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ALAMI
Oud Junkie
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Designing a Golden Mean based oud
Let me start by saying that I am not an amateur of all that Golden Mean / Fibonacci serie esoteric mania, but I agree with the assertion that there is
an aesthetic side related to the golden proportion (some call it the divine proportion)and the beauty of the underlying math.
It all started with a very interesting article I read recently :
The Foundations of Scientific Musical Tuning by Jonathan Tennenbaum:
http://www.schillerinstitute.org/fid_91-96/fid_911_jbt_tune.html
This made me go back to an old book I have discussing the Golden Mean and I was struck by the Fibonacci spiral, I saw it as a oud bowl and I was
wondering if oudmakers have used the golden calculation in their oud designs and then I remembered an old thread on these forums about a mysterious
sign on some of Manol's ouds.
http://www.arabicouds.com/messageboard/viewthread.php?tid=5788&...
I think that it is a Greek "PHI" and it means (just a theory) that the oud with a phi is designed according to the Golden Ratio. PHI is the symbol of
the Golden Ratio (le nombre d'or) and it is attributed to PHIDIAS who designed the parthenon.
That's how I decided to start a new oud design based on the Golden Mean.
All I know about oud making is limited to what I read here (the projects of Jameel, Riad, Jonathan and the others) I also have Dr Oud book and I have
talked with some lebanese oudmakers (Nazih Ghadban and Fadi Matta)
With this kind of "virtual" knowledge it is safer to start with "virtual" oudmaking, kind of a "digital" oud project that I hape it will end with a
REAL oud:
First step the concept:
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ALAMI
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Step two was the actual 3D virtual making.
I started with the overall proportion obeying the rule of x=y+(x-y) and using the golden spiral as base for the bowl and face shapes.
Here an amazing thing happened, everything was directly falling in place the oud seems to be "naturally" in compliance with the golden proportion:
The images will illustrate better what I am saying
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ALAMI
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Those spirals did the job, I just love the harmony in this image:
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ALAMI
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Now time to see the volume, I started with a single hole version, but as you'll see later I have the position and the size of the 2 small holes, I
don't know which is better and in which way
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ALAMI
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This is the initial bracing.
Only for this I had to go to the equations of the of the Fibonacci series I am not sure if it is final or if it is enough to have only 7 braces,
please comment on this, ideas and suggestions are most welcomed.
I really want to bring this oud to reality and once ready I think that I will work it out with a professional luthier,.
Work is still in process, will keep updates
One Last Note: Sorry for the big images that are making this thread slow but those thin lines were suffering a lot when reduced and compressed
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Ararat66
Oud Junkie
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Hello Alami
I really enjoy your enquiring mind - this is a lovely post. I've looked into Golden sections, Phi, Fibannacci etc in relation to architectural spaces
and have wondered the same about the oud. One thing though, the oud is asymetric in terms of the pitch and tension of strings so there may well be
another variable here to complement this.
I've noticed that the harmonics on my Turkish oud correspond to lines passing the centres and edges of sound holes and also the ogee of the neck to
the sound board. There is a slight flatness in the curve of the back when seen in profile which I have seen in pictures of many other ouds. The
geometry is fascinating and I would love more time to look at this (I often try to figure it out visually).
Best wishes
Leon
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Microber
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Very interresting project.
Good luck.
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Ronny Andersson
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Looks very much as a theoretical lute by Arnault de Zwolle 
and some here David van Edwards
Best wishes
Ronny
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mourad_X
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good work alami
and very interesting thread
/Users/Mourad/Desktop/logoleoperga.jpg
what 3d programm are you using for this exambles
regards
mourad
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mourad_X
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good work alami
and very interesting thread
what 3d programm are you using for this exambles
regards
mourad
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Jameel
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Very cool drawings Alami. I'll have to take some time and look at these closer. This looks like it could be a very interesting thread...
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jdowning
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Interesting project and nice graphics ALAMI - good luck.
The Tennenbaum article presents a viewpoint on musical tones and pitch, bel canto singing, 'music of the spheres' etc.
The author discredits the great monumental work by Hermann Helmholz on the sensations of tone claiming that every essential assertion made by Helmholz
has been proven to be false but without much further elaboration.
For those interested in reading further about the Helmholz theories and forming their own opinions a modern, low cost reprint of his work "On the
Sensations of Tone", by Dover publications translated into English by Alexander Ellis, including detailed additions by the translator, is a
comprehensive reference book of great interest and historical value. It also includes a section on Arabic and Persian musical systems.
For those interested in exploring the spiritual and philosophical dimensions of music "The Harmony of the Spheres - a sourcebook of the Pythagorean
Tradition in Music' by Joscelyn Godwin traces the history of the idea of a harmonious universe from Plato through Kepler and Newton to modern times.
All fascinating stuff (if one has the time to to read into it!)
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ALAMI
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thank you guys for your encouragements,
thanks Ronny for the manuscript, I've also found the plans of a modern luthier, Joel Laplane, who actually did a luth with a very similar design to
the one you posted, a pdf of his the design and final luth he did:
http://assoc.orange.fr/la-passion-du-bois/rencontres2003/conference...
They both seem to think "circle", with the oud I am trying to think "spiral" which is an open shape, if does mean anything when it comes to sound I
don't know, and thanks jdowning for the infos, "The harmony of the Spheres" seems very interesting, I ordered it.
The software I am using is Softimage XSI
All the work I've done till now was based on the relative proportions and not on actual dimensions.
I decided that the leading unit will be the scale length, which means that the entire design should end up encapsulated into one formula with one
input: the length of the strings.
This way I would have the plans for 58.5 60 or 62 cm without having to touch the design.
The problem I am facing is from where to where I have to measure the bowl and the fingerboard:
Should I consider the whole "theoretical" length of the bowl knowing that it is going to be cut to fit the fingerboard, or consider the realistic
"cut" size which may break the spiral proportions ?
Any Ideas?
For now I have a fingerboard of 22.4 cm for a string length of 60 cm.
Here is sketch of my problem
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ALAMI
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And if everything works that's how I hope it will look
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zalzal
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i did not understand much because math and me are like 0 and 1 (guess who is the 0) but the enthousiasm showed by Alami is really contagious.
the pegbox will be really innovating.....i think Jameel will have to adapt a special set of his soft cases once industrial production will
start....
ALAMI dont you think strings will have an enormous tension, specially that this will be a seven course oud.
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jdowning
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I built a lute following the Arnault de Zwolle geometry and barring instructions during the 1970's as an experiment. I made the neck shorter to
accommodate 8 frets - basing the neck, pegbox and peg design on the lute depicted in the famous "Ambassadors" painting by Hans Holbein (1497 - 1543)
in the London National Gallery. I felt at the time that the "Ambassadors" lute - shown in perspective view - must have had a geometry similar to the
Arnault lute but was unable to easily transform this to a plan view using simple geometry in order to confirm my speculation. Note the apparent "heavy
rounded" shoulders of the lute in the painting.
This instrument was quite successful but I did get a few comments about the very 'heavy' neck section that did not fit in with most people's opinion
at the time about how a lute neck should look. Making the pegs was an interesting project in itself!
I no longer have this instrument as I gave it away to an American friend years ago but - as I recall - string length was about 60 cm. It was fitted
with six double courses with a single top string.
Of course, the geometry of the Arnault lute is not based upon the Fibonacci Spiral.
ALAMI is your software Softimage XSI also based on finite element engineering software that might also be used to calculate stresses in the shell
geometry?
Could the program readily analyse the "Ambassadors" lute to give a plan and section profile?
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ALAMI
Oud Junkie
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You're probably right about the tension zalzal, I like playing 7 course but the utility behind it is to be able to test a broad range of pitches on
this experimental model, floating bridge may be ? (am already contracting a factory in China for a 1000-piece-a-day-mass-production)
however....Nazih has a fixed bridge seven course ( the sada al rouh model).
The 3D software I am using is mainly designed for character animation and effects and is useless for any kind of engineering application like finite
elements or stress maps calculations but I think that I could use it extract the plan of the lute from "The Ambassadors", the full painting shows
tiles on the floor which would help defining the scene perspective and pegbox seems to be perfectly vertical, so if you know (or can guess) the height
of the pegbox in mm it would help to get the dimensions of the luth, a high resolution image of the full painting will also be needed (a 300 dpi scan
from a high quality print). A nice challenge!
Any tips on a special gluing for the bridge to sustain a 7 course?
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excentrik
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Wow.
Alami- you really are moving into an interesting realm here- I can see the pick guard reflecting the spiral as well- or would that throw off the
math?
man keep updating us- this is really amazing stuff (I wish I fully understood the math).
tarik
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jdowning
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I have a high quality print only of the area of the painting as posted. I will see if I can find my working drawings to determine the pegbox length
that I used - which should be around the same depth as the lute body.
A quick check might be to rotate your generated image of the oud to about the same orientation of the lute to see how closely (or not) they match
visually? However, I suspect that the artist Holbein may not necessarily have been using a 'true' perspective representation.
As lutes of the 17th and 18th C carried up to 14 double courses, a 7 course oud bridge should not be a problem even when using traditional hide
glues?
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ALAMI
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Good Eye Jdowning, the bowl is a match and the overall shape is very close but not the hole and the bridge positions
I can't say it is absolutely accurate because the perspective is not real (as you said) so I did an almost orthogonal view, I used the oud model I am
working on, just changed the pegbox (at 96 degrees relative to the neck).
So if you think it is close enough, it would be easy to extract dimensions (they can be relative to the pegbox or to the overall length)
And Tarik you're right about the spiral in the pickguard, I am trying different designs.
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jdowning
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Thank you for taking the time and trouble to do this work
ALAMI . This is a very interesting (if not astonishing!) result. I would judge the results to be very close.
Hans Holbein as a Renaissance artist likely would have attempted to use a 'vanishing point' perspective to represent the lute, rather than orthogonal.
In which case both soundhole and bridge on your model (if transformed to a vanishing point perspective) would appear rotated more to the left and
would even more closely represent the lute in the painting? I have always thought that the centre line of the lute in the 'Ambassadors' painting
seemed to be distorted or curved to the left so your graphic comparison may be a confirmation that this is the case. No wonder I failed to transform
the image - years ago - using simple geometry. Thanks to modern computer technology!
In this painting - full of symbolism and allegories (but that is another story open to many interpretations) - Holbein is playing with other
perspective ideas like the anamorphic perspective view of a skull in the lower part of the painting. So nothing can be taken for granted.
The painting also represents articles of Arabic origin like the tapestries and - perhaps - the scientific instruments. The painting of the ambassadors
from the French court of Francis 1 (dated 1533) may depict an old, neglected lute from an earlier time (one of the strings is broken) so the
instrument might be an early example of a transitional instrument - from oud to lute? Just my speculation, however.
For those unfamiliar with the painting I attach, for information, an image of the whole painting as well as an image of the skull when viewed from the
required angle.
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ALAMI
Oud Junkie
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I've been busy fine-tuning the design of the golden mean oud according to 2 simple rules:1- Oud rules and 2- golden mean (phi) and it is working.
Every important construction and bracing point is "in ratio" with phi. In terms of practical oudmaking all what should be done is placing one point
and trace the relative golden spiral, and decide for the string length (62, 60 or 58.5) this will determine the constant "s" in the formula which is s
= (scale length/3) and by this I am respecting rule 1, and then all the other points are obtained by an amazingly simple formula for each one.
The formulae have only the integers: 1,2,3 and Phi, all multiplied by s to give the dimensions in mm or inches.
on the attached image all the points show their relative Golden ration connection by thin lines of the same color.
Another very interesting issue was raised by jdowning, it is a speculation, a very tempting one, suggesting that old arabic ouds MAY have followed
this type of geometry ratios. The match with the 1533 Holbein's painting is really "astonishing".
I plotted the final design on a 1:1 scale and took it to Fadi Matta who is a real fine luthier and he was enthusiastic about the project.
The oud construction will start next week, we are still reviewing the bracing formulae.
A mould will be made to ensure the accuracy to the mm.
This is going to be a big oud with 43cm height for a 60 cm scale length.
Still not sure for the wood, I would go for walnut that was used on old arabic ouds but it seems that no high quality walnut is available, we found a
nice palissander.
The rosette is another story to come, it is also going to be another experimental feature.
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oudipoet
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dear alami
i ve been reading your theory and i really like your calculations and designs esp the shape of the oud and the peg box there is only one thing that
bothers me that the distance betwen the bridge and the sound hole somehow they look so close to me it looks there is not enough space for a pick
guard and enough space to play confortably ofcourse that s my oppinion i am not a mathematician or anything close to that so my oppinion is just an
oud players oppinion anyways so i was wondering what would happen if you were to move to sound hole up and bridge little bit down would that be too
much out of your calculations?
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Marina
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Here is what happens if folk player tries to count the frequenses up to 440
Here is what happens if folk player tries to count the frequenses up to 440.
SO, DON'T DO IT AT HOME!
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jdowning
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Another early lute image that makes an interesting comparison is depicted in the painting by Italian painter Lorenzo Costa (1495 - 1535) in the London
National Gallery. The artist did not seem to quite manage to correctly represent the longitudinal symmetry of the instrument so one might choose
either the upper or lower outline of the belly as the intended geometry.
The most obvious difference from ALAMI's computer generated oud image is that the bridge is somewhat lower - not sure about the soundhole position
though. However, if the artist incorrectly represented the instrument symmetry he may also have erred in the precise bridge/soundhole postioning?
Interestingly the "rule of thumb" for early lutes is that the soundhole diameter should be 1/3 of the belly width measured across the centre of the
soundhole. The computer generated model comes very close to that criterion.
This also suggests that artist Costa may have depicted the lute profile fairly accurately but that the centreline is distorted - offset too much
towards the top edge of the belly (about 7% at the soundhole location I would estimate) - affecting the true bridge and soundhole positioning as well
as the orientation of the neck?
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