Palazzo Ducale, Urbino, 1478 – 1482.

          It is also true that the exact theoretical values of the slopes calculated by the linear-regression analysis and  given in Table 4 above can all be expressed as the n^th root of 2 (column 4).  However those involved in the design of the clavichord image in the Palazzo Ducale would not have had the mathematical tools to be able to carry out these exact calculations since this would have involved the use of logarithms.  Because, as mentioned previously, the practical use of logarithms was invented only much later in 1614 by Baron John Napier of Merchiston in Edinburgh.  Napier (Neper in Latin), who was known as ‘Marvellous Merchiston’ and as ‘Napier of the Logarithms’ in his time, was widely celebrated not just for his work on logarithms, but also for his inventions of one of the first mechanical calculators (a series of marked white square rods called ‘Napier’s Bones’), and he can also can be credited with his introduction to into the field of mathematics, of a practical use of decimal fractions,[19] his being the same common procedure still in use today.  The latter is by far the most common practice of a method first introduced by John Napier.

          However, Napier’s method of carrying out the calculations for the scaling design of the RCM clavicytherium and the studiolo clavichord in the Palazzo Ducale in Urbino would not have been available to those working on these instruments almost 140 years earlier than the publication of Napier’s work (published in Edinburgh in 1614), and so at a time about 140 years before the creation of the intarsias in Urbino.  As mentioned in a footnote above, the process could, however, also have been done using one or more of several iterative procedures that would have produced a highly accurate result, although rather laborious to carry out.  But since the scalings are logarithmic in nature, it also means that the situation is somewhat simplified since the length of one string can be calculated in a very simple way from the previous one, simply by multiplying (or dividing) its length by a constant factor.  Some of the numbers that might have been used to do this are given here in column 5 of Table 4.  These numbers, although they do not correspond exactly to the theoretical factors, do give results that are very close to those obtained using the exact method calculated using logarithms.  These are shown here to give some idea of how these calculations might have been carried out without invoking the use of logarithms.  For example, the resulting error differences given in Table 4 in the last column, between the exact and the pragmatic methods, are all less than 0.25%. 

          The kind of procedure utilised above is the same as that still suggested by many senior-school text books, or practical handbooks for designing stringed-keyboard instruments, when calculating Pythagorean string lengths.  A simple high-school ‘rule-of-thumb’ often used to calculate Pythagorean scalings is to multiply each string length by  in order to calculate the length of the string for the next lower note relative to the one just measured.  Because this is not, strictly, an exact method since multiplying  by itself 12 times in succession gives 1.98556 instead of 2.0000 . . .  The difference amounts to only 0.7%, so that using this approach is still very accurate, and any slight differences can be corrected by the instrument tuner.  This therefore results in an adequately-accurate result, it avoids the exact calculation of the 12th root of 2, and is very easy to apply using normal long division and multiplication which were mathematical operations that were well within the capabilities of those working on the intarsia in about 1475.

          The analysis carried out in Table 3 above is critical to our understanding of the design of this clavichord.  This table shows two notable features of the design very clearly:

1.      The close similarity of the numbers seen in Table 3 above shows that the stringing design, and not just the design and layouts of the case and keyboard, is based on the length of the oncia used in Fossombrone/Castel Durante.  Table 3 shows that the lengths of the strings for the notes f³, d^#2 and e¹ were designed to be 3 Fossombrone/Castel Durante once, 7 Fossombrone once and 13 Fossombrone once respectively.  The design based on these three simple, easily-remembered lengths measured in Fossombrone/Castel Durante once, and the simple multiplication ratios for each section, is a clear indication that the intarsia was designed and made in Fossombrone/Castel Durante and not in Urbino where it might initially have been thought to have originated.  Taken together with the case measurements discussed above which were found also to be based on the Fossombrone/Castel Durante oncia, it is therefore an almost certainty that either Fossombrone/Castel Durante is the centre in which the intarsia clavichord was designed and carried out – and therefore not in Urbino itself where the intarsias are actually now located.

2.      It shows further that the lengths of the strings for the notes in each section below f³, d^#2 and e¹ were designed so that the lengths of the strings of the notes below these critical design scalings were almost certainly multiplied repeatedly by the pragmatic multiplication coefficients M_f = ,  and  respectively in order to determine the length of the next lower notes.  This system was then ‘fine-tuned’ by the accurate positioning of the tangents to get the exact note according to the precise theoretical lengths required for the accurately-tuned pure fifths required by Pythagorean intonation. 

          That the string-scaling design is based on integral units of the Fossombrone oncia (point 1 above) should not be surprising since we have already seen above that the baseboard measurements – the structural basis of the instrument design – were also measured out in units based on the Fossombrone/Castel Durante oncia (see Figure 4 above).  This establishes clearly that the design of the intarsia originated in Fossombrone or in Castel Durante, and not in Urbino itself.  No other unit with another size could have produced these results which are in the relation 3:7:13, a series of numbers clearly without any common factors.  It might also suggest that the creation, cutting and assembly of the intarsia panels also took place in Fossombrone/Castel Durante and not in Urbino, but no actual archival evidence has yet come to light to confirm or refute this possibility.

Section 7 – Are the string scalings and the tangent positions measured from the studiolo intarsia correct for tuning in Pythagorean intonation? 

          Not surprisingly for a tuning system that is as far removed from equal temperament, where every semitone has the same size in cents, the tuning system of Pythagorean intonation produces semitones that are strongly unequal.  Whereas in equal temperament all semitones have a size of exactly 100 cents, in the tuning system of Pythagorean intonation used here, the major semitones have a value of 113.69 cents and the minor semitones have a size of 90.23 cents.  But, because of the error of the measurements of Pierre Verbeek, added to the error of the intarsiatore (intarsia cutter) who created the image in Federico da Montefeltro’s studiolo in Urbino, none of the major or minor semitones calculated from the tangent positions of the intarsia clavichord has semitones of exactly these values.  The error in the measurement of the tangent positions in millimetres is the same for all of the measurements taken and calculated by Pierre Verbeek.  However, the percentage errors in the treble, where the lengths of the strings are short, is greater than the percentage error of the strings in the tenor and bass which have longer string lengths. 

            What is at first striking about Figure 5, is that the tangents are so positioned that, within any given fretting group, they result in notes pitched perfectly for Pythagorean intonation with pure fifths (except for the fifth from the notes b up to the notes f^#).  However, both the calculated sizes of the semitones – and their position in the circle of fifths for Pythagorean intonation – are all correct for Pythagorean intonation as depicted in the intarsia image of the clavichord represent there.  AND THIS IS TRUE EVERYWHERE EXCEPT for the sizes of the calculated intervals of the measured lengths crossing over between one fretting group and the next.  Because these ‘false’ intervals are almost random in their size because of the imposition of the multiplication coefficients  and the  to the overall string-scaling scheme, the calculated sizes of the intervals between the fretting groups using the measured string lengths are correspondingly random in their size.  Between the fretting groups, the calculated sizes of the semitones all have errors that mean that they lie very slightly outwith the expected values of 113.69 cents and 90.23 cents.

            However, within the fretting groups the semitone intervals have both the correct sizes and the correct position within the tuning scheme for Pythagorean intonation, with the ‘wolf’ interval between the notes b and f^#.  No other tuning scheme would give correct values for both of these two factors. 

In addition the sizes and positions of the semitone intervals indicate that the instrument was designed so that the ‘wolf’ fifth, for this instrument, was positioned between the notes b and f^# right from the start of the tuning process.  This therefore indicates that, without a doubt, the fretting scheme was designed for Pythagorean intonation. 

          At first it might seem strange that a clavichord should not, overall, have Pythagorean scalings, especially given that it is such a strongly-fretted instrument like the one under discussion here.  It is, of course, true that an un-fretted clavichord can only have Pythagorean scalings in order that the pitches it produces correspond to those of the normal musical scale.  Therefore it seems completely counter-intuitive to see that here the string scalings are not Pythagorean in two different sections of the compass where different logarithmic scaling coefficients are invoked by the clavichord’s designer.  The notable difference here is that this clavichord is very strongly fretted with fretting groups composed of alternating groups of 3 and 4 notes.  Such strong fretting is exceedingly rare.[21]  However, it is easily possible to achieve the correct tuning of such an instrument because of the large groups of notes all fretted together in groups of 3 and 4, taken together with a non-regular spacing of the tangents between the fretting groups.  The same applies, of course, to un-fretted instruments like virginals, spinets or harpsichords.  But the correct Pythagorean intonation of this type of strongly-fretted clavichord is possible without the scalings, overall, actually being Pythagorean.  It is only because of the large sizes of the fretting groups that this is possible.  What the designer did here was, in the bass design section shown in dark blue, to space the tangents between each fretting group more tightly together than the space between the tangents of the notes of the fretted group itself.  This pushed the tangents of adjacent fretting groups tightly together in such a way that the overall scalings for the dark-blue design group (as seen in Figure 5 and in Figure 6) had a reduction coefficient for the design group taken as a whole, that was less than the averaged reduction coefficient for Pythagorean scalings. 

          The way this was achieved by the maker of this instrument is surely one of the greatest achievements in the entire history of stringed-keyboard instrument design.  It is a design feature that, to the author’s knowledge, occurs only in this one instrument made near the beginning of the historical period of stringed-keyboard instrument building and design.[22]  This is but the first indication of the unusual, but extremely brilliant nature of the design principles used in this instrument.

          Regular string scalings that appear not to be Pythagorean in this way, were achieved relatively easily as follows.  In Figure 6, it is clear that, for example, the keylevers for the notes for the fretting group with c, c^T and d have frets spaced along the string pair they have in common, in such a way that they give the correct pitches for each of the notes in this fretting group.  Here it is just the spacing of the frets based primarily on the width of the tails of the keylevers, that gives rise to accurate Pythagorean intonation.  This is also true for the following quadruple-fretting group for d^#, e, f and f^#, and then for the fretting group for g, g^#, a and b^b.  However, it is very important to note in Figure 6 that the two fretting groups – from c to d, and the fretting group from d^# to f^# – although they have the correct sizes for major- and minor-interval semitones within each of the two fretting groups, they are not placed a distance along the strings equivalent to a major or a minor semitone in pitch, relative to one another.  These fretting groups are, instead, placed very tightly together.[23]  This does not matter since the strings involved in the two fretting groups are independent of one another, and can therefore be correctly tuned for each fretting group on its own, and are therefore at slightly different tensions.  The situation between the notes f^# and g, and between a and b^b (see Figure 6 above) is even more extreme where, indeed, the tangents of the keylevers of each fretting group need to be placed very tightly together indeed.  The same applies to the keylevers and tangents at the ends of the fretting groups for the notes c^#1 and d¹ which are also placed tightly together.  But each fretted group can anyway be tuned separately to the correct pitches with each fretting group producing notes tuned in Pythagorean intonation.  This is true simply because they occur on different, independent string pairs.  The next fretting group from f¹ and above corresponds to a new stringing design, drawn here in magenta with Pythagorean scalings that double in length every 12 notes (instead of below f where the string lengths, on the average, double in length every 14 notes).

          The values in Table 4 above show that the assumed values (Theoretical M_f) for the multiplication coefficients are indeed remarkably close to those calculated from the linear-regression analyses (Calculated M_f) using the measured string lengths given by Pierre Verbeek.  All of these have differences between the measured and the calculated results that are smaller than 0.1%.[24]  This small difference between the assumed multiplication coefficients and the theoretical values are so small that it can therefore be safely assumed that the results determined here  are, indeed, the values of the multiplication coefficients used by the designer of the clavichord and by the intarsia artist.  This result gives confidence to both the assessment of the calculated size of the unit of measurement of Fossombrone/Castel Durante used to design this clavichord and to the calculations of the scaling multiplication/reduction factors.

Section 9 – Other features of the intarsia drawing whose measurements use the Fossombrone/Castel Durante oncia.

          It has been shown above that the case measurements, the keyboard measurements and the string scalings of the intarsia clavichord in the studiolo of the Palazzo Ducale in Urbino all have a design based on the length of the oncia used in either of the small centres Fossombrone or Castel Durante, only a few kilometres away from Urbino itself.  However, it seems clear to the author that all of the other components of the intarsia clavichord must also have been designed using the Fossombrone/Castel Durante oncia.  One isolated and arbitrarily-chosen example of a part of the clavichord which must also have been designed on the basis of the Fossombrone/Castel Durante oncia is the bridge of the clavichord, seen at the right-hand end of the instrument in Figure 3 above, with a detailed enlargement of the bridge seen in Figure 7 below showing it more detail.

Figure 7 – A detail of the bridge of the Urbino intarsia clavichord.  Image not to scale.[25]

Based on the measurements he has taken of the clavichord bridge, Pierre Verbeek has made a drawing of it[26] and labelled it with the measurements that he has derived.  Some of these millimetre measurements translate into totally plausible measurements when converted into units of the Fossombrone/Castel Durante once using the value of the length of the Fossombrone/Castel Durante oncia determined here (see Table 5 below).

Table 5 – Verbeek’s measurements of the bridge in mm and in units of the Fossombrone/Castel Durante oncia.

However, as is obvious from this table, some of the measurements do not at all correspond to simple measurements using the common fractions of the Fossombrone/Castel Durante oncia, which was divided into 12 punti, and which should have resulted in ‘tidy’ fractions of the Fossombrone/Castel Durante oncia.  It is also the case that, by assigning different lengths to the left- and right-hand ends of the bridge, Pierre Verbeek’s analysis implies a strong asymmetry in the shape of the bridge that does not appear in the actual image of the bridge in the intarsia itself (see Figure 7 above).  So, admittedly without any basis in measurement or in scientific analysis, the author has been motivated to suggest some possible measurements of the bridge which give sizes for its various elements that correspond to simple fractions of the Fossombrone/Castel Durante oncia, and that give a shape for the bridge that seems to correspond closely with the actual image.  These are shown in Table 6 and in Figure 8 below.

Table 6 – The author’s suggestions for the measurements of the intarsia clavichord bridge in mm and in units of the Fossombrone/Castel Durante oncia.

Clearly there is very little difference between the nominal size of the clavichord elements measured in units of the Fossombrone oncia, and the size of same element when measured in millimetres.  These measurements are shown in  REF _Ref90548443 \h Figure 8 below, but with the exact equivalent millimetre measurements in the top drawing of the Figure.

Figure 8 – The dimensions of the bridge suggested by the author.  Scale 1:1.

           To me, the drawing of the lower part of Figure 8 seems to represent the size and shape of the image of the intarsia bridge seen in Figure 7 above very well.  This gives the author confidence that the suggested size and shape of the bridge given in Table 6, and in the drawing of Figure 8, are a good representation of the actual bridge shape and size seen in the photograph of the actual intarsia bridge in Figure 7 above.

          So it would appear that the bridge size and shape can also be expressed in units of the Fossombrone/Castel Durante once, along with the case measurements, the keyboard measurements, the elements of the string-scaling design and even the fretting pattern of the instrument. 

Section 10 – What is the relationship between the RCM0001 clavicytherium and the intarsia clavichord in the studiolo of the Duke of Montefeltro in Urbino.

          It has already been noted here that the string-length multiplication coefficient used in the tenor part of the compass of the intarsia clavichord between c to e¹ utilises exactly the same multiplication ratio as that found for the treble part of the RCM0001 clavicytherium, and seen above.  This characteristic, and highly unusual, multiplication coefficient appearing in both instruments (along with the usual Pythagorean scaling coefficient) strongly suggests to the author that there is some kind of a connection between the maker/designer of RCM0001 and the maker/designer of the Urbino studiolo intarsia clavichord.  Indeed no other historical keyboard instrument is known to the author that has a string-scaling design that uses the unique multiplication coefficient found here in these two instruments of  .  This suggests the strong likelihood, therefore, that these two instruments, which both originated in the Court of Federico da Montefeltro in Urbino during roughly the same period, shared a common maker/designer.  It also suggests further that, although RCM0001 was made using the Urbino oncia, and the Urbino intarsia was designed using the Fossombrone/Castel Durante oncia, there was, in fact, some connection between them reflected in the similarity of the string-scaling designs using the pragmatic multiplication coefficients  in the parts of the designs using Pythagorean scalings, and  in the part of the designs with string-length doubling every 14 notes.  These two factors are, remarkably, the same for both instruments.  And these two scaling coefficients are not found in any other instrument(s) known to the author.[28]  This encourages the author to say that the two instruments not only have some design elements in common, but that they share the same polymath designer!

          In the part of the compass of the clavichord between f¹ to d^#2 the scaling design is perfectly normal with Pythagorean scalings that double every 12 notes.  But from e² to f³, a compass of slightly more than one octave, there is a change in the scaling design of the studiolo clavichord which results in string lengths there that double in only 11 notes, rather than in 12, or rather than in 14 notes.  However shocking this may at first seem, the close adherence of the fitted points to the design-straight-line plotted for string lengths doubling every 11 notes, indicates that this was, indeed, the design intention of the maker/musician/artist who designed the intarsia instrument.  This can be seen in the 3 sections of the scalings graph seen in 5 above.  For the notes in this part of the compass, the difference between the exact ratio, and the pragmatic ratio calculated by the linear-regression analysis to fit a line that doubles every 11 notes, is only 0.13%.  Clearly the designer of this clavichord was not burdened nor weighed down by the later (nor by the modern) obsession with Pythagorean scalings!

          On an instrument with an F,G,A to f³ compass such as is depicted in the studiolo intarsia clavichord, the changes in the scaling design from one multiplication/reduction coefficient at the notes e¹/f¹, and at the notes d^#2/e² should not be surprising since, as Denzil Wraight has shown correctly, most early Italian instruments were designed, not on the basis of their c string lengths, but on the basis of their f string lengths.[29] Although the scaling design of the Urbino intarsia clavichord does not follow the Wraight ‘f’ criterion exactly, it does inform the somewhat later Italian practice in not changing at the ‘c’ notes and in having a scaling design based on the ‘f’ notes.[30]  The extremely small errors calculated above, the sophistication of the fretting pattern when used in conjunction with Pythagorean tuning with pure fifths, and the incredible simplicity of the design when seen from a mathematical point of view, all point to a competent designer/maker/polymath of absolutely superb abilities. 

          What is most startling to the author about this analysis is firstly that the person who drew the drawing from which the intarsia was made did so in such a geometrically correct and technically and mathematically accurate way that the string-doubling principles with doubling in 14, 12 and 11 notes is actually retrievable from the intarsia drawing that was, in turn, probably made from the artist’s or maker’s original drawing or his actual instrument.  The drawing of the intarsia is so accurate that even the notes at which the scaling design changes – at e¹/f¹ and at d^#2/e² – becomes evident when the scalings are retrieved from the intarsia and plotted on a semi-logarithmic scale.  This means that, not only was the drawing made using the correct principles of perspective drawing set out by Alberti[31] at Federico’s Court, but also that the intarsia cutter was so incredibly accurate in his work that it is now, almost 550 years after the design was cut and installed in the studiolo, still possible to recover many of the important aspects of the clavichord maker’s design of this instrument, including even the fact that it was tuned in Pythagorean intonation.[32]  Secondly what is remarkable about this analysis is the outstanding work of Pierre Verbeek in analysing the perspective principles being used in the intarsia drawing to arrive at the completely internally-consistent numbers that he has calculated, and that have been used here in the author’s analysis. 

Section 11 – The pitch of the Urbino studiolo intarsia clavichord.

          Clearly, in the unfretted, foreshortened bass part of the compass of the intarsia clavichord below tenor c, the string lengths deviate strongly from Pythagorean theory.  A measurement-scaling factor for the whole intarsia has been calculated by Pierre Verbeek and he uses this to calculate the ‘real’ lengths of the strings and, from these, a speculative pitch for the instrument.  It seems clear to the author that Verbeek is correct in assuming that the front of the clavichord case in the intarsia represents the actual size of the instrument since this results in the same 3-octave span for the keyboard, seen just in front of it, of the intarsia clavichord as for the ‘flesh-and-blood’ keyboard of the RCM0001 clavicytherium.  However, a pitch comparison is, in general, possible only if the scalings are Pythagorean.  Since they clearly are not Pythagorean throughout the whole of the compass of either instrument, this is not possible.  However, the scalings of the clavichord are Pythagorean in the part of the compass from f¹ to d^#2.[33]  A moment’s reflection makes one realise that there is no way to calculate the relative pitches of two instruments when both, or even only one of them, uses non-Pythagorean scalings. 

          On the other hand, in the particular case of RCM0001 and the Urbino intarsia, both instruments do each have at least a section of their compass with Pythagorean scalings, where a pitch comparison is possible.  So the string lengths from these two separate Pythagorean sections in each of the two instruments were compared.  What has been done therefore is to make a comparison on the basis of the length of the string of the note c² = 226.3mm found for the Pythagorean part of the design in the intarsia clavichord (see  Figure 5) with the lower section of the scaling design of RCM0001 (see the graph of where the c²-equivalent of the notes with Pythagorean scalings is 192.3mm.  It is this note, and this part of the scaling design that have been used to calculate the pitch and stringing material(s) of the Urbino intarsia clavichord analysed in the section below. 

Section 12 – The design pitch and stringing materials used in the clavichord depicted in the studiolo intarsia in the Palazzo Ducale of Federico da Montefeltro in Urbino.

          It will be demonstrated below that the clavichord in the Urbino intarsia drawing was designed, like the RCM clavicytherium, to sound at a pitch a fifth high at R + 5, relative to normal pitch R.  The top axis of Figure 5 has therefore been additionally labelled according the sounded pitch of the notes being played, whereas the lower axis is labelled according to the actual played note.  The reader is warned to take note of this, and to keep the two in mind, but still separate.  The argument starts by assuming that the pitch and stringing of the clavichord in the intarsia image are the same as those of the real and tangible RCM clavicytherium studied above.  As with the calculation of the pitch of RCM0001 made above, the string length for c² for this clavichord can be compared with the normal c² brass scaling of about 292mm calculated for the instruments of the Ruckers/Couchet families and, in the Italian peninsula, for the instruments of Gianfrancesco Antegnati among numerous others.  Antegnati is one of the earliest makers in the Italian peninsula who left a large number of instruments that, taken together, can be compared with one another and can be used for a pitch assignment.  Comparing these, the relative pitch ratio is:

String-length ratio R =  = 1.290[34]

Assuming the same stringing material as determined for RCM0001 above, a pitch level a fifth high would have a ratio near  = 1.500, which is totally different from the value of 1.290 found here.  A pitch level a fourth high would have a ratio near  = 1.3333, and a pitch level a major third high relative to ‘normal’ pitch would have a ratio near  = 1.2500.  So all of these, mathematically, are notably different from the value of 1.290 found for the intarsia clavichord.  Obviously none of these gives us a satisfactory result if it is assumed that the intarsia clavichord was strung with strings of brass wire and tuned to a pitch of R + 5 in a way similar to RCM0001. 

So was this clavichord strung using iron as a treble stringing material and not using brass?

          The answer, it is felt, can be found after a close look and analysis of the string scalings used in the intarsia clavichord.  For most sixteenth-century virginals and harpsichords built in Italy in the century after the intarsia clavichord and RCM0001, a typical iron scaling for c² – in Venice for example[35] at ‘normal’ pitch R – is about 340mm to 345mm or, about one Venetian piede (foot) long.  Instruments with iron treble scalings near this measurement are at what the author calls ‘normal’ pitch – roughly the same as the pitch R that has been assigned to the pitch at the basis of the design of the harpsichords and virginals of the Flemish Ruckers/Couchet family.  Indeed, the string scalings of the iron-strung Flemish instrument are actually very similar to what has been found here for the intarsia clavichord.

          The inter-relationship between all of these scaling measurements can be seen below in Table 7.  Here column 2 in this table gives the scaling for the Pythagorean part of the design according to the sizes and units actually used in the design of these two instruments and seen in the scaling graphs of Figure XXX and Figure 5 above.  These, however, are based on different notes from one another: one is based on tenor g, the other on f¹.  Therefore, in order to compare these scalings with one another and also with those of other instruments, we need to relate them both to the usual c²-equivalent scaling designs of the later instruments at ‘normal’ pitch, rather than at a pitch of R + 5.  In order to do this, the scalings are given in column 5 of Table 7 below, both at the same pitch of R + 5, simply by using the ratios of the frequencies of the notes g and f¹ used here, to that of c².  In order to compare the scalings at this high pitch to ‘normal’ pitch, both values are then multiplied by 1.5 to give their normal, c²-equivalent scaling at a pitch of R.  Since R is the ‘normal’ pitch used generally to determine pitches and stringing materials, the values given in column 5, can be compared with the scalings (labelled ‘Normal’ scalings in Column 6) of the instruments made in the later period in both the Italian peninsula and in Northern Europe generally, since, as a rule, they used the same stringing materials with the strings tuned to a pitch that was roughly similar in both of these extended geographical regions. 

Table  SEQ Table \* ARABIC 7 – A comparison of pitches, string scalings and stringing materials for the intarsia clavichord in the Palazzo Ducale in Urbino with those determined above for the RCM clavicytherium.  All measurements are given in millimetres unless otherwise indicated.

Note for abbreviations:  (U.o.  = Urbino once; F.o.  = Fossombrone/Castel Durante once).

          Table 7 above shows that these two instruments must both have been designed to sound at the same pitch of R + 5, a fifth higher than the ‘normal’ pitch that survived into the Renaissance and Baroque periods, but notably in two different stringing materials.[38]  The R + 5 pitch must therefore have been close to the pitch found for the 4-voet Ruckers virginals[39] at this high pitch.  But these Ruckers instruments are all strung with iron strings in the treble and brass in the bass part of the compass.[40]  So R + 5 is a pitch that even survived on into the seventeenth century, some 200 years after the two instruments discussed here were designed and built.  A number of small Italian virginals and spinets at this high pitch – and not at octave pitch – has also been found.  These instruments are not, as has been previously generally assumed, at octave pitch.  The author hastens to add here that none of the authors who has so far reported on instruments at octave pitch has resorted to desperate measures, and actually calculated the pitch of these instruments.  Had they done so, their results would have been quite different and would, for all of the examples seen so far by the author, pointed to a pitch of R+5 a fifth above ‘normal’ pitch R.

          But perhaps the most important thing about Table 7 is that it shows that both types of stringing material – brass and iron – were used in the design of stringed-keyboard instruments by the polymaths working in Federico’s Court, even at this very early stage of the history of the design and construction of such instruments.  Many authors have shown that stringed-keyboard instruments in the period after these instruments were built used one of two different treble stringing materials – iron and brass.[41]  The two instruments discussed here in this work therefore show that the use of iron and brass as treble stringing materials – along with their typical design scalings – had already been established almost at the very dawn[42] of stringed-keyboard-instrument design and building in the middle of the fifteenth century.  And because the instruments using both brass and iron at this very early stage are so well designed, it has to be assumed that this practice arose out of an already well-established tradition that was already much older than the date of these two exceptional instruments.

          These two instruments therefore show that their designer(s) already had an extraordinary grasp of the elements of harpsichord and clavichord design even during this very early period.  It would seem from this that even in about 1470 the designers and makers of keyboard instruments were knowledgeable and confident in their understanding of the basic principles involved in the design of instruments using different stringing materials[43].  It is truly extraordinary that these same principles used in Federico’s Court 570 years ago then extend further right up to the present day, and are still used in the design of modern harpsichords, virginals, spinets, clavichords and pianos. 

          To the author this must surely point to the fact that, although there is virtually no evidence for it except for these two instruments, there must already have been a well-established tradition of stringed-keyboard-instrument design principles at the time these instruments were first designed and built.  It also points out clearly the important role that the Court of Federico da Montefeltro played in early keyboard-instrument design and building.

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          I consider the discoveries made about these two instruments – one virtual as only an intarsia image of a clavichord – and one a real instrument made of wood, wire and metal – to be the most important discoveries that have ever made by the author in his long career in this field.[44]

Section 13 – The tuning system used in the design of the intarsia clavichord found in the studiolo of Federico da Montefeltro, Urbino, 1473 – 1476.

          Perhaps the most impressive feature of the intarsia image of the clavichord in the studiolo of Federico da Montefeltro in Urbino is the accuracy with which it has been drawn and cut by the intarsiatore.  The whole of the clavichord intarsia is considerably less than 1 metre long in its largest dimension.  An error of only 1mm in the position of any one element of the clavichord along this length therefore amounts to an error of only .  But even this small error would result in a pitch difference for a string length with this much of an error, of close to 12 cents.  Most of the strings are much shorter than this and would therefore, with the same 1mm measurement error, have a pitch error of more than 12 cents.  Clearly the scalings do not display errors of anything like this much.  Indeed the actual errors committed by the designer/intarsiatore  are of the order of only 0.001% or an accuracy of 100 times greater!  This high accuracy, and the associated small error, gives some idea of the accuracy of the intarsia drawing.  In addition, one of the many things that is remarkable about the clavichord depicted in the Urbino studiolo intarsia is, as explained above, that it is very strongly fretted in a way found on only a very few instruments that have survived up to the present day.[45]  From the tuner’s point of view this would be a very convenient situation as it means that once one pair of strings in each fretting group has been tuned to the correct pitch, the whole fretting group consisting of the 3 or 4 notes fretted together with it has, as a result, also been tuned correctly and accurately.  The fretting pattern is certainly not a casual feature of this instrument: it is rather, an underlying feature that is the basis of the design of the whole instrument.  It is the single feature that gives rise to the musical characteristics of the intarsia instrument in a medieval, Gothic context, that affects many of its properties in a fundamental way as will be shown below. 

          The fretting pattern with 4- and 3-note fretted groups strongly suggests that the instrument was designed for Pythagorean intonation as noted previously by a number of authors.  Indeed, Pierre Verbeek is among many of those who have suggested that the pattern of the guide slots in the rack, which are clearly visible in the intarsia, are arranged to give Pythagorean intonation with a high level of precision as well.[46] 

          I want to add here by way of an anecdotal remark that, although the author has taught a course about historical tuning systems for a number of years at University level, he admits that, during the time spent teaching this course, he had never really taken Pythagorean intonation seriously as a useful system with any musical or historical value.  This is almost certainly because of the author’s ignorance of Medieval music and of Medieval music theory.  It is also true that virtually none of the modern authors on tuning gives any weight to the importance of Pythagorean intonation either.  The prevailing opinion (it is only an opinion and is not backed up by fact) although it still continues to be promulgated despite Lindley’s evidence to the contrary, is that the Pythagorean intonation tuning system is of only a passing, curious historical (but otherwise of no) interest.  The evidence for this instrument being designed to use Pythagorean intonation was published as long ago as 1967 (see footnote 6 above).  However, what will be shown here is that, following on from the publications of Edwin Ripin and Mark Lindley, Pythagorean intonation is found to have played a very important role in musical history, in a way that is quite contrary to what the author, at least, once believed, and which was based on the modern literature on the subject. 

          Usually Pythagorean intonation is disregarded by modern organologists and musicologists because, in this tuning, the major and minor thirds in the ‘home’ keys such as F major, C major, G major, etc (but really only in the ‘home’ keys) are badly out of tune in this system when the ‘wolf’ fifth is placed between B and F^#[47], so that it cannot therefore be used in the later polyphonic music after about 1500.[48]  Because of the importance of the major and minor thirds to post-medieval music, it is really impossible to play any of the later music using the major thirds in most of the ‘home’ keys in Pythagorean intonation when it is used with the ‘wolf’ fifth placed normally (for meantone temperament) when the music modulates to any significant degree from ‘home’.  In Pythagorean intonation these major (and minor) thirds are so excruciatingly out of tune that they are completely unplayable.  But, of course, the use of all of these major and minor thirds in the ‘home’ key signatures is not a feature of Medieval music.  Quite the contrary!

          The important contribution made by Mark Lindley, who pointed out what was patently obvious to anyone, like myself, capable of calculating the musical intervals involved, was that not all of the major and minor thirds are badly dissonant when using Pythagorean intonation.  This is shown in Figure 9 below.

Figure 9 – A possible circle of pure fifths in Pythagorean intonation with an F^#/B ‘wolf’, shown here with a zig-zag line.[49]  The usable major thirds are shown here with heavy lines, and the usable minor thirds are shown with thin lines.

          The ‘circle of fifths’ that Mark Lindley gives in a number of his papers (see Figure 9 above) shows a succession of pure fifths going step-wise around the circle of fifths with the dissonant fifth – the ‘wolf’ fifth – shown with a zig-zag line between the notes F^# and B.  Putting the ‘wolf’ in this position does mean that things are not as bad, musically as it might at first seem, so far as 1-3-5 chords with good major and minor thirds are concerned,.  There are four major thirds (those shown here with heavy lines in Figure 9) – D to F^#, A to C^#, E to G^# and B to D^# - that, calculation shows, are out of tune relative to a pure 5/4 major third by only about 2 cents.  Comparing this with the usual modern equal-temperament tuning with major thirds that are about 14 cents out of tune, this can only be said to be very well in tune.  It goes without saying that, if the fifths are pure and if the major thirds are so very well in tune, then the minor thirds will also be well in tune.  So this is true in the key signatures of D major, A major and E major.  In addition there is a good major third above B but, because the ‘wolf’ lies between B and F^#, a B major chord is not playable because the minor third from D^# to F^# is badly out of tune because of the dissonance of the ‘wolf’ fifth.  So there are three minor thirds (shown with light lines in Figure 9) - F^# to A, C^# to E, and G^# to B that are only about 3 cents different from a pure  minor third interval.  This means, for example, that a D major chord would have a pure fifth between D and A, an almost pure major third between D and F^# that is only slightly out of tune, and with a minor third above the F^# that is also only very marginally out of tune.  Needless to say, this was a tonality that was often chosen by composers of the High Renaissance, and almost certainly accounts for the large number of composition of this period written in D major.  Both the major and minor thirds in the D major chord using this tuning system are therefore much more accurately in tune than in modern equal temperament[50] and are also more accurately in tune than in quarter-comma and third-comma meantone temperaments with strongly-tempered fifths.  This makes it quite clear that, although restricted as to the small number of playable tonalities, what is normally said about Pythagorean intonation is simply not true!

          Therefore, while it is true that the number of usable major and minor thirds in the ‘home’ keys in Pythagorean intonation is small, with the ‘wolf’ placed between B and F^#, there are some tonalities where the use of these two intervals is quite possible and where they are, indeed, very well in tune.  In fact, the dissonance of the major and minor thirds in those usable tonalities in Pythagorean intonation is much less than it is for the same intervals and tonalities in modern equal temperament – or even in any of the so-called ‘good’ Baroque temperaments. 

          What is both convenient and useful about Pythagorean intonation it that, just by moving the position of the wolf-fifth step-wise along in the series of pure fifths around the circle of fifths, one can re-position the good and bad major and minor thirds at will.  For example, if one tunes the B to F^# pure getting rid of the ‘wolf’ there, and puts the ‘wolf’ fifth between A and E instead, then the configuration shown in Figure 10 below results.

Figure 10 – Another possible circle of pure fifths in Pythagorean intonation with an E/A ‘wolf’ fifth shown here with a zig-zag line.  The usable major and minor thirds are again shown here with heavy lines and thin lines respectively.

          Here, with the ‘wolf’ fifth placed between E and A, there are good major and minor thirds on C, G and D, and pieces in these major tonalities would be very well in tune.  A certain limited modulation around the circle of fifths would be possible starting in G major and modulating by a fifth in either direction.  This makes it clear that, if one chooses the right position for the ‘wolf’ fifth and also then the correct key signature when using Pythagorean intonation, it is possible to play with pure fourths and fifths, and with major and minor thirds that are only imperceptibly out of tune.  It gives rise therefore to a scale which, although restricted in the number of tonalities that are playable, and the associated restricted possibility of modulation, the effect is highly musical at least in-so-far as being harmonious.  Not surprisingly, this is reflected in the tonalities of the written compositions of the time.

          This simple argument means that what is usually written about the limitations of Pythagorean intonation is untrue.  And if one chooses the position of the ‘wolf’ fifth and the extent and direction of the modulations in a piece, then what is achievable with Pythagorean intonation is simply not possible in any other tuning system.  Until this is understood correctly, the effects achievable with Pythagorean intonation cannot truly be given the credit that they deserve.[51]

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          What is of critical importance here is that the designers of the intarsia clavichord, and those who followed on from them in the subsequent years, were opting for the benefits of intervals that were extremely well in tune, rather than the benefits of an extensive range of playable tonalities and the possibility of a wide range of modulations, both of which became possible (although still limited) only with the advent of some type of meantone tuning. 

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There is no doubt in the author’s mind that the designer(s) of the Urbino intarsia clavichord were capable of designing a clavichord which, like the Leipzig Pisaurensis clavichord discussed below had (some) pure major thirds rather than (some) pure fifths and fourths.  The Urbino intarsia clavichord is therefore one of the last surviving tangible pieces of evidence that we have of the late medieval practice of the use of Pythagorean intonation in keyboard instruments before meantone temperament became the standard Baroque keyboard tuning system. 

This clavichord drawn in intarsia is therefore a pivotal feature of musical history and performance practice between the Late Medieval Period and the Early Renaissance Period which, in turn, then leads on into the modern period.  To the author this also points to the use of Pythagorean tuning in the RCM clavicytherium with this instrument tuned to a pitch of R+5.

          It is meaningless to judge whether a system where all playable intervals are essentially pure, but where modulation is impossible, is more ‘musical’ or superior (or inferior) compared to a system where some intervals are very slightly out of tune but where some degree of tonal modulation is possible.  To the author both systems are each equally valid, are equally musical, but have very deep-rooted musical differences.  But to the author it also suggests that we should pay much more attention to Medieval music performed correctly at the correct pitch a fifth above the later ‘Baroque’ pitch, and with the correct tuning and the correct system of intonation.  This means that we need also to utilise the correct instruments with the correct stringing and, of course, the correct tuning.  The purity of the sounds and intervals using the appropriate instrument with its appropriate stringing material would result in chords (albeit without octaves because the keyboard 3-octave span was too great to play them!) of unheard of purity and musical qualities.  The present fashion for the rattle of tabors and bells to accompany Medieval music to make it appealing to the modern ear would surely not longer be felt to be necessary.

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          The tuning of the intarsia clavichord is clear in telling us what the tuning system of the instrument was, and in indicating the musical benefits of this system.  But it is felt securely that the RCM clavicytherium, which is probably somewhat earlier than the intarsia clavichord, must also have been tuned in Pythagorean intonation.  Both instruments tuned in this way, with their strings held at a tension within a hair’s breadth of their breaking point would also have had (essentially) perfectly-tuned harmonics.  They must both have had an incredibly musical sound with almost pure, perfectly-tuned intervals, perhaps unequalled by any of the later Renaissance, Baroque or modern keyboard instruments.

Section 14 – Who designed the RCM clavicytherium and the clavichord in the studiolo of Federico da Montefeltro in Urbino?

          The similarity in the string-length reduction coefficients seen in the graph of the scalings of the RCM clavicytherium, and those seen in Table 4 of the intarsia clavichord scalings, is striking.  To the author it suggests very strongly that the RCM clavicytherium and the Urbino intarsia clavichord were both designed by the same person, or at least in the same workshop, where the same design principles were in everyday use.  The features that these two instruments, one a real instrument made of wood and wire, and one only an intarsia illustration, have in common are the following:

1.         They were both made for the Court of Federico da Montefeltro – one in Urbino and one in Fossombrone/Castel Durante, but probably in a space of time separated by only about 25 years or less.  The RCM0001 harpsichord uses the unit of measurement in its design and construction of Urbino itself, where 1 oncia = 29.48mm.  The use of this unit in the design of the clavicytherium means the RCM clavicytherium was designed and made in Urbino with a high degree of certainty.  The intarsia clavichord, although now located physically in Urbino, uses the unit of measurement of Fossombrone/Castel Durante, and was made at the same time that the new Palazzo Ducale (Corte Alta) in Fossombrone was being designed and built for Federico.  The connection between the architects and artists, most of whom worked in both centres, is a strong suggestion that both of these instruments were constructed for Federico’s Court.  To understand this is only to accept that Fossombrone was a part of Federico’s empire and dominion. 

2.         Although the two instruments were designed in different (although closely related) places with different units of measurement, the two instruments use exactly the same 3-octave keyboard span to within the error of the measurements, and to within the perspective calculations:  RCM0001 has a 3-octave span of 529mm (measured) and the Urbino intarsia clavichord has a 3-octave span of 532mm (calculated from the measurements of Pierre Verbeek).  These are only 3mm different from one another, even though the two were designed using clearly-different units of measurement.  To the author it seems clear that the intention was to give them both exactly the same octave and 3-octave span within the constraints of the sizes of the units being used.  Any difference can be explained by the attempt by the designer to use the same octave span in both instruments, even though the unit of measurement was different, in conjunction with his desire to make his design use simple, whole numbers.

3.         They were both designed to sound at the same pitch of R + 5, a fifth above ‘normal’ pitch.  However, RCM0001 was designed to be strung entirely using brass strings, whereas the intarsia clavichord used both iron and brass treble stringing.  Mathematically the brass string scalings in the two instruments were almost identical despite the difference in the unit of measurement being used in the two different designs made in two different centres – although both centres were in the same province.

For all of these reasons it is felt that both of these instruments were designed and built in the same workshop tradition, and may even have been designed by the same person.  Relative to the clavicytherium design, the intarsia clavichord design was modified slightly for stringing with treble strings in iron, and to increase the keyboard compass in accordance with the requirements of the later music.  But the same unique, individual scaling-reduction-rates occur for both instruments. 

            There are also some additional features that they share, but the subtlety of the common reduction ratios used in the design of their string scalings is certainly the most compelling.  It is also possible that the organetto from the studiolo in Gubbio, and the small portative organs in the Urbino and Gubbio studiolo intarsias, may all have been designed (not including their pipe-length ratios, of course) in exactly the same way and in the same brilliant artistic and keyboard-building workshop tradition.[52]  Whether or not this is true, the accuracy with which the maker who built the RCM clavicytherium worked, and his conformity to the Urbino oncia, are nothing short of brilliant.  In a similar way, the accuracy with which the intarsia clavichord in Urbino was drawn and cut, means that not only are the dimensions of the case and the string scalings clearly evident, but also even the tuning system – Pythagorean intonation – can be inferred from the intarsia.

            It is said that the intarsias in Gubbio, a centre that is also within the boundaries of Federico’s Dominion, were drawn and cut in Florence[53], and that they were then transported overland to Gubbio, a very large, for the time, road distance of more than 150km.  However, no evidence based on the unit of measurement used in the design of the Gubbio intarsia panels has, however, been presented in the literature to back up this assertion.  It seems, instead, to be based on the modern obsession with Venice, Florence, Rome and Naples among modern art historians.  And although some have suspected that the Urbino intarsias were also made in Florence and brought to Urbino, it is quite clear that the clavichord intarsia panels, at least, were made and designed in Fossombrone/Castel Durante and that they originated there without a shadow of a doubt.  They certainly did not originate in Florence where the difference in the size of the unit of measurement of Florence places this assertion in the realm of complete fantasy. 

          One of the architects who was engaged to work on the Palazzo Ducale (The Corte Alta) in Fossombrone, but who was also, seemingly, marginally involved in the Palazzo Ducale in Urbino was Baccio (Bartolomeo) Pontelli.  Pontelli arrived in the service of the Duke’s Court only in 1478, and so at the very end of the construction of the studiolo in Urbino.  The archives record that he was engaged by Federico as a “legnaiolo” or wood-working specialist.[54]  But his knowledge and abilities clearly went much further than that mere carpentry.  Even if Pontelli didn’t actually design the clavichord in Federico’s studiolo, his obvious skill in carrying out the cutting of the intarsia is breathtaking.  The political and physical connection between Fossombrone/Castel Durante and the studiolo in Urbino is otherwise unknown, and is in need of further research for confirmation.

            The question then still remains: “Who was the brillian  polymath who was responsible for the design of the RCM clavicytherium and the design of the studiolo intarsia clavichord?”  A vast amount of work has already been done to find out who, exactly, was employed at Federico’s Court, how much they were paid, and what, exactly, they did.  As has been mentioned above the whole of Federico’s library and virtually all of the remaining documents relating to Federico’s Court were, with great foresight, purchased by the city of Urbino on the death of Francesco Maria II della Rovere in 1631.  These documents were then purchased from the city of Urbino by Pope Alexander VII and moved to Rome.  Federico’s library was then merged with the existing part of the Vatican Library.  But virtually all of the minor papers associated with the two Libraries and with Federico da Montefeltro and his heirs were ‘purged’ – in other words – they were destroyed.[55]  Among these papers there would almost certainly have been the names of those who designed and carried out the studiolo intarsias.  So now, with the relevant documents ‘purged’ from history, any hope of knowing who the amazing and brilliant master of the Urbino studiolo intarsias was has disappeared entirely.  Also along with the documents regarding the work carried out in the studiolo in Urbino, we have also lost any hope of finding out who designed and built the great RCM clavicytherium.

Section 15 – What work still remains to be done before the history of the RCM clavicytherium can be settled completely.

          Unfortunately the lack of any proper analysis using dendrochronology by the Royal College of Music can only be described as tragic.  Because of this it has not been possible to suggest either a date nor a centre of construction using the results of the dendrochronology method.  A good dendrochronological analysis could provide both of these for one of the most highly-important keyboard instruments in the world, and in the whole of the field of organology.  The lack of any dendrochronological analysis by the RCM is a most regrettable situation and, given the vast number of dendrochronological databases now available, and the ease of carrying out such an analysis, is not really understandable given the importance of this instrument.  The back of the instrument and the soundboard are both of a needlewood and the grain of the wood is clear and evident on both sides of the instrument despite its age.  The sizes of the growth rings on both of these surfaces could easily be recorded photographically and then measured from the photographs.  Such photographs must already have been taken and must still exist from the time of the previous restricted dendrochronological analyses (which were incorrectly pointed towards Ulm?).  An analysis of these should be quite straightforward.  Nonetheless a match to neither of these parts of the instrument has been found, seemingly because only the area around Ulm was considered in the past in evaluating the dendrochronology of the woods. 

          It is the author’s opinion that the wood growth-ring structure of the back and soundboard need now urgently to be analysed and used to date and to locate the centre of origin of the woods of these parts, using the full range of dendrochronological databases now available for the whole of Europe.  Until there is confirmation of its place of origin along with a dating of the woods of the instrument using the dendrochronological method, it will not be possible to confirm the results presented here.  The centre in which the instrument was almost certainly made is based here on the size of the unit of measurement used in its design and construction, and is discussed at length above.  This centre is, surprisingly, found to be Urbino which, as has been stated a number of times here, is otherwise unknown as a centre of stringed-keyboard instruments. 

But without a scientific dendrochronological analysis it is, of course, difficult to estimate a date of construction for the instrument with absolute certainty (or even with the uncertainty of the dendrochronological analysis), although it does seem likely that it would have been designed and made during the time of Federico da Montefeltro’s dominion in Urbino.  Given the quality and state of preservation of the boards at the back of the clavicytherium, it seems incredible that such an analysis has not yet been carried out by anyone at the RCM in London.  A careful analysis of the growth rings on the back of the instrument would mean not only that it could be dated to a specific period, but also that the region of the origin of the wood – and therefore also of the instrument itself – could also be confirmed.  Because the original compass of the clavicytherium appears to be distinctly earlier than that of the intarsia clavichord (c.1476) studied above, it seems likely that clavicytherium would have a date about 25 years or so earlier.  Because of the rapid development of both the music and the instruments at this time, by 1476 (the time of the clavichord intarsia) the compass of the RCM clavicytherium would probably have been totally out of date for the thoroughly ‘modern’ music and the equally modern instruments being built in Urbino in 1476. 

So RCM0001 may, at about the time of the construction and decoration of the studiolo in the mid 1470’s, already have left Federico’s Court and found its way to Ulm.  There seems to be no feature of the clavicytherium to suggest that the date of the RCM clavicytherium was, in fact, much later than, say even 1550.  The dating of the handwriting of the Ulm parchment is inexact, unreliable and unscientific, but it can be used, at least as a goalpost, to estimate the date in which the instrument was moved north to Ulm.  It seems that a date of about 1455, near the height of Federico’s dominance of the Urbino Court, is a quite reasonable estimate of the date of the instrument, at least until further evidence is provided by a scientific dendrochronological analysis.[56]  Federico came to power only in 1444, so it seems unlikely that the clavicytherium dates to a period before this when Oddantonio or Guidantonio were the holders of the reigns of power in Urbino. 

Although no direct evidence has been found for this conclusion, it is strongly suspected that the name(s) of those working in the keyboard-instrument building workshop(s) in Urbino in the period of Federico’s reign there, have been lost to posterity forever.  But there is always the possibility that evidence, buried somewhere in the archives, probably in either Urbino, Fossombrone, Florence or in the Vatican Library still exists.  The clear importance of these two instruments to the history of the art of keyboard-instrument making, and to the history of music itself during the transitional period when the two instruments studied here were made, is of the utmost importance to our knowledge of the transition from Medieval to Renaissance music .  It is the author’s hope therefore that someone might be inspired by the author’s work here to carry out some archival research to try to discover the name(s) of the individual(s) involved in the incredibly sophisticated design and construction of these two instruments.  There must have been some connection between the intarsia cutter, the architect who designed the studiolo and the actual designer of the clavichord portrayed in the intarsia. 

This relationship may provide the critical clue to discovering who was at the basis of the extremely elegant design of both the Urbino clavichord and clavicytherium.

          But this clearly points out the urgent need for a dendrochronological analysis.  Needless to say I won’t stop trying to get this analysis done as soon as possible, whether or not I am able to include the results before the publication of this work.

Section 16 – Conclusions based on the study of the RCM clavicytherium and of the clavichord intarsia in the studiolo in the Palazzo Ducale in Urbino.

            The contribution of the person (or persons) who designed the clavichord in the Urbino studiolo intarsia and of the Urbino RCM clavicytherium to the later history of stringed-keyboard instrument making is enormous.  Among the features instituted and handled with confidence by the designer(s) of these two instruments at this early stage of the history of keyboard-instrument making are the following:

1.         One of the most recognisable differences between the RCM clavicytherium and the Urbino studiolo intarsia clavichord, and a difference that shows how these two instruments demonstrate the transition from the earlier Medieval, Gothic music systems and the later Renaissance system is to be seen in the difference of the compasses of the two instruments.  The RCM clavicytherium compass was clearly based on the old Guidonian Medieval system which used the compass Г to g² (Gamma Ut to g²) with the three notes of variable tuning Ψ₁, Ψ₂ and Ψ₃ below the Г ut.  Within the space of about 25 years, this had already changed to the High Renaissance compass of F,G,A to f³ of the studiolo intarsia clavichord.  The later compass used the bass F,G,A compass in place of the Ψ₁, Ψ₂, Ψ₃, and Г ut, and extended the treble compass by almost an octave from g² up to f³.  The F,G,A to f³ compass endured in the clavichords, virginals, harpsichords, and especially in the organs of the period from at least 1476 until about 1590, and therefore well into the beginning of the Mannerist Period following on from the Renaissance. 

2.         Although it might at the present moment seem of less importance because virtually no-one now uses Pythagorean intonation, the master who designed the intarsia clavichord ties the fretting pattern used in his design very closely to the tuning system being used by the contemporary musicians in such a way that, even though the clavichord was tuned in Pythagorean intonation, the fretting design maximises the number of tonalities that the music played on it can use and in which the music can be composed and played.  The use of Pythagorean intonation is as intimately tied to the 3-4-3-4 etc fretting pattern of the intarsia clavichord as is, in a more subtle but no less important way, the use of meantone temperament and the normal irregular double- and triple-fretting patterns of the clavichords built during the late sixteenth, seventeenth and eighteenth centuries.  

Because the tuning system being used in the Urbino clavichord was Pythagorean intonation, the fifths and fourths were perfectly pure intervals by definition except, of course, for the single ‘wolf’ fifth wherever it was placed.  But, as has been shown above, there was also a number of very accurately-tuned major and minor thirds in this system that could be used alongside the pure fourths and fifths which could be used to marvellous effect by the composers and musicians of the period.  This means that, although the keyboards of both instruments had very wide octave spans so that octaves could not be played, there was still a number of tonalities in which pure fourths and fifths could be used with major and minor thirds that were almost perfectly in tune.  These were exactly the requirements of the polyphonic music being composed and performed at that time, meaning, in turn, that this clavichord could play certain major triads in a way that was musically very satisfying and harmonious – and in a way that was not achievable in any of the later tuning systems, even in the presence of keyboards with split accidentals.  This intarsia clavichord is probably the first keyboard instrument that shows clearly how musical fashion, musical performance and the composition of music had moved on from the medieval plainchant, parallel-fifth style, with highly elaborate ornamentation, to the major and minor triadic schemes so typical of the Renaissance and Baroque periods. 

3.         The establishment of the use of both iron and yellow brass as stringing materials to the field of clavichord and harpsichord design is of enormous importance.  These materials are still a fundamental feature of even the modern reproductions of historical keyboard instruments, and also of the modern piano right up to the present day.  The use of these two stringing materials tuned to a pitch at or near their breaking point (and therefore at the correct pitch) in such a confident way by the designer of these two instruments, strongly suggests that – even at this early date – they were already a feature of the earliest stringed-keyboard instrument design.  This then seems to point to a clearly-established tradition that was already in place, and pushes this tradition back to a date well before the actual design and construction of these instruments in about 1476, and so much further into the past than has been previously recognised. 

4.         These two instruments taken together are to be seen as a vital link between the medieval, Guidonian music using Pythagorean intonation with pure fifths, during the very early period – and the later music-writing and performance of the Renaissance and early Baroque periods, with meantone tuning and pure major triads and well-tuned fifths and minor thirds.

5.         The ‘extra’ notes in the lowest basses of the RCM clavicytherium discussed above should, in the author’s view, be regarded as a kind of ancestor to the later ‘normal’ bass short-octave whose use became standard in the later Renaissance and Baroque periods.  But the ‘short-octave’ in use in the second half of the fifteenth century was unlike the later short-octave arrangement with the fixed notes C/E, D/F^T and E/G^T.  Instead the compasses of these early short-octave instruments need to be seen as instruments with a Ψ₁, Ψ₂, Ψ₃, Г to g² compass (like the RCM clavicytherium) and not F,G,A to f³ but rather with a F/Ψ₁, G/Ψ₂, A/Ψ₃, B^I/Ψ₄, B to f³.  In the latter case, the four lowest notes could all be capable of a variable tuning, and these would then be followed by the ‘standard’ notes, for Medieval keyboard instruments of either B to a², or occasionally, of B to f³.  In the author’s view, in both the clavicytherium and in the intarsia clavichord, the bottom 3 notes and 4 notes respectively are independent notes that could be tuned to any desired note depending on the music and the choice of how the musician wanted to play the music.  We are used to the E, F^#and G^# of the normal short octave not actually being tuned to these apparent notes, but to the diatonic notes C, D and E that are essential as roots to so many of the normal tonalities playable in meantone temperament.  In the author’s view we need now to accept that the four lowest notes of a medieval stringed-keyboard instrument can have a variable tuning and also that their actual pitch has nothing to do with their apparent pitches of F,G,A and B^I.  The F,G,A to f³ table organs obviously had to play the apparent notes of their bass compass, but the F,G,A compass was short-lived, presumably because of the confusion of the pitches of the lowest notes of the organs with the pitches of the lowest notes of instruments like the Urbino intarsia clavichord. 

What has been shown above is that the clavichord depicted in the Urbino studiolo intarsia and the clavicytherium RCM0001, stand clearly and brightly at the crossroads where the direction of music and stringed-keyboard instrument design changed direction from the earlier Medieval-Guidonian era, and moved down a new road in the direction of polyphony and the music of the early Renaissance.  The role of the Ducal Court and of Federico da Montefeltro in this transition is of fundamental importance to our understanding of the transition from Medieval to Renaissance music and is exemplified by the design of RCM0001 and the Urbino intarsia clavichord.  There is no other centre known to have made the giant steps made by the designers of these two instruments, except for Urbino. 

This now needs to be recognised and re-assessed. 

          In parallel with this, it is important to remember that these instruments would never have existed in the first place without the favourable cultural and intellectual climate that existed at the Court of Federico da Montefeltro, Duke of Urbino.  Federico was immensely wealthy, and without him financing these new moves,ss which were capable of sustaining those artists, scholars and some of the greatest minds of the time within the Medieval walls of Urbino, it is very hard to imagine that any of this would ever have happened.  Those who inhabited Federico’s Court were all of the highest calibre imaginable, and were all fostered by Federico’s Court.  This influence extends beyond Urbino itself, to those other centres where Federico da Montefeltro’s influence extended such as Fossombrone/Castel Durante and Gubbio. 

          The brilliance of the keyboard designers and makers working for Federico is clearly illustrated in the two instruments studied here in the two previous chapters.  But without Federico it is unlikely that either of these instruments would have been designed and built in the first place, and therefore they would not have come down to us today.  This makes the Court of Federico and these two instruments created at this Courti, factors of immense importance and fundamental significance to the history of music and to the history of stringed-keyboard instrument design in particular.

©Grant O’Brien

Edinburgh,

July, 2025