Old Oud compared to Old Lute Geometry

Under the topics "Old Oud - New Project", "Oud or Lute?" and "Analysis of Nahat Bracing" on this forum, the geometries of three oud profiles were analysed - the 14th C engraving of a 5 course fretted oud in the Kitab al-Adwar, ALAMI's late 19th C Al- Arja oud and the recently restored early 20th C George Abdo Nahat & Sons oud. (see those threads for more detailed information).

The task now is to see if there might be any correlation between these geometries and those of surviving European lutes of the 16th and 17th C.

Over the years since I started out making lutes in the early 70's, I have acquired a collection of full size drawings of surviving lutes of the 16th and 17th C measured and drawn by luthiers of established international reputation. These drawings will now be analysed individually to determine if there is any match with the oud geometries so far established.

To summarise:

The first and earliest geometry is that of the 14th C Kitab al-Adwar oud that has close similarities to the 15th C drawing of a lute by Henri Arnault de Zwolle - manuscript in the Biblioteque Nationale de Paris (Ms Latin 7295).

The second oud geometry is that of the Al- Arja oud that compares closely with a late 15th C carving of a lute in Ulm Cathedral, Germany.

The third is a development of the Al-Arja oud - the Nahat oud with its elliptical shaped lower profile. The geometry of the elliptical profile is traced using a loop of string stretched taut between two pins.

Next to analyse the profile of a late 16th C. lute.

The first of the geometries of original lutes to be analysed is one familiar to most lute makers - a lute by Giovane Hieber, Cat. No. 1561 in the Musee Instrumental Conservatoire Royal de Musique de Bruxelles. This rather plain instrument is considered to be in original condition. String length 591.5 mm.
Working from a full size drawing of the instrument made by luthier Stephen Murphy in 1976 the following geometry is a close match allowing for some slight asymmetry of the profile.

The upper part of the sound board profile is identical to that of the Al Arja and Nahat ouds based upon a basic 3:4:5 unit 'Pythagorean' right triangle XZN with a sound board width of 4 units and profile generated by an arc of radius R1with centre at Z.

Like the Al Arja oud, the front edge of the bridge is 1 basic unit from X and the bottom of the sound board F, 2 basic units from X.
Unlike the Al Arja oud, however, the lower profile is not semicircular but 'flattened - similar to the Nahat elliptical shape in appearance but generated differently as follows:
The square ABDG has sides equal to the sound board width. Diagonals AF and BD intersect at point O the centre for an arc of radius R3 that just touches arcs traced by R1 and R2. This profile, therefore, is not an ellipse.

As with the Al Arja geometry the location of the neck joint is determined by the fingerboard width - in this case 70 mm, just sufficient width for 7 courses. The centre of the sound hole C is then positioned midway between the neck joint and front edge of the bridge. The diameter of the sound hole is 1/4 of the distance between neck joint and bridge.

This proposed Hieber geometry might, therefore, be considered a development of that of the Al Arja oud (which in turn is a close match to an earlier lute geometry of the late 15th C - represented by the carving 'Pythagoras with Lute' in Ulm Cathedral).
Note that Hieber was a luthier of German origin working in Northern Italy during the 16th C - hence the Italianate 'Giovane' or 'Giovanni'.

Before leaving the Hieber lute example I should mention that most of the surviving lutes of the 16th and 17th C have a bowl section that is 'flatter' than the semi circular section commonly found in oud bowl geometry. 'Baroque' lutes of the 18th C often had 'deeper' than semi circular sections.
Also, the neck joint on lutes slope whereas on ouds the joint is vertical. This is necessary on the wider finger board lutes to ensure that neck thickness at the neck joint does not become excessive.

I built a lute modelled on the Hieber instrument geometry in 1979 - that I still use today on a daily basis. The attached image illustrates the 'flattened' bowl section which is about
10 mm less than a perfect semicircle in section - just to make construction a bit more difficult (all of the ribs being slightly non symmetrical)!

Here is another example of very similar geometrical profiles between the Al Arja oud, the 'Pythagoras lute' of Ulm and an early 17th C lute.

The lute, a well preserved example of an extended neck lute - a tiorbino by an anonymous maker - is in the Cleveland Museum of Art, accession number 1918.368. A gallery of high resolution images of the lute, courtesy of Ed. Greenhood and the Lute Society of America can be viewed at:

http://www.cs.dartmouth.edu/~lsa/links/Tiorbino

The attached geometry is self explanatory in comparison with the Al Arja/Ulm and the Hieber lute profiles previously posted.

The next example of interest in this investigation is the Dean Castle Unverdorben 'lute-guitar' subject of topic 'Lute or Oud" on this forum.
It is assumed that there has been little or no distortion of the original profile of the bowl on this instrument since the 16th C.

Once again the geometry of the upper part of the sound board profile can be defined using a 3:4:5 right triangle as a basis. The front edge of the original bridge is placed one basic unit from X. The centre of the sound hole C is 2.5 units from X as is the distance to N. The bottom of the sound board F is given by R4 with centre H at the bridge
The diameter of the sound hole is 1/3 the width of the sound board at that point - a common relationship with 16th C lute geometry.
Below the widest point of the sound board, the geometry of the profile becomes a little more complicated than in previously posted geometries. The profile is not elliptical.The attached proposed geometrical construction is self explanatory.
The slight mismatch between the arcs drawn by R1, R2, and R3 can be blended smoothly by an arc drawn by R5 with centre D, midway between X and H.
Given this proposed geometrical construction, the original bridge would have been a bit lower (and now covered by) the
19th C bridge - giving an original string length of about
66.5 cm.

The relative consistency of the results so far (old ouds and old lutes) may imply that both instruments (or at least some of them) were traditionally designed to a strict formula based upon geometric designs easily replicated - without any knowledge of more advanced mathematics - using only dividers as a universal simple tool. Early days yet, however, to draw any firm conclusions.
It should be noted that not all surviving lutes conform to the 3:4:5 right triangle geometrical basis and so, no doubt, neither do some old ouds. Nobody said this was going to be easy!

One thought is that the current method of building an oud bowl "free form" without a mold (and, therefore, lacking precise, repeatable geometrical profile) is not how it was done historically.

UPDATE 21 Nov. 2013 - the proposed sound board geometry of this lute has now been revised in the light of new information and not based upon a Pythagorean 3:4:5 triangle. See page 5 of this thread.

Most of the images of old ouds posted on this forum (and elsewhere on the Internet) do not lend themselves to precise geometrical analysis - usually because the images are not taken 'face on' with a long focus lens and so are subject to some degree of optical distortion or are of too low a resolution to precisely define the profiles.

Here is one example of an image of an oud by Rhoufan Nahat, 1908, that - although not high resolution - seems to have been taken pretty well face on. I do not know who the owner is (lucky guy!).
Working with a 40% full scale scan, the geometry and construction of the lower half of the sound board profile appears to be identical to that proposed for the 1925 Abdo George Nahat and sons oud recently discussed in "Analysis of Nahat Bracing" on this forum.
The only difference is that the Rhoufan oud has a single sound hole whereas the 1925 Nahat has a triple sound hole.
Interestingly the sound hole of the Rhoufan oud is 1/3 the diameter of the width of the sound board measured at the centre of the sound hole. This is a proportion sometimes found on surviving lutes from the 16th and 17th C. It is also the proportion given by Arnault de Zwolle in his geometrical construction of a 14th C lute.

An 'oversized' pair of dividers has now been made so that the profiles of the many full sized drawings of historic lutes that I have on file may be analysed in detail.
The first step will be to identify others (if any) that conform to the now familiar basic 3:4:5 right triangle geometrical construction.

Working through my files and drawings of early lutes to identify any profiles that may have a geometry based on a 'Pythagorean' 3:4:5 right triangle, I found this lute by 16th C luthier Wendelio Venere that seems to closely match this geometry. This lute, dated 1592, in the Bolognia Academia Filarmonica, Italy is in original condition with 7 double courses and a bowl made from 25 ribs of yew. String length is 58.3 cm. The label inside states "In Padova Wendelio Venere"
W. Venere (a luthier of German origin working in Northern Italy from about 1570) made lutes of differing geometry as can be seen in this comparison of the 1592 instrument and another in the Dean Castle, van Raalte collection. The latter - now in a mutilated state having been crudely converted to a 'lute-guitar' in 19th C Germany has its original 13 ribbed ivory bowl with a sound board dating from either the 17th or early 18th C.
The maker labels inside trace the history. the original printed label reads " Wendelinus Tieffenbruker Dictus Venerius Fecit" with the date 1571 written in ink. The second printed label reads " Johannes Rossman/ Lauten und Geigenmacher in Breslau" with the date 1686 written in ink. The third label reads "Christian Gottlieb Hoffmann Leipzig Anno 1726". Two other small labels are indecipherable.
So the labels tell us that luthier Wendelio Venere is non other than the renowned German lute maker Wendelin Tieffenbruker. They also tell us that the lute went through at least two conversions during the 'Baroque' period before ending up as a 19th C 'guitar-lute'.

The attached proposed geometry of the 1592 lute is largely self explanatory being based upon a 3:4:5 right triangle. Note that the front edge of the bridge is positioned at 1/6 of the length of the bowl NF - a classical proportion for the lute (as well as the Al Arja oud, for example). The sound hole diameter is 1/5 of NF. The top edge of the sound hole is defined by arcs R2 and, at the centre of the sound hole, the diameter is 1/3 the width of the sound board at that location - another classic lute proportion.

The 'cut in' rosette of the 1592 lute is oud like in design (compared to the 17th/18th C geometrical design of the Dean Castle example).

Note that there is a slight deviation from the 3:4:5 geometry at the neck joint location. This may be due to the luthier simply adjusting the profile slightly at the neck block to fit a narrower 7 course rather than a wider 8 course fingerboard.

The proposed geometry of the 1592 lute was developed from a full size drawing by luthier Stephen Murphy. The image of the lute and drawing of the rosette are by Stephen Murphy :

http//:www.murphylutes.com

An old oud that I purchased in Cairo in the early 60's has so far been assumed to have been made in that city and, as a consequence, to be an Egyptian oud. But is it?

A hand written label (in Arabic) inside the bowl translates as "School of Ornamentation, Department of Musical Instruments, made by Hosain Mohy al Deen Helmy, Third Year". There is no date and the location of the "School of Ornamentation" is unknown.

Allowing for some asymmetry on the treble side of the bowl (about 3mm maximum) the proposed geometry attached fits the profile closely and reveals that the sound board was fitted by the luthier about 4 mm towards the end of the bowl than it should have been. The diagram attached shows the corrected sound board geometry.
The geometrical layout is self explanatory and, once again, is based upon the now familiar 3:4:5 right triangle. The profile of the upper part of the sound board is defined by an arc of radius R1, the bottom part by an arc of radius R2 - both joined by an arc of radius R3. The front edge of the bridge is located at one basic unit from X and the bottom of the sound board is 2 basic units from X.
The centre of the large sound hole is mid way between the neck joint and front edge of the bridge. The top of the sound hole is 2 basic units from X which defines the sound hole diameter (compare this with the Al Arja geometry previously posted).
The centres of the small sound holes are each a distance of one basic unit from the sound board centre line. I was unable to find any geometrical correlation that gives the diameter of the small sound holes so assume that their diameter was determined as simply the maximum that would fit between the brace fitted at the widest part of the sound board (centre at X) and the brace located just below the bottom edge of the sound hole.

So the question now is does this geometry represent the traditional profile of an Egyptian oud - which is very similar if not identical to the geometry of early ouds made in the Lebanon/Syria region?
Or is this oud not Egyptian but one that originally came from Syria or Lebanon?

The rosette designs are a bit unusual for an oud so might turn out be another clue in the puzzle.

For information, the attached image of the bracing geometry of the old 'Egyptian' oud may be of interest - although bracing geometry is to be considered as a separate study for the future.
This scale drawing was made in the mid 1970's - before PC's and the convenience of digital graphics - the dimensions being transferred on to squared paper. As a consequence the geometrical profile of the sound board may lack some precision although it should be pretty close. The view is from the underside of the sound board.
Of interest is how closely the bracing geometry matches the geometry of 'standard' lute bracing given by Marin Mersenne in his monumental theoretical work "Harmonie Universelle", Paris, 1636.

Reviewing this drawing caused me to re-examine the sound hole geometry as the centres of the small sound holes appeared to be slightly wider spaced than given in the previous post. Rechecking the full size dimensions confirms that this is indeed the case although the discrepancy is only about 2 or 3 mm (but a bit outside the accuracy of measurement of say plus or minus 0.5 mm).
I now think that the luthier may have intended for the relative locations of the sound hole centres to be at a 45 degree angle to each other but just didn't get the measurements 'spot on'
The attached image shows the exact full size geometry of the sound holes.

Here are some basic dimensions for information.
String length 622 mm - six double courses. Width of neck joint 60 mm. Maximum width of sound board 349 mm and length from neck joint to bottom of the bowl 512 mm. Maximum depth of bowl is about 182 mm so the bowl section is slightly deeper than a semicircle by 15 mm.

Note also that the bridge is 1/6th of the total sound board length (taken to the intersection of the arcs described by R1 on the geometrical construction). This is also the proportion found on many surviving lutes from the 16th and 17th C.

Danielo has kindly sent me a 'full face' high resolution image of his beautiful, yet unadorned, 1921 Hanna Nahat oud for geometrical analysis - to add to the data base on this thread (thanks Dan). More donations would be welcomed!

Working with reduced scale images that may be subject to optical distortion has its inevitable drawbacks regarding precision of any proposed geometry so, as more information becomes available, these proposed geometries may be subject to future refinement and revision.

The attached proposed geometry is again based upon a 3:4:5 right triangle - giving an exact fit to the upper sound board profile as defined by R1.
The front edge of the bridge - distance XB - is 3/4 of basic triangle unit. The distance to the bottom of the sound board BF is 1 basic unit.
The centre of the sound hole C is midway between the neck joint and the front edge of the bridge tie block (not the front edge of the bridge). The bottom edge of the sound hole is 3/4 basic unit from X which in turn defines the diameter of the sound hole.

The profile of the lower part of the sound board is not parabolic but is a simpler 'pseudo parabola' constructed from a blending of three arcs described by R2, R3 and R4.
(In the case of instrument geometry I am of the opinion that the simpler the construction the more likely it is that this may have been the original method used by Hanna Nahat - a combination of simple arcs taking precedence over the more complex parabolic geometry).

The attached rough sketch of a Nahat bridge cross section compared to a more 'conventional' traditional oud bridge is intended to clarify the dimensional difference between the front edge of the bridge and front edge of the bridge tie block. It would seem that the Nahat design imposes a greater rotational torsion on the sound board - string tension being equal.

When working with reduced scale drawings or images, a simple tool that is a time saving aid in determining if the bottom curve of a sound board profile is a simple arc (rather than a more complicated elliptical curve) can be made from a piece of thin 'Plexiglas' (transparent Acrylic sheet). A series of arcs are scratched into the plastic using a pair of dividers (the exact radii are not important as the arcs are for comparison purposes only). The centre of the arcs is then drilled out to about 0.7 mm diameter to allow a standard pencil lead to pass through in order to mark the centre position.

In use the tool is placed over the drawing to match the arc profile and the centre marked with a pencil.
Here, a drawing of a lute made in 1644 by Pietro Railich, a German luthier working in Venice during the 17th C. is the current subject of analysis. This instrument, Cat. # MI 45 is in the instrument collection of the Germanisches Nationalmuseum, Nurnberg.
It can be seen that the profile of the bottom part of the sound board is a simple arc not an elliptical curve.
(I am beginning to suspect that most if not all of the geometric profiles of the bottom half of historic lute and oud sound boards are not elliptical but may be described by a series of simple arcs - using dividers - blended together to provide a uniform curve).

The next step in this study is to examine those surviving lutes (like this example by Railich) and ouds (19th C Turkish style?) that may be a development of the 14th C. Arnault de Zwolle lute/ 13th C. Kitab al-Adwar oud geometries posted at the beginning of this thread.

More to follow.

So far, some old ouds and lutes that fit an upper sound board profile based on a 3:4:5 'Pythagorean' right triangle geometry have been identified. Although much more work needs to be done, to establish a more extensive data base, it is clear from the few examples already posted that the upper sound board profile consistently defines this particular geometrical type. Lets call this type 2 geometry.
As can be seen from the examples posted, the lower sound board profile can match a variety of proposed geometries ranging from a simple semi circle to a 'flattened' elliptical shape - or perhaps more likely - pseudo elliptical profiles constructed from simple arcs generated by a number of possible radii and radii centres. The geometry of the lower sound board then dictates bridge location, sound hole placement and diameter(s) and bowl volume. Furthermore, these parameters in turn then dictate relative placement of the sound board bracing (e.g. those braces positioned at the widest part of the sound board, at the centre and on either side of the main sound hole and on either side of any additional small sound holes).
It is likely, therefore, that individual luthiers - choosing to use the type 2 geometry - may have then varied the lower profile in order to achieve particular acoustical characteristics from their instruments.
Note that the air volume of the bowl can also be modified by changing the cross section from a semi circle to a more 'flattened' profile (often found in lutes of the 16th and 17th C) or a deeper profile (often found in lutes of the early 18th C or 19th/ early 20th C ouds). As no ouds survive from the 16th/ 17th C it is impossible to determine if they, like the lutes, ever had a flattened profile.

The next geometry to be investigated is most likely an earlier type so lets call it type 1. This is the geometry of the 13th C Kitab al Adwar oud/ 14th C Arnault de Zwolle lute. Again, the upper sound board profile defines the geometrical type - in this case an arc described by a radius equal to the maximum width of the sound board. Like the type 2 geometries, the lower sound board profiles may range from a semi circle to a more complex elliptical or pseudo elliptical shape with all of the consequential acoustical implications mentioned above.

Before moving on to specific examples of type 1, the attached image compares - side by side - two basic examples of type 1 and type 2 drawn to the same scale. Here the type 1 example is the Arnault de Zwolle geometry with the length of sound board divided into 6 equal parts, the bridge located on the first part and top of sound hole at the 4th part, Sound hole diameter is 1/3 the width of the sound board at the sound hole centreline.
The type 2 example, for comparison, is that of the late 15th C carving of a lute in Ulm cathedral. Here the sound hole diameter is 1/4 the maximum sound board width.

Surviving lutes that match the type 1 geometry are in the minority but two potential examples will be examined next. As for the ouds, I suspect that the traditional design of Turkish ouds might also conform to type 1 geometry - but that has yet to be established as I note - on preliminary examination - that old Turkish ouds seem to vary greatly in their geometric profiles.

Thanks

The first example of a lute that fits the type 1 geometry is in the musical instrument collection of the Germanisches
Nationalmuseum, Nurnberg - cat. MI 55. Made by Christofolo Hoch, Venice, first half (?) of the 17th C. I am not certain about the details but this German luthier's original name may have been Christopher Koch later becoming the Italianate Christoffolo Hoch or Choc or Choco when working in Northern Italy during the 17th C. The geometry of this lute is only one of a several used by this maker.

I do not have any images of this lute and have developed this geometry from a half full size museum drawing of the sound board and its bracing (copyright restrictions prevent posting of the drawing).
In order to simplify the geometrical construction so that it is pretty well self explanatory, it has been broken down into three steps.

Step 1. The maximum sound board width VZ is divided into 4 equal parts VW, WX, XY and YZ. The profile of the upper part of the sound board is described by an arc of radius R1 (equal to the sound board width) with centres at V and Z.
The vertical axis of the sound board is first divided into three parts with an arc of radius R3 (equal to half the sound board width) and centres at W and Y. Each of the three parts is in turn equally divided to give a total of 6 equal parts LM, MN, NO, OX, XP and PQ. The bottom of the sound board is located at point Q, the front edge of the bridge at P and the top edge of the sound hole at N. The profile of the bottom edge of the sound board is described by an arc of radius R2 (of length LQ) with centre at point L.

Step 2. With the top edge of the sound hole at N, distance XO is divided in two to give the bottom edge of the sound hole at point B. This then defines the centre of the sound hole (mid way between N and B) and sound hole diameter NB.

Step 3. With the centre of the sound hole established, the distance CY (R4) gives the third arc defining the remainder of the profile of the lower part of the sound board. The centre of the third arc is quickly found - by trial and error - using dividers so that the arcs defined by R1, R2 and R4 blend together.

So it can be seen that the entire geometry can be constructed using only a straight edge and pair of dividers.

A second example of a lute with a 'type 1' geometry is that of an instrument by Pietro Railich made in Venice in 1644. The lute is in the instrument collection of the Germanisches Nationalmuseum, Nurnberg, cat. MI 45.
The label inside reads "Pietro Railich gioia Venetia 1644".
Railich was born in 1615 in Fussen, Germany, later setting up his workshop (Bottega di Lautaro al Santo" in Padua, Italy where worked until his death in 1678.

The lute has a string length of 61.4 cm with 11 courses - 2 single the remainder double.
The bowl section is significantly 'flattened' by about 32 mm at the widest part.
The pattern of the 'cut in' rosette is oud like.
Unfortunately, I do not have an image of the lute on file.
The geometry that follows is only one among other different types used by this luthier.

Working with a half scale drawing of the sound board there appeared to be a discrepancy in the vertical axis coordinates that could not be fully resolved at the reduced scale (a disadvantage of trying to establish instrument profiles from reduced scale images).
However, it was possible to resolve this apparent discrepancy by working with a full scale drawing of the lute made by luthier Stephen Murphy that I have on file (Stephen also drew the rosette pattern posted here).

To clarify the proposed geometry, the construction has been broken down into 3 steps - the whole geometry being created using only a straight edge and dividers.

The procedure will be described in the next posting later this evening.

Here is the proposed Railich lute geometry - mostly self explanatory.

Step 1 - the maximum width of the sound board VZ is divided into 4 equal parts VW, WX, XY and YZ. The upper and lower sound board geometries are initially constructed separately before being combined together.

Radius R1 (equal to the sound board width VZ) describes the arc of the upper sound board meeting at point L, the top of the sound board profile.
The vertical axis of the upper sound board as far as L is also divided into 4 equal parts. Point C is at one unit from X on the horizontal axis. Note that a horizontal axis unit is larger than a vertical axis unit.
R5 describes a secondary arc giving the profile at the neck joint location.

For the lower part of the sound board geometry
R3, equal to 2 horizontal axis units, describes arcs that meet at point Q - the bottom of the sound board profile. Distance QX is divided into 2 equal parts to give the position of the front edge of the bridge - each part is identical in length to the vertical axis units already established for the upper part of the sound board.
R4 - equal to 1 horizontal unit - crosses the vertical axis at point C.
R1 describes the profile of the outer edges of the lower sound board.

Step 2 - the geometrical layouts of the upper and lower sound board are combined together so that points C coincide. C is then the centre of the sound hole. The sound hole diameter is equal to 1 unit of the horizontal axis (i.e. same length as radius R4 or 1/4 maximum sound board width.

It can be seen that the alignment of point C results in a slight elongation of the total vertical axis LQ of the sound board (by about 16 mm in this case) This is the apparent discrepancy in the vertical dimension previously noted.

Radius R2 then defines the profile of the bottom edge of the sound board.

Step 3 - Radius R6 is measured from C to point W or Y on the horizontal axis of the lower part of the sound board. By trial and error, using dividers, R6 describes an arc that blends with R1 and R2 to complete the profile of the lower part of the sound board.

Other possible contenders for lutes of type 1 geometry have been identified but have yet to be subject to analysis.

Next - to try to find examples of early oud that also fit type 1 geometry.

Turkish Oud Geometry.

Checking the images of some early Turkish ouds posted on the Internet indicates that some appear to conform in profile to
type 1 geometry.

However, in an article about Turkish instruments posted about 5 years ago on the website 'Musik ve Bilim', information giving the relative dimensions of a Turkish oud in its four traditional sizes (girl, woman, boy and man - respective string lengths 54, 55.5, 57 and 58.5 cm) - is included as well as a sketch (that appears to be drawn to scale and otherwise proportionally correct) giving a profile of the oud.
Using this sketch as a starting point in this examination of Turkish oud profiles, the attached image is a proposed geometry constructed according to this data.

The geometry is largely self explanatory and may be constructed using only a straight edge ruler and a pair of dividers.

What is immediately apparent is that the oud profile is not type 1 but a type 2 geometry based upon the now familiar 3:4:5 right triangle.
If the length of the finger board is X then the distance from neck joint to the centre of the main sound hole is also X as is the distance from the sound hole centre to the front edge of the bridge (i.e. string length is 3X). The front edge of the bridge is a distance 0.5X from the bottom edge of the sound board.
The width of the sound board at the widest point is equal to 4 units of the 3:4:5 triangle. The diameter of the main sound hole is 1 unit and the small sound holes 0.5 unit. The centreline of the small sound holes is distance B from the widest part of the sound board which is also half the distance from the widest point to the bottom edge of the sound board. The spacing of the small sound hole centres is given by R3 and the distance between sound hole centres R4 is equal to the radius of the arc connecting arcs R1 and R2 to form the profile of the lower sound board. The centre of the arc described by R4 is quickly found - by trial and error - using dividers.

Next to examine the geometry of some old Turkish ouds from their images.

Napoleon Bonaparte commissioned publication of the monumental and historically important "Description de l'Egypte" in 1802. Containing 3000 illustrations and 837 copper-engravings the work employed 400 engravers for a period of 20 years to complete.
Among the engravings are two pages of musical instrument illustrations. The first shows "Instruments orientaux a cordes connus en Egypt" including a 7 double course oud and its case as well as long necked lutes of the Saz (?) family. So these were all instruments known in Egypt by the late 18th C (but were not Egyptian).
The second page illustrates "Instruments a corde qui paroissent propres aux Egyptiens" or stringed instruments that seem to be peculiar to the Egyptians. No ouds or oud like instruments are included on this page.
How could this oud - a 'foreign' instrument - come to be known in Egypt? Well it should be noted that in 1517, Egypt - under the governance of the Mamelukes since the mid 13th C - became a part of the Ottoman Empire that had spread by the early 17th C as far as Algeria to the West. This might support speculation that the type of oud represented in the engraving had been introduced from countries further to the East such as Turkey, Persia or Syria?

The engraving of the oud on the first page is interesting - rather quaint in appearance compared to a modern oud. At first glance it would seem that the engraver has not represented the instrument in its correct proportions. However, as the engravings in 'Description de l' Egypte' are of the highest quality it must be assumed that this representation of an oud is quite accurate in most respects. So what are the 'unusual' features compared to a modern oud?
A) - the peg box is straight sided (like a lute).
B) - the neck joint is not vertical but is slanted and not covered by a 'bracelet' (like a lute).
C) - the bowl (judged from the perspective view) is not semi circular in cross section but seems to be deeper from mid point to the neck block.
D) - the rosette is set flush with the surface of the sound board or may be 'cut in' (like a lute).
E) - the relative positions of the large and small rosettes suggests that there is no brace located immediately under the rosette as is normal with both oud and lute but with one exception - the 15th C lute drawing by Arnault de Zwolle.
F) - the pick (or plectrum) guard is 'unusually' large, covering the entire area between bridge and rosettes.
G) - the bridge is of an 'unusual' design - shaped like a mustache but a design not found on other Type 1 geometry ouds of the late 19th C/ early 20th C ouds. Interestingly this style of bridge can be found on some present day Turkish ouds. The upturned ends of the bridge is typical of lute bridge design.

The Arnault de Zwolle lute has only 3 braces. One at the top of the sound hole and two about mid way between the bridge and rosette. There is no brace located below the bridge - only a large tail block with its inside edge located at 1/3 distance from the bottom of the bowl to the front edge of the bridge (This is where the below bridge bar on more modern ouds is located)

Next - to compare this representation of an oud with the old oud in the Brussels M.I.M. collection #0164

The Brussels M.I.M. oud #0164 is an interesting instrument.
It bears a very close resemblance to the engraving of an oud in Napoleon's "Description de l'Egypt" in all major respects. Could it even have been the actual model used by the French engraver at the end of the 18th C - given that the engraving contains some practical simplifications such as single rather than double courses (both instruments have 7 double courses)?

The low resolution images provided for this analysis - courtesy of the Brussels Musical Instrument Museum - nevertheless make the similarities clear enough. Here we see an oud with a straight sided peg box, neck joint cut on a slant with no 'bracelet', a bowl that is not semi circular in section, a 'cut in' rosette, closely spaced small rosettes that make the fitting of a brace (4 mm wide) immediately below the large rosette impossible (it must be located below the small rosettes instead), a large pick guard that extends from bridge to the small rosettes and a 'mustache' style bridge. Note also that the design of the small rosettes is a six point star motif in both cases.
Although the resolution of the images is not sufficient to be absolutely certain, the peg heads seem to be almost identical in design.

The half sound board overlay demonstrates that the deep bowl section is not semicircular. Modern lute makers once assumed that lute bowls should be made perfectly semicircular in section but few, if any, surviving lutes, in fact, have semi circular section bowls. The same may apply to historical ouds.

The absence (or otherwise) of a brace just below the rosette needs to be verified by examination of the original oud. There is no obvious sign of a brace in the rosette images.

Next to look at the geometry in detail.

The Brussels #0164 oud is an example of Type 1 geometry - the profile of the upper half of the sound board being described by an arc of radius equal to the maximum width of the sound board.

The geometry of the oud is somewhat similar in many respects to that of the Type 1 Christoffolo Hoch lute previously posted which incorporates an ancient geometrical shape of sacred significance in many cultures - the so called 'Vesica Piscis ("fish bladder").

A Vesica Piscis is created when two circles of equal diameter intersect - the centre of one of the circles being located anywhere on the circumference of the other. This produces an 'eye' or almond shape (also known known as 'mandorla' in Italian = almond nut ). The attached image shows the construction of a Vesica Piscis.
It can be readily proven that if the minor axis of the Vesica Piscis is one unit then the length of its major axis is the square root of 3 = 1.7320508 .......

The sound board profile of the Brussels oud is part of a Vesica Piscis (V.P.). If a smaller V.P. is created inside this profile with its minor axis of length equal to 2 units (or half the maximum width of the sound board) then the top of the V.P. (point B) is locates the top of the sound hole and the bottom of the V.P. is the location of the bottom of the sound board. The front edge of the bridge is located at 1 unit from the bottom of the sound board or 0.7320508 Unit from E, centre of the widest part of the sound board.
It is not possible to be absolutely precise when working with this low resolution image of the oud (and there is also some of the inevitable asymmetry of the original instrument to take into account). However, this is my preferred solution (A) in the absence of a higher resolution image being available. A very close alternative solution (B) for locating the front edge of the bridge is to use a 3:4:5 triangle (as proposed on some of the geometries previously posted). This gives a slightly greater distance from the bridge to point E of 3/4 Unit or 0.750 Unit (about 2.5% difference).

The proposed geometry is as follows:
The maximum width of the sound board is 4 units and the half profile of the upper sound board is described by an arc of radius R1 (4 units) with centre at X. Drawing a Vesica Piscis
2 units wide with centre at E defines the top of the sound hole, the bottom of the sound board and the front edge of the bridge. The curve of the bottom of the sound board (point G) is described by an arc of radius R2 with centre at A.
Dividing the distance from E to the top of the sound hole B into 3 equal parts gives the bottom of the sound hole at 1 part from E and the sound hole centre at 2 parts from E. The profile of the lower part of the sound board is described by an arc of radius R3 equal to the distance EC - its center quickly found by trial and error, using dividers, to blend in with arcs R1 and R2.

The diameter of the rosette (not the sound hole - an important detail) is 1/3 the width of the sound board measured at the centre of the sound hole.
All a bit complicated to put into words but the attached diagram of the geometry should make it clear.

The geometry of the sound hole/rosette will be examined next.

The rosette of the Brussels #0164 oud is cut directly into the sound board like a lute rosette - unlike a modern oud where the rosette (Shamsa) is separate and glued behind a circular sound hole.
The sound hole in a lute rosette is the diameter of the open area of the rosette pattern that may be less than the overall diameter of the rosette. This is the case with the Brussels #0164 oud - the whole area of the rosette being stained a dark colour.

With the usual caution about working with reduced scale, relatively low resolution images, the overall diameter of the rosette is 1/3 the width of the sound board measured at the centre of the rosette. The sound hole diameter, however, is equal to the distance EC (see Proposed Geometry image previously posted) - less than 1/3 sound board width.
(Interestingly, Arnault de Zwolle states that the sound hole diameter of his lute is 1/3 the width of the soundboard yet his geometrical construction results in a sound hole that is of smaller diameter than this).

The geometrical relationship of the large and small sound holes appears to be that the diameter of the open area of each small sound hole is 1/4 the diameter of the large sound hole. The centres of the small sound holes are spaced equal to the large sound hole diameter with the distance from the main sound hole centre being determined by a 3:4:5 right triangle construction.

The complicated looking rosette pattern is very simply constructed using a pair of dividers set to a fixed radius of 1/6 sound hole diameter.
Step 1 is to describe a circle for the centre of the rosette. The dividers are then used (at the same radius setting) to divide the circle into 6 equal parts. The 6 intersection points on the circumference then form the centres for another series of circles (of the same radius) - see Step 2 - and so on to complete the pattern.
This construction results in a complex of intertwined Vesica Piscis figures - confirming, perhaps, the overall theme of the oud geometry?

A series of supplementary half radius circles is used to create small 'cross links' in the pattern - best made clear by the attached sketch of the rosette pattern.
The six point geometry of the main rosette is reflected in the six point pattern of the small rosettes.

So, if the geometry proposed here is valid, then this rather roughly made example of an oud may represent a simple yet sophisticated design - based upon ancient geometry - requiring only a pair of dividers and a straight edge ruler to construct.

Quote: Originally posted by jdowning

The attached rough sketch of a Nahat bridge cross section compared to a more 'conventional' traditional oud bridge is intended to clarify the dimensional difference between the front edge of the bridge and front edge of the bridge tie block. It would seem that the Nahat design imposes a greater rotational torsion on the sound board - string tension being equal.

Brussels oud #0404 is quite different in geometry from oud #0164 yet both are designated as 'Egyptian' by the Brussels Musical Instrument Museum. Neither Type 1 nor Type 2 geometries generate the required narrower elongated profile or the relatively smaller sound hole diameter.
Like oud #0164 the bowl is not semi circular in section but is considerably deeper - particularly around the widest part of the sound board.

This profile is reminiscent of the oud arbi once common in Morocco and Tunisia. The oud arbi has a number of lute like features - relatively long neck, fretted and with cut in rosettes. It has four courses and speculation has it that it may represent a design of oud that originated in Moorish 'Spain' - at a time when ouds were fretted and carried four courses.
The attached image is of a Tunisian Sheik with an oud arbi. As far as can be determined from this photograph the profile of this instrument and the Brussels #0404 oud are practically identical.

In order to generate the profile of the upper part of the sound board the maximum width of the sound board is divided into four equal parts or units. The upper sound board profile is an arc described by R1 (6 units in length) with its centre at Z - 4 units from the sound board centre line. The lower sound board profile is semi circular described by R2 (2 units long or half the sound board maximum width).
The centre of the sound hole C is located at the intersection of arcs described by R3 (2 units in length - i.e. half a vesica piscis).
The diameter of the sound hole is 1 unit or 1/4 maximum sound board width.
The front edge of the bridge is located by means of a 3:4:5 right triangle - dimension '4' being 1 unit in length (so it follows that dimension '3' is 3/4 unit).

So far 3 distinct geometrical profiles have been established - designated in this thread as Type 1, Type 2 and Type 3 that define upper sound board profiles. Lets take this a step further.

The basic assumption throughout this investigation is that the ancient luthiers generated their oud and lute geometries not by application of complex mathematics but simply - employing only a pair of dividers and a straight edge and using whole numbers 1,2,3,4,5 ... etc. or fractions comprised of whole numbers (harmonic proportions).
This assumption has been verified so far in the Type 1, 2 and 3 geometrical constructions that define the upper sound board profiles. (The lower sound board profiles on the other hand can vary from a simple semi circle to a more complicated 'flattened' shape generated by blending arcs of different radii).

Logically, the upper sound board profiles can be increased in relative length by increasing R1 by one unit at a time to produce Type 4, Type 5 ... and so on.

The attached image is a sketch showing the variation of profile with R1 increasing in length in steps of 1 unit. The lower sound board profile is drawn as a semi circle for simplicity.

In order to examine this possibility further let's next look at some examples of surviving lutes.

The 14th C Persian Kanz al-Tuhaf manuscript gives the overall dimensions of an oud that do not make much sense in that they describe an instrument that is proportionally very long yet pencil thin. This apparent anomaly has been attributed to scribal error in recording the ancient measurements. In article #32 in the Galpin Society Journal, May 1979, Curtis Bouterse proposes corrected dimensions that produce a more reasonable looking oud.

The attached geometry has been drawn according to the dimensions proposed by Bouterse (and assuming a finger unit is equal to 2.25 cm as given by Farmer).
Bouterse does not propose a profile of the upper part of the sound board (the lower part is assumed to be a semi circle).

However, assuming that the width of the neck joint is about
45 mm (2 finger units) for a 5 course oud and that the upper sound board profile is a simple circular arc described by radius R then - if the sound board is 4 basic units wide (or 15 finger units) - an R equal to 8.53 units connects the widest part of the sound board to the neck joint very closely.
Note also that if the neck length is extended to accommodate 7 frets (as it would be for a European lute of the late 15th/early 16th C) R becomes equal to 8 basic units making this a Type 5 geometry.

A crude drawing of an oud in the Kanz al-Tuhaf confirms this elongated almond shape - one that clearly represents a distinct transition at the neck joint unlike many early representations of early ouds (and mediaeval lutes) in the iconography where there is a smooth transition from the bowl profile to the neck.
The attached images of early Sassanid (Persian) metalwork 6th/7th C show the early style of oud without neck joint.
For comparison the oud represented on a 12th C. ivory box from the Iberian Peninsula ('Spain') shows a five course oud with the same early general profile with no neck joint (? but hard to say for sure). Note the 'mustache' style bridge located close to the widest part of the belly and semi circular profile of the lower part of the sound board.

The string length of the Kanz al-Tuhaf oud - deduced from the measurements given in the manuscript (again using Farmer's value for a finger unit of 2.25 cm) - is 67.5 cm.

(Post revised and updated 22 March 2011)

The renowned German luthier Laux Maler was active in Bologna, Italy during the first half of the 16th C. There are only 5 surviving examples of his instruments - non complete only fragments and altered originals. They all have an elongated almond shaped profile. Surviving lutes by Maler's contemporary Hans Frei also have identical profiles.

The attached image is an example of a lute bowl by Maler in the Victoria and Albert Museum in London. (Note that the 'neck' and 'sound board' have been added for display purposes only and may not necessarily represent the original relative proportions of the lute neck, sound hole and bridge size and placement).

Working from a full size drawing of an original Maler lute sound board (#M.1.54 in the Germanisches National Museum, Nurnberg, Germany) the attached diagram gives a proposed geometry for the original instrument.
The construction is self explanatory. The maximum width of the sound board is 4 equal units and radius R1 of 2 units gives the position of the centre of the sound hole and the bottom of the sound board. The sound hole diameter is 1 unit and the front edge of the bridge is placed at 1/4 YZ the distance from the bottom edge of the sound hole to the bottom edge of the sound board Z. (Distance YZ = 3.5 units).

The profile of the upper part of the sound board is an arc described by R = 8 units (i.e. a Type 5 geometry). The profile of the lower part of the sound board is a blended combination of arcs generated by R, R2 and R3 = 1.5 units.

The attached image is a reconstruction of the Maler lute that I made some years ago based upon the M.1.54 lute sound board geometry. This has been made with a neck of sufficient length to accommodate 8 frets - as would have been commonly found in the second half of the 16th C. This results in a string length of 73 cm. However, new evidence now suggests that the original lute may have had a shorter neck than this - sufficient for 7 frets - and a string length of 67.5 cm.

(Post revised and updated 22 March 2011)

A preliminary examination of 2 full sized drawings of lute sound boards by Laux Maler (Prague National Museum # 65 4408E and # 6551931D both modified from their original state) are both Type 5 geometry and similar to the construction previously posted for the #M.1.54 lute. Sound hole diameter, however, is 1/3 the width of the belly measured through the centre of the sound hole.
Examination of full sized drawings of surviving lute sound boards by Hans Frei - Maler's contemporary in Bologna - #67/1965 in the Warwick County Museum and another (unknown cat. number) in the Kunsthistorisches Museum, Vienna (both modified from their original state) again are
Type 5 geometry and closely follow the Maler design.
These four examples will be examined in more detail at a later date.

Maler lutes were later prized in both the 17th and 18th C fetching very high prices even in poor condition.
Thomas Mace writing in 1676 gives two examples of Maler lutes ("pitiful old battered and cracked things") costing 100 pounds sterling - an enormous sum of money in those days.
Ernst Gottlieb Baron writing in 1727 mentions lutes by Maler and Frei that in his time still "commanded very high prices because they are rare and have a magnificent tone" However this is not the whole story as to why these old lutes continued to be in demand 175 years after the death of their makers. E.G. Baron inadvertently gives the reason in his observation that "it is remarkable that they (i.e. Maler and Frei) were working in today's fashion" However, it is obvious that this style of lute attributed to Maler and Frei was in fact the style copied by the luthiers in the late 17th and early 18th C. if original Maler and Frei lutes were not available for conversion into the 11 or 13 course lutes of the time.
If this is the case then the surviving lutes from that period will also be of Type 5 geometry like the Maler and Frei lutes of the early 16th C. More on this later.

For information I attach an article written in the 1970s that shows how this type of 16th C lute was converted in later years to suite contemporary music styles.
Note also that Maler and Frei made lutes of other geometry than Type 5 - but none have survived to this day.





Attachment: MF Lutes 2.pdf (594kB)
This file has been downloaded 574 times

So the early 16th C 'long string length' ouds of Maler and Frei survived because they were not only outstanding examples of fine luthier craftsmanship but also were suitable for conversion into the 'long string length' (around 70 cm stopped string length) 11 and 13 course lutes of the second half of the 17th C and first half of the 18th C.

Here are three representative examples from the iconography that illustrate fairly accurately some of the Type 5 geometry lutes popular in the late 17th C.

The first is an engraving from "Livre de Musique pour le Lut" made by the author Sr. Perrine in 1682 - an 11 course French lute.

The second is a painting "The Lute Player" by Flemish artist Hendrick Maertensz Sorgh in 1661 showing a lute with extended bass courses.

The third is the well known painting of French lutenist Charles Mouton by artist Francois de Troy, 1690, in Le Louvre, Paris. The lute depicted is an 11 course French lute.
It is interesting to observe that the rosette - given the low resolution of the image - seems to be of the distinct pattern found on surviving Laux maler lute sound boards. The attached rosette pattern is copied from the converted Maler lute #65 1408E in the Prague National Museum.

Note the proportionally small diameter rosettes in all cases.

Another note for interest. The 'banding' around the edge of the sound board in each case is most likely a strip of parchment (thin leather membrane) glued in place to reinforce and protect the edges against damage and wear. Thomas Mace calls this parchment strip a "lace" and describes, in detail, the procedure for removing and replacing it when a sound board has to be removed for repairs (something that was regularly required in those prevailing humid conditions in 17th C England).
It is also interesting to observe that this method of sound board edge reinforcement was also used on some ouds like the oud arbi (and my old 'Egyptian' oud) - although the leather strip usually only covered the lower half of the sound board edge.

In this search to find examples of comparable geometry of old ouds and lutes, the maximum radius of the upper sound board profile found to date is in the proposed geometry of an oud given by the 14th C Persian Kanz al-Tuhaf with an R value of 8.53 basic units (maximum sound board width being 4 basic units).

In Europe, a small lute like instrument known as a mandola (larger) or mandolino (smaller) - popular in the 17th and 18th centuries - with gut double courses was played 'finger style' like a lute. (Not to be confused with the later wire string Neapolitan Mandolin). Many of these instruments and their patterns survive in original condition including some of those made by luthier Antonio Stradivari.

I have about 10 full size original Mandolino patterns - traced from the original instruments. The profiles of these instruments vary but include some that are very slim and elongated.
The attached example is an ivory mandolino from the Charles van Raalte Collection, Dean Castle, Scotland that I had the opportunity to examine and measure some years ago. The instrument has a string length of 33.6 - 33.7 cm.

The attached geometry of the full size tracing of the sound board profile shows an upper sound board profile described exactly by an arc of radius R1 equal to 14 basic units.
Radius R2 (2 basic units) defines the bottom of the sound board D and bottom of sound hole A.
The front edge of the bridge from the bottom of the sound board - distance BD - is 1/3 of the distance CD from the centre of the sound hole to the bottom of the sound board. This relationship in turn defines the diameter of the sound hole.
The lower profile of the sound board is modified from a semicircle to a more 'flattened" shape by an arc of radius R3 equal to distance BD.

It is interesting to note that the R value for one of the surviving Stradivarius mandolino profiles is 16 basic units which may be the top limit for lute upper sound board geometry.

Apart from the 14th C Persian manuscript 'Kanz al-Tuhaf' that gives the dimensions of an oud there is the 14th C description of a 4 course oud by the Arab writer Ibn al-Tahhan. This description - like that of the 'Kanz al-Tuhaf - is corrupted due to scribal error in recording of the dimensions. This is discussed in more detail in the post "Ancient Scales of Measurement?" on the Forum.

The corrected dimensions and proposed geometry is shown in the attached image.
It can be seen that the profile of the upper sound board is identical to that of the surviving Maler lutes of the 16th C. The Maler lute geometry previously posted differs in the neck length and the slightly lower bridge position this difference being half a finger unit - increasing string length from 36 to 361/2 finger units. So, is it possible that Maler used the Ibn al-Tahhan oud geometry as a model for this style of lute?
Maler's lute would have required a slightly longer and wider neck - to accommodate 7 frets and six courses. He might have achieved this by lowering the neck joint position by 1/2 a finger unit and then lowering the bridge position by the same amount to give a string length of 36.5 finger units. In order to maintain structural integrity, the length of the neck block would have been maintained (i.e. by adding 1/2 finger unit of material on the bridge side).

Dependent upon the metric value chosen for an ancient 'finger' unit, the string length of the Ibn al-Tahhan oud might have been 67.5 cm using a finger unit equal to 1.875 cm (Stecchini's 'natural' unit).

The width of the surviving Maler M.I.54 sound board is 29.6 cm equivalent to 16 finger units equating to a finger unit equal to
1.85 cm (Stecchini's trimmed finger unit). This gives a proportional string length of 67.5 cm. Interesting!
The bridge position and sound hole diameter of the Maler sound board also agree closely when a trimmed finger unit is used

Ibn al-Tahhan provides no information about sound hole size and position but this, perhaps, might now be deduced from the relative proportions of the Maler lute?

For completeness, the attached image shows the proportions of an oud described by the Ikhwan al-Safa (Brotherhood of Purity) in the 10th C. as well as an image of a proposed development of the geometry that suggests a link to the 19th C ouds of Lebanon and Syria (for example the Type 2 ouds by the Al Arja and Nahat families).
The details are discussed in the topic "Ancient Scales of Measurement?" on this Forum.

The Ikhwan al-Safa oud had four courses "no more no less" and was fretted.

For information.
The proposed rosette pattern of the Brussels #0164 seven course oud, previously posted in this thread, is another very ancient geometrical construction with sacred or mystic meaning in many societies - known today as the "Flower of Life".

One of the earliest representations of this pattern - carved in stone - can be found at the Temple of Osiris, Egypt - said to date to about 3000 BC.
The attached image shows one of a connected pair of "Flowers of Life" - identical to the Brussel's oud rosette pattern. Not to suggest that the oud is that old, however!!

No lutes made prior to the 16th C survive today.

There is an interesting carving in the Lutheran cathedral, Ulm, Germany made in 1470 by Jorg Syrlin the Elder. It depicts 'Pythagoras' playing a six course lute and seems to be rendered with some precision, accurately representing the proportions and geometry of the lute.

Placing the proposed developed geometry of the 10th C Ikhwan al-Safa oud, previously posted, as an overlay on an image of the lute demonstrates a remarkable agreement between the oud and lute geometries. Both are Type 2 sound board profiles with a semi circular lower part.
The lute has six courses (compared to four on the oud) so the lute neck joint has been placed lower (towards the bridge) to make the fingerboard wider. The lute fingerboard has also been extended at the nut end sufficient to increase the total fingerboard length to just accommodate 8 frets (common during the 16th C).

From the oud geometry the string length is 27 units and sound board width is 16 units so if an average value of 2cm is taken for a 'finger width' the string length becomes 54 cm and sound board width 32 cm. neck joint width is 4cm at this scale. Note also that the distance from the bridge to the widest part of the sound board (X axis) is 3 'finger' units - exactly the distance (3 'asabi') given by Al Kindi writing in the 9th C.

For comparison see the proposed geometry of ALAMI's 19th C
Al Arja oud posted at the beginning of this thread. A more detailed analysis of the geometry of this oud has been published in FoMRHI Quarterly No 116, August 2010. Comm. 1911.

http://www.fomrhi.org

I came across another image of the Brussels #0164 0ud today. Taken from another angle it confirms that the 7th course runs outside the fingerboard so is only played 'open' and not 'stopped' on the fingerboard.
It also shows that the bridge is not drilled for the strings but is slotted in the way that early guitar and vihuela bridges were made during the 16th and 17th C.

'Libro de los juegos' (Book of Games) by king Alphonso X of Castile (1221 -1284) contains this illumination of three ladies playing chess - one also playing an oud (how does she do that?!).

Like the Brussels oud , the oud depicted has a straight sided peg box. Another connection with Moorish 'Spain' perhaps?

Quote: Originally posted by jdowning

The second oud geometry is that of the Al- Arja oud that compares closely with a late 15th C carving of a lute in Ulm Cathedral, Germany.

I'm interested in knowing more about this geometry.

Are there other ouds besides the Al-Arja oud using this layout for the bowl?
Based on your analysis breakdown of the pattern, there seems to be only two radii to complete the bowl. Is this a simplfied version of the Arnault de Zwolle example?
Would this be considered the most elementary pattern for a lute?

This seems to be using the same pattern. I assume early lutes used the semi-circular, two radii pattern for their layout.

It is likely that both early oud and lute makers designed their instruments from first principles based upon Euclidean geometry - using only a compass and straightedge - and a belief in the proportions of universal harmony.

The sound boards of some of the earliest surviving lutes still bear the scribed layout marks of dividers used to determine bridge and bracing layouts.

The attached images (copyright of the Trustees of the British Museum) are of the well known late 16th C engraving of renowned luthier Gaspar Duiffoprugcar (Italianate name of the German Tieffenbrücker family of lute makers) showing the variety of instruments made by this maker. Note the prominent display of a pair of dividers in the maker's hands - clearly an important tool for this 16th C luthier.

For information, the Latin text at the bottom of the engraving translates as :

"I was alive in the forest; I was cut down by the cruel axe; In life I was silent; In death I sweetly sing"

- referring, of course, to the wood from which stringed musical instruments are made.

Like many artists, architects and craftsmen of his time the famed 16th C German artist Albrecht Dürer (1471 - 1528) sought methods for producing various geometrical forms. Dürer published four books on geometry the " Underweysung der Messung ..."

The true ellipse shape is not easily created using just dividers and a straight edge. The asymmetric form of an ellipse is egg shaped and so was of particular interest to the artist and craftsman.

The attached image (#34) by Dürer shows the construction of a true ellipse derived from the section of a cone. Dürer, however, was confused in thinking that this construction should form an egg shape (wider at the bottom than the top).
However, just as eggs in nature can range in shape from almost a sphere to an elongated profile, oval shapes are not precisely defined like an ellipse. An oval shape can be easily created using just a compass and straight edge by smoothly blending together a number of simple arcs. Indeed it is possible to replicate a true ellipse profile very closely with an oval construction - hence, no doubt, Dürer's confusion.

The attached image is one example given by Dürer of an oval shape. Note how 'lute like' the shape is - indeed the proportions are almost identical to those given for an oud in the 9th C by Ikhwan al-Safa.
Trying to accurately create a lute upper sound board profile as a true ellipse is complicated. Creating an oval profile, on the other hand, is simple and so is perfectly adapted for describing an 'elliptical like' lute sound board profile using only compass and straight edge.

This upper sound board profile is well adapted for a late
16th C lute with wide neck carrying up to 10 double string courses but looks distinctly odd and out of proportion if a narrow neck is attached as in the Arnault de Zwolle lute. And so would likely also look out of place on a Mediaeval oud

Lets look next at some other oval constructions using Euclidean geometry.

There are many methods used to construct oval shapes based upon intersecting arcs with tangents in alignment.

The attached image is just one example based upon three intersecting circles of equal radius (forming two so called 'vesica pisces'). The construction is very simple and self explanatory.

This form of an oval matches that of the frame used by the original engraver - Pierre Woeiriot, 1562 - of Gaspar Duiffoprugcar's portrait previously posted.

An even simpler example of an oval construction based upon two intersecting circles of equal radius to produce a 'vesica piscis' (see previous postings for details) - a form regarded by many ancient societies as having sacred significance.

The attached image shows the geometry. Simple and quick to construct this oval was recommended for its beautiful proportions by 16th C architect Sebastiano Serlio in his publication "Tutte l'Opere d'Architettura".

A 'Vesica Piscis' profile itself can also form the basis of an asymmetric oval as shown in the attached image. Again the construction is straightforward and - lo and behold - this is the construction used by Arnault de Zwolle in the mid 15th C for his lute.

About a hundred years earlier an engraving of an oud - included in a late copy of Kitab al-Adwar by Safi al-Din - uses the same construction but without the rounding of the top part of the sound board at the neck joint.

Arnault de Zwolle's lute with its narrow neck looks odd while Safi al-Din's oud looks to be correctly proportioned for both an oud and lute of the late Medieval period - to judge from the iconography of the time.
So was Arnault de Zwolle working from incomplete information (or memory) having seen an oud and assumed that the profile should (ideally) have been egg shaped? Or was the European lute an instrument developed quite independently from the oud? After all a lute does look similar to an oud so perhaps has been assumed by historians to be an instrument derived directly from the oud through some kind of Darwinian 'origin of the species' theory applied to musical instruments. If so, where is the concrete evidence in support of this thesis?

The attached image is of a late 16th C lute by German maker Michielle Harton , working in Padua, Italy, illustrating the 'ellipse like' profile of the upper sound board that distinguished the design of many surviving lutes of this period - e.g by the German Tieffenbrücker family of luthiers.

Although some researchers claim that the upper sound board profile of these lutes is a true ellipse (as they may well be) creating an elliptical profile to fit a particular instrument size is not a straightforward procedure.
The question, therefore, is did the luthiers of this period use a simpler procedure to produce a very close approximation to an ellipse (i.e. an oval) using only dividers and a straightedge?

This theory will now be tested using as reference some full size museum drawings of surviving lutes of the late 16th C. that I have on file.

Another related question - addressed to forum members. Are there any surviving old ouds that appear to have the same or similar upper sound board profiles to these lutes?

Quote: Originally posted by jdowning

So was Arnault de Zwolle working from incomplete information (or memory) having seen an oud and assumed that the profile should (ideally) have been egg shaped? Or was the European lute an instrument developed quite independently from the oud? After all a lute does look similar to an oud so perhaps has been assumed by historians to be an instrument derived directly from the oud through some kind of Darwinian 'origin of the species' theory applied to musical instruments. If so, where is the concrete evidence in support of this thesis?

The image of this late 16th C lute by Michielle Harton is interesting in the proportions that appear to divide the string length into the 'classic' oud proportions - the distances nut to neck joint, neck joint to centre of rosette, centre of rosette to front of bridge all being equal (each being 1/3 string length). So the fingerboard is only of sufficient length for 7 frets in the Western 12 tone Equal Temperament tuning. This is unusual for a late 16th C lute where a longer fingerboard sufficient for 8 frets was the norm.

Note also the proportion of rosette diameter to sound board width (at the rosette centre) which is a third of the width - i.e. the proportion given by Arnault de Zwolle.

The upper sound board profile appears - from the low resolution image - to have been created not as a true ellipse but as a composite of two arcs one of radius equal to twice the sound board width blended with an arc of radius equal to the sound board width - a very straightforward geometrical construction it would seem. This method of construction will next be checked more accurately against a full size drawing of another lute by this maker.

The string length of this lute is 65 cm (10 courses) so scaling from the image gives a body width of about 35.4 cm.

It is possible that the neck of this lute may have been shortened at some time (judging from the finger board inlay?) but this is not certain. The proportions otherwise are pleasing to my eye.

There has been insufficient time to undertake an in depth analysis of some of the late 16th C Harton and Tieffenbrucker lutes. However, it would appear that so far the upper sound board profiles of lutes by these makers might be oval (rather than elliptical) and so easily constructed using dividers and a straight edge.

Analysing the image previously posted of a lute by Harton indicates that the attached geometrical construction might apply (within the accuracy than can be achieved with the relatively low resolution image).

As with all of the oud and lute profiles so far examined, the upper and lower sound board profiles may be separately constructed.

In this case, the upper sound board profile is produced by blending together two arcs R1 of radius 8 units and R2 of radius 4 units. In order to blend smoothly together the tangents must coincide at a chosen point X. Here X is located by R1 passing through the centre of the sound hole C but there may be other alternatives - the most straightforward solution being as shown in the attached sketch.
Here a radius of R equivalent to 1 1/4 units (or 9 'Finger' units) gives a location of X that is a very close alternative to that given by a line passing through the sound hole centre.

The lower sound board profile - in this case - is produced by blending three arcs of radius R3, R4 and R5. The geometry should be self explanatory.

The proposed geometry of another lute by Harton is shown in the attached image - this time derived from a full size drawing of the instrument (by luthiers Miranda and Stephen Murphy in 1975). The lute was made in 1599, Padua, Italy and is artifact #1808 in the Bologna Museo Civico.
String length is 69.7 cm and the fingerboard length is the same as the distance between the neck joint and centre of rosette. The bridge is roughly made and so may not be original and is placed midway between the widest part of the sound board and the bottom of the bowl which may not be exactly the original position.

The geometry is self explanatory. The upper sound board profile is an oval created by arcs of radius R1 and R2 equal to 7 and 4 units respectively - point X being determined by an arc of radius 2 units. (R1 in this case passes very close to the centre of the rosette C).
The lower sound board profile is created by blending arcs of radius R3, R4 and R5 - R5 being the distance CD from the centre of the rosette to the widest part of the sound board.

Looking at another original lute from the late 16th C - made in Padua by renowned luthier Wendelin Tieffenbrucker (a.k.a. Wendelio Venere). This is a little Descant lute - 7 courses string length 44.1 cm.
The attached image of the lute is rather old and of poor quality. Note that the neck should be fitted with 8 frets not 6 as shown.

Working from a full size drawing by luthier Stephen Murphy it can be seen from the proposed geometry in the attached image that - like the contemporary Harton lutes (also made in Padua, Italy) - the upper sound board profile is oval created from two contiguous arcs radius R1 and R2 equal to 7 and 4 units respectively. (Note that 4 units is equal to the sound board maximum width or - if preferred - 16 'finger' units).
Contiguous point X for the arcs is determined by R equal to 2 units.

The lower sound board profile - in this case is made by blending three arcs R1, R3 and R4 - R4 being equal to the distance from the centre of the rosette to the widest part of the sound board CD.
The bridge (probably not original?) is located midway between the widest part of the sound board and the bottom of the bowl.

The distances from neck joint to sound hole centre NC and sound hole centre to bridge CB are equal and so conform to the traditional division of the string length of an oud into 3 parts. However - in this case - the neck has been increased in length to accommodate 8 frets, typical for a lute of this period.

For those who may be interested - a complete facsimile of a first edition of Albrecht Dürer's 'Underweysung der Messung ...." of 1525 (previously reported in this thread) is available for viewing in high resolution on line or for free download (page by page) at

http://www.commons.wikimedia.org/wiki/Category:Underweysung_der_Mes...

Or alternatively there is an original first edition of the book for sale from booksellers 'Buddenbrooks' of Boston for a mere $52,250 (plus $14 shipping and handling!).

The book is written in old German and comprises 4 books in one volume - dealing with aspects of Euclidean geometry of practical use for artists, architects and artisans.

It is said that Dürer was confused about the shape of an ellipse by incorrectly referring to it as egg shaped. However, on reading the original text of Underweysung, what Dürer actually says about an elliptical curve is "Die Elipsis will ich ein eyer lini nennen/darumb das sie schner einem ey gleich ist" or "I will call the Ellipse an 'egg line' because it is very nearly the same (shape) as an egg". He does not say that the ellipse and egg shapes are identical only that they are very nearly the same. Furthermore he correctly names the ellipse shape, on the page describing its construction, as "the ellipse line" - so there is no confusion in Dürer's mind at all.

Dürer earlier in Book 1 also describes the construction of an oval or egg shape (see previous posting on this thread). To test the validity of Dürer's claim the attached image is his construction of an oval on which I have placed an overlay of a true ellipse (quadrant) - the shape marked with little x's.
From this it can be seen that the match is indeed a close one. The significance of this is that an almost perfect elliptical curve can be simply created from a series of arcs of a circle using only dividers and a straight edge - which is most likely how the lute makers of the late 16th C determined the upper sound board profiles of this kind of lute.

I have yet to find images of any ouds of this particular shape so - if the European lute was developed from the Medieval oud - this may be the point in time at which the two instruments finally went their separate ways from a design point of view?

Here a late 19th century Kuitra from Morocco.

John,The lute is in the collections of the Stockholm Music Museum The photos I got about 10 years ago when I asked about the lute after becoming aware of its existence in a book from 1928. Unfortunately I had no more information about the lute than it was from Morocco. It is not on display as well as many of the most interesting instruments. I know many lnstrument has been damaged due to poor storage and some ten years ago there was a TV program that showed a lot of destroyed cracked instruments.
The decorations at the bridge is made of cloth and probably edge decoration as well. I have seen identical decorations on other Kuitras.

An interesting old Syrian oud owned by Yair Dalal is currently undergoing restoration by Yaron Naor.

Although details of the proposed geometrical construction has already been posted on Yaron's thread 'Repairing a "Nahhat" oud' it is appropriate to include the geometry as part of this thread - for comparison with what has already been posted.

The attached image of the geometry is largely self explanatory but more details can also be found on Yaron's thread.

Note that the geometry is based upon a 3:4:5 Pythagorean right triangle and that the profile is an oval in construction - created from conjunct arcs of a circle - similar in concept to some of the old surviving lutes of the late 16th C as previously detailed on this thread.

Note also that the entire geometry is created using only a straight edge and dividers - no measurement with a ruler being required although the luthier may have taken an ancient Persian measure of a 'finger' (28 fingers to the cubit) as a starting point for creating the design (1 unit = 4 'fingers').

For those interested in some of the history behind ancient units of measurement that may have influenced oud and lute design I attach a copy of a recent article written for FoMRHI on the subject " Ancient Metrology, Ibn al-Tahhan and the Maler and Frei Lutes"






Attachment: FoMRHI Comm Ancient Metrology.pdf (839kB)
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.... and here is the proposed bracing geometry.
See "Repairing a 'Nahhat' oud" for more detail.

Lute 651408E by Laux Maler has been converted during the 17th C from its original 5 or 6 course state to an 11 course instrument by replacement of the neck. The additional extra width of the fingerboard at the neck joint (without increasing the depth of the neck) being achieved by re-cutting the neck block joint to a shallower angle (relative to the fingerboard surface).

Referencing a full size drawing of the instrument by luthier Stephen Murphy that shows the sound board profile of the lute, the longitudinal bowl section as well as two cross sections of the bowl - the attached images indicate that the bowl has a slightly flattened semicircular cross section - similar to the Frei #C34 lute geometry previously posted.

Note that there is no perfect symmetry of the bowl due perhaps to slight distortion of the original bowl geometry over time following repairs/modifications etc.

The full size drawing of the Laux Maler lute in the Prague National Museum # 655 1931 that I have on file appears to have a draughting error but I shall post the results nevertheless for information. The drawing shows two bowl sections - one at the widest point of the soundboard and the other at the soundhole centre - and a bowl longitudinal profile. Unfortunately, the bowl section drawn at the rose centre does not match (in height) the drawn longitudinal profile of the bowl. As the bowl sections appear to be semicircular - modified with additional height (max. soundboard width section) and height reduction at the soundhole centre (see attached sketches drawn to scale) I have adjusted the bowl longitudinal profile accordingly assuming the sound hole centre bowl section has the offset shown.

I do not have full frontal and side images of this lute to verify these assumptions so these would have to be independently checked out. However, the soundboard profile relative to bowl longitudinal profile appears to be close to the Vienna #C34 Frei lute previously reported.

Precise measurement of a surviving lute or oud (from first hand experience!) is a time consuming process. Capturing the sound board profile accurately is straightforward enough - just (carefully!) trace around the instrument inverted on a sheet of card. Determination of the bowl geometry is another matter and requires an apparatus that will allow plotting of the bowl surface in 3D - a relatively simple apparatus to design but a time consuming procedure to execute and record the data. Usually, however, time is of the essence when it comes to measuring museum artifacts and in the rush to record information errors can be made or important measurements missed - the omissions only discovered at a later date (but too late) when trying to create a drawing from the recorded data.

Just to complicate matters, most if not all of the surviving instruments are rarely of perfectly symmetrical geometry (if they ever were in the first place).

What is interesting - for the earliest surviving lute bowls at least - is that the bowl sections (if correctly represented in a drawing) appear to be based on a semicircle with extra depth added to increase the bowl depth or subtracted to produced a more 'flattened' section (the 'Warwick' Frei lute composite profile, previously reported, not withstanding).

However, lots of scope for error - so beware!

First to examine the small descant lute #C39, by Wendelio Venere in the Kunsthistorische Museum, Vienna. This lute has seven courses with a string length of 441 mm. date thought to be circa 1600.

The full size drawing that I have on file shows only one bowl section at the widest point of the sound board. Nevertheless, as the neck joint is drawn in longitudinal section it is likely that the bowl section at this point is a complete semi circle. Not so, however, at the widest point of the bowl where the section is a flattened semicircle of radius AB with centre at A offset by about 7mm - as shown in the attached image.

The proposed longitudinal profile of the bowl compared to the sound board profile is as shown in the attached image. Maximum offset at the clasp end of the bowl is about 9 mm.

Here the flattening of the semicircular bowl section is similar to lute #C34 by Frei in the collection (previously posted).

Let's next look at another example by the same maker.