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Thomas Coleman

Violin geometry references

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And taking another go at it....    (Perhaps this isn't for anyone but myself?  Regardless, as time allows I'll see it through.)




There are some additional relationships showing a simple ratio between horizontal and vertical elements.  

For one, there is generally a simple relation ship between vertical elements of a classical violin family instrument viewed from the side and compared to the length of the body.  Although rib heights and edge thicknesses have often been reduced or altered some with time, still a basic 1::9 ratio is still generally apparent with most classical violins and violas.   Most often this takes both plate edges into the '1', and the '9' runs from end to end of the plates.

We can see this relationship running through classical violins and violas, even ones that in other ways might be quite different form each other:

 1721 Strad Lady Blunt--5a382cc78ecac_1721LadyBLuntanalysis.thumb.jpg.97b69a2a9eadc21a302a8125b136e2cd.jpg           1613 Bros Amati piccolo violin-- 5a382d12dc073_1613BrosAmatipiccoloviolinsidetobody.thumb.jpg.a5ef3adc6d8d62a7142b1f4db7a1e18b.jpg                                                 

1696 Strad viola Archinto--  5a382e8bc0ace_1696StradArchintoviola.thumb.jpg.b75bd6717eb40314a18a5b837243a090.jpg           1574 A Amati small violin--     5a382efbb2517_1574AAmatismallviolinsvb.thumb.jpg.7c663cbc929cadd1145297561ea01a1d.jpg                            


1624 N Amati violin--5a382f3d1b98e_1624NicoloAmativlnsvb.thumb.jpg.db66ecf99f7bd99fdef3c5298eda3c28.jpg         1730 Del Gesu 'Kreisler' --   5a382f8c40874_1730DelGesuKreislersvb.thumb.jpg.7a18150951c5c10d5a1ae8a6345574c5.jpg

But, typical of classical usage with other guides and methods, the makers tended to create some freedom of choice for themselves to push or stretch a rule by varying the exact application.  In the example below, A Guarneri makes the ribs a bit deeper by not including both plate edges in the 1::9 ratio.  He only includes one plate edge.   While this creates a variation away from the main tradition, he does so in an entirely traditional way.   And this process is very much consistent with what we can observe of classical making practices.


1664 A Guarneri tenor -- 5a38309ba89ff_1664AGuarneritenorsvbminuse.thumb.jpg.deda2c067d69a2734619d663050f5108.jpg                                                  


Cellos instead used a 1::6 ratio, most commonly including only one plate edge in the ratio. 

1690 Ruggieri cello-- 5a383177b56c3_1690FrancescoRuggiericelloperhapsuncutsvb.thumb.jpg.d1e264d6b11e2baf3c0de2dfe0b5ad08.jpg          1690c Gofriller cello-- 5a3831c163bfb_1690cGofrillercellosvb.thumb.jpg.a61ba72dd896cf00f4b6dde0a712544f.jpg     


1742 Montagnana cello--   5a3832069d968_1742Montagnanacellosvb.thumb.jpg.6ef6899b94cded0c826c471deb386404.jpg          1699 Strad cello Castelbarco--5a3832a2c44aa_1699StradCastelbarcouncutlrgcellosvb.thumb.jpg.58fec6c4daea7d67728c61f556ef31fe.jpg  


Wear and alteration can at times obscure these ratios, but not for nothing, very pristine instruments from clean workers tend to show the traditional ratios very clearly:

1690 Strad tenor  Tuscan-Medici---5a38333600fd8_1690StradtenorMediciTuscansvb.thumb.jpg.c36d7ce3247b037760f7e7abc264ae65.jpg     


While we're looking at these vertical heights form the side, a view 'guide' relationships should be pointed out.  I say 'guide' relationships because perhaps these elements were always or at least at times actually worked by other more direct methods. But still, these heights in actual Cremona work don't normally stray very far from the 'nominal' sizes given by these guide relations.  So one, is that with violins and violas the edge height is basically 1/8th the rib height.  Which in most of these examples means the edges are about 1/10 the ribs plus edges height we get from ratio 1::9 for side height to body length.   For a body length of 354mm, this would equate to a nominal edge height of 3.93mm, so not dissimilar to modern standards either.  This kind of nominal calculation would also predict the main rib height to be 31.46mm.  Again this comes very close to a modern 31.5mm guide to rib height.

However, a tradition of using ratios as a starting point for things like plate edge thickness as an advantage of the more modern approach of using fixed numbers, ratios give us guidance for instruments of varying size.    Thus we see that same ratio gives us a fair starting point for edge thickness in standard violins, but also in a piccolo violin or a viola:

 1624 N Amati violin -- 5a3843d52bc9c_1624NicoloAmativlnedges.thumb.jpg.d7180a38da9aa0f27ddf9ebed4562641.jpg         1613 Bros Amati piccolo violin-- 5a38440992863_1613BrosAmatipiccoloviolinedges.jpg.e1d75208bb299f33a52a1242901dcc9c.jpg                                          

1696 Strad viola Archinto--  5a384441a255b_1696StradviolaArchintoedges.thumb.jpg.634895435242914ecf298ef409147440.jpg               

Though only nominal or 'guide' relationships, it should probably be mentioned that for violins and violas the plate heights roughly correspond to 1/2 the rib height, and the bridge height roughly equals the rib.

The plate height to rib relation particularly is one that Cremona makers seemed to have moved away from.  In the earliest generations of makers it seems fairly meaningful, but with time becomes considerably less so.

Here the plates heights including the edges are very much equal to 1/2 the rib height:

1574 A Amati small violin-- 5a384b296719d_1574AAmatismallviolinplates.thumb.jpg.4973f4560b7e32e488cbd146369730d4.jpg   

And in an early N. Amati, there seems to still be awareness of the idea.  The plates have been made taller, by excluding the plate edge in setting the height.   But I don't think this idea directly guided plate heights as time went on.

1624 N Amati--  5a384c43c6551_1624NicoloAmativlnplates.thumb.jpg.31c94cb48acb1e82d573865c116f75cd.jpg



There are also a couple places were an equal or 1::1 horizontal to vertical relation is important in the traditional designs.  A square provides an easy method to illustrate these relationships.

Perhaps the most interesting of these sets the level of the upper eyes for the soundholes.   Generally, soundholes are one of the less consistent features in Italian making.  We see the basic shape evolve through the generations of classical making.  And what holds for one maker or region, or for one time period, doesn't necessarily hold across the board.  Many or the rules we find traditionally governing other features often hold more consistently, and many times hold broadly in Italian making beyond Cremona.   The traditions of soundhole work tend to be more varied, and specific by region, maker, and time period. 

One tradition that is consistent for Cremona work, and much Venice work, is placing the level of the upper eyes in a 'square' relation with the upper bout width.  Most typically, the eyes are placed just touching either above or below the square.  In some cases the eyes center on the square.  When a lower placement of the eyes is desired, if will be found in Cremona work to be placed set number of eye radii form the square.1721

 1721 Strad  Lady Blunt-- 5a385ba884edf_1721LadyBLuntanalysis.thumb.jpg.9b5624fc5aae5ef6a40b1cc50c62b61e.jpg            1624 N Amati--5a385beb70c5e_1624NicoloAmativlnUBsqr.thumb.jpg.def74eb3465717794d898026c12288dd.jpg       

1730 Del Gesu   Kreisler--  5a385c2823023_1730DelGesuKreislerUBsqr.thumb.jpg.891c9d7b9d350b3501ae8abdf8a61c62.jpg      1714 Strad Soil--  5a385c52a58eb_1714StradviolinSoil.thumb.jpg.58ac4cc542f70534e0fc6d84314a5bd4.jpg   


And here are two examples where the eyes are placed lower by some eye radii below the square around the upper bout:


1700 Strad cello  Christiani--5a385cddd4bd8_1700StradcelloChristianismalluncut.thumb.jpg.e6d82fd977c06b970bcf1966cb7d917d.jpg     1693 Strad long violin Harrison--  5a385d1a295b7_1693StradvlnHarrisonUBsqr.thumb.jpg.39d904347f613bb82174d5c363ea15c5.jpg   


This kind of placement of eye level is not necessarily shared broadly outside Cremona.  An interesting related method is to place the upper eye level in relationship to a square around the lower bout instead of the upper bout.   This is seen in some Zanetto violas.   And, Del Gesu brings this idea back to locate the upper eye level in his Chardon:

1735 Del Gesu Chardon-- 5a385e6b12d14_1735ChardonLBsqr.thumb.jpg.77c0fb8893a90eec5cfc42075cffd3b1.jpg






Out of time again, so more later.













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On 12/16/2017 at 11:11 AM, Marty Kasprzyk said:

Hi Ben

The attached pdf is a straight line shot at violin geometry.

Hi Ben.pdf

Once the general parallel line proportions are  chosen it is fairly easy to free hand sketch the various bout shapes used.  Bent ribs (splines) can be used as drawing aids if smoother and more natural looking lines are desired.



violin parallel drawing  ◊ Layer-1 ◊ 1 _ 1.jpg

shape sketches.jpg

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On 16/12/2017 at 5:11 PM, Marty Kasprzyk said:

Hi Ben

The attached pdf is a straight line shot at violin geometry.

Hi Ben.pdf

An Initial step is missing to your framework. The placement of the openings use to be the initial step of any design

(I'm not speaking of the late XVII°C here)5a38e78aaf814_Capturedecran2017-12-19a11_15_30.thumb.png.f6e503cdf40244021934875dfb8ea1c3.png


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On 12/19/2017 at 5:22 AM, francoisdenis said:

An Initial step is missing to your framework. The placement of the openings use to be the initial step of any design

(I'm not speaking of the late XVII°C here)5a38e78aaf814_Capturedecran2017-12-19a11_15_30.thumb.png.f6e503cdf40244021934875dfb8ea1c3.png


I don't have a slightest idea of how to do the opening positions.

I used to think that the tick marks of the f hole were half way along the f hole's length and the tick marks were lined up with the bridge thus centering the f holes around the bridge in the up and down direction.

But the spacings of the f holes and their inclination angles (amount tipped inward at the upper eye and outward at the lower eye) seem to vary between makers and even for the same maker.  The lengths of the f holes also seem to vary so I don't see how the position of the f hole eyes is inherent in the violin's design.  Their positions seem like an after thought rather than an initial decision.

Maybe its a which came first, chicken or egg, type of thing.

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7 hours ago, Marty Kasprzyk said:

I don't have a slightest idea of how to do the opening positions.

It's very simple, It's just because you never learned it !


7 hours ago, Marty Kasprzyk said:

Maybe its a which came first, chicken or egg, type of thing.

Indeed you're right  if you consider that the dimensions of a musical instrument are a set of measures all comparable two by two. BUT,  at the time of the invention of the violin, this type of presentation of the measures is still a practice reserved for a few educated. For many good reasons on which I will not come back, the systems used are more likely to be the ones that have survived in all crafts since ancient times.
It is very interesting to study because one realizes that the universal thought that prevails up to the quarrel of the Ancients and Moderns had very pragmatic origins. I like to think that all this was within reach of a bored shepherd keeping his flock, trying to understand the world around him. That please me to imagine such a beginning 

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The beast is back!  But fed with holiday bird and tasty goodies. 


As Marty and Francois point out above, there are many ways to depict layout choices and proportions.   Marty's lines and Francois' frames can in fact be used to say exactly the same things I'm observing about the proportions that guide the layout and sizing of elements in classical violin making design.   Exactly equivalent ways of expressing such information.   

Also, as Marty points out in his wonderful drawing of different outlines from the same proportions, you can complete the shapes for an instrument in many different ways, even if you're using the same proportions for sizing and placement.  There is great freedom in recognizing that!  

I am perhaps limited in that I'm trying to dig out a less creative understanding, out of the many proportions that can be used, I'd like to know which ones the Cremona makers did use, and under what circumstances.    And once a proportional layout is in hand, out of the basically unlimited number of shapes you can create following those proportions, which shapes did the Cremona makers use?

Anyway, very interesting how different approaches end up connecting in so many ways.


Looking now at the neck and body stops, and some of the proportions for the head and volute, we'll use both horizontal versus vertical proportions, and proportions along a line as needed:

      5a42c02f6d2be_hvvproportion.thumb.jpg.62d9237f8c2302268df3211814219647.jpg     5a42c036313a2_lineproportion.thumb.jpg.bf7a805bed8212784c2b4ba66c9c1278.jpg  


In classical work, there kinds of relationships set the not just the neck stop in relation to the body stop, but also set the basic sizing for the scroll.   One of the few ratio relationships that commonly survives in modern violin making awareness is the 2::3 ratio that is standard for violin and contralto viola neck stops to body stops.    This same relation is commonly seen in classical work also.  But beyond that, the height of the volute is normally taken in relation to units of the neck stop.   For a general rule, classical Cremona making takes the height for the scroll/volute as 'the unit of the neck stop reduced by a part'.   So that might be 2/3 the unit, or 3/4, or sometimes 4/5.

As in these examples:

   1574 A Amati small violin--  5a42c2a2cb78d_1574AAmatismallvoluteheight.thumb.jpg.69a21eac0d4234c6c063515469786e3f.jpg                              


1648c N Amati violin--   5a42c2f9d6446_1648cNAmativiolinvoluteheight.thumb.jpg.4b7e41350bb4a2d7d49f323b421d4c69.jpg                  


1675c Ruggieri violin --    5a42c354b1ddc_1675cFRuggieriviolinvoluteheight.thumb.jpg.86723c01ca3ac61603ec8c83b57c7938.jpg       



1684 Strad violin Lord Elphinstone-- 5a42c3b507e56_1684StradviolinLordElphinstonevoluteheight.thumb.jpg.8a89634d9d21f7fe49ee2ba8b9babac4.jpg   

1710 H II Amati violin-- 5a42c42d4da52_1710HIIAmativlnvoluteheight.thumb.jpg.1c852c8c2836470d906ceb42aaab183d.jpg    


1711 filius Guarneri violin --   5a42c4a9e68ed_1711filiusGuarneriviolinvoluteheight.thumb.jpg.4df1476216e130f2d6f17da00a143936.jpg


1726 Strad violin  Sleeping Beauty--  5a42c51b41704_1726StradviolinSleepingBeautyvoluteheight.thumb.jpg.be77fa338348bef62e46f3f03fabfe9c.jpg   


1743  Del Gesu violin  Sauret--  5a42c57a4feb5_1743DelGesuSauretvoluteheight.thumb.jpg.80d5f1a95d39c92526d2162cfc297eb2.jpg  

(Note that because of the angle of the necks, I've used a circle to compare the volute height to the ratios from the neck stop.  For each instrument, the two green circles are identical)



All these violins from different makers use the exact same ratio recipe for the neck to body stop, and to obtain the volute height.   All except the Ruggieri example took the volute height as 3/4 the unit of the neck and body stops.    Ruggieri chooses to get a slightly smaller volute height by getting from 2/3 the unit instead.  This makers the volute height about 11% smaller than it would've been.

Below, we can see Del Gesu trying a slightly larger ratio for the volute height in the 1742 Soldat.  This is done by using 4/5 the unit instead of the normal 3/4.  The result is a little less than 7% larger as a result.   I've also shown a comparison to the 1735 Plowden where Del Gesu used the typical 3/4 ratio.

5a42c8965ef09_1742DelGesuSoldatvoluteheight.thumb.jpg.34cc8b6eb33706c95e1f9bca80bca660.jpg        5a42c89dda809_DelGesuSoldattoPlowdenvoluteheightcompare.thumb.jpg.735013cd78613a927307f4846697e0aa.jpg  



The old makers also had a standard procedure for producing somewhat longer or shorter neck results when needed.   This was to start from the basic 2::3 ratio, but then reduce or augment the neck by 1 part of the basic unit.   Thus (2 and 1/4)::3 would give a lengthened neck stop, while (2 - 1/3)::3 might be used for a somewhat shortened neck stop.  While typed out in text this might look odd, still if you're using dividers and proportions and working in wood, it's the simplest possible way to create a variation on the normal 2::3 lengths.

We can see this carried out in different ways in the following small violins and large violas:

1613 Brothers Amati piccolo violin--    5a42ca970d240_1613BrosAmatipiccoloviolinvoluteheight.thumb.jpg.750116b253e033237bb43fdb05c7ea14.jpg              


1664 A Guarneri tenor viola--   5a42cafcd21cd_1664AGuarneritenorvoluteheight.thumb.jpg.7b577c2ff85a882bfd63ed57197d6d91.jpg                


1690 Strad tenor Tuscan-Medici--  5a42cb469af5c_1690StradtenorMediciTuscanvoluteheight.thumb.jpg.d1404fc94d3d4ca227be137fd2a23cbe.jpg    


Cellos are challenging in that so many of the necks are very substantially altered.   Conclusions should probably have a caveat for cellos, but it's still interesting to take a look.   Note that the modern 7::10 neck to body stop ratios sometimes used with cellos can be obtained through the old method of variations.  7::10 is what you get if you augment the normal 2::3 ratio by 1/10.   Old or altered, that is I think what is seen here in the 1730c Strad cello Pawle:


Here are more cello examples.

1673 Strad  cello Du Pre --       5a42cd769ab23_1673StradcelloDuPrevolteheight.thumb.jpg.5ad78f2712c8af5e9d0cad46cb7b7ec7.jpg


1699 Strad cello Castelbarco --   5a42cdbab92be_1699StradCastelbarcouncutlrgcellovoluteheight.thumb.jpg.076109bac195e8ba0dcbb4282db7ffd6.jpg     


The basic sizing of the head then proceeds from the volute height.  A primary relationship seen in classical Cremona scrolls is that height of the pegbox is 1/2 the volute height.



Beyond that, this same 1/2 the volute height gives the length of the interior section of the volute.  These things, as well the most typical 3 by 4 frame for the overall volute are shown below in the 1574 A Amati small violin:



We also see this 1/2 the volute height is critical in setting the width of the scroll work, and the width of the pegbox.  

(same violin)



Overtime, we see later Cremona makers creating many variations on the shape of the pegbox to obtain a bit more room, or perhaps just for elegance?   But we cal always see that they are working with this same basic plan for sizing.


1690 Strad Tuscan-Medici viola---  5a42d19ea7aae_1690StradviolaTuscanMedicipegbox.thumb.jpg.179e63b684c98c520044ab700353d610.jpg     1743 Del Gesu Sauret--  5a42d2198d883_1743DelGesuSauretpegbox.thumb.jpg.26ba65a445dbd107ed441cd92b74bcae.jpg 


The other features of the scroll will be found to similarly have solid proportional relationships behind most of their features.   Some of the most prominent Amati family style relationships are shown in these A Amati and Ruggieri ecamples:

A Amati 1560s violin-- 5a42d2d5345d8_1560cviolinAndreaAmatiKurtzboxwalls.thumb.jpg.c2e46fd86b04066512c5bd0bc88ae487.jpg     5a42d2dc5c135_1560cviolinAndreaAmatiKurtzelevations.thumb.jpg.9625bfc4fb7c5999f66412e6cfa81f74.jpg    5a42d2e12ee8d_1560cviolinAndreaAmatiKurtzstraightsides.thumb.jpg.8e99dc66f8e44d80c5c4646816788c3d.jpg    5a42d2e8147fd_1560cviolinAndreaAmatiKurtztophalfwidth.thumb.jpg.6b4f3b0cc6b16ab94b87b163905e22f9.jpg        


Ruggieri 1680c violin Milanolo --  5a42d3b98cce0_1680cRuggieriMilanoloAnalysis.thumb.jpg.069bb7498d6a20a09c97c74895adbb88.jpg      5a42d3bc8d8b4_1680cRuggieriMilanoloelevatoins.thumb.jpg.55ecd3cb626734b179e7a338faf36145.jpg     5a42d3bfa2b88_1680cRuggieriMilanolostraihtedges.thumb.jpg.7c4686805760303b815a2beed7a33d4b.jpg      5a42d3c365ec8_1680cRuggieriMilanolotophalfwidth.thumb.jpg.0f83ee8688c4a8a4558c55b876c486ed.jpg                                        
















1743 Del Gesu  Sauret  volute height .jpg

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Hi Thomas.

I do not understand why you all are so interrested in the out line of an violin. As shown by many very complex as it is.

What does that tell us about the function??

Instead I studied the struvture of the vibration arching shape and found 2D as well as 3D solution with very simple geometry without any calculation!!

Just read and consider the geometric result and if you need some more explanation what I did finding this result just ask. Yes there where made a lot of calcutaion in order to find the simple solution.

But drawing the solotion no calculations are needed.

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Ya hace mucho tiempo que se inició esta discusión acerca de la geometría del violín. Yo propongo este sistema para el diseño desde cero. Díganme que les parece. La ausencia de marcas, tanto en plantillas dobladas, utlizadas para trasladar las siluetas del contorno a los moldes,  como en los moldes, hace que tengamos que suponer la geometría utilizada para dibujarlas. Hay muchas teorías al respecto. Para los instrumentos antiguos, anteriores al XVI, es casi seguro que las curvas fueron trazadas a compás. Pero desde la aparición de los primeros violines y familia, creo que mi teoría tiene cierta entidad, ya que la plantilla que yo propongo permite el trazado de curvas aúreas y sirve para proporcionar y medir el instrumento completo.La instrucción de Durero sobre la forma de dibujar esa espiral se publicó en 1525 y los primeros violines aparecieron años más tarde. Entiendo que el propósito de esas plantillas dobladas era, sobre todo, lograr una simetría perfecta. El propósito del sistema que yo propongo es la consecución de una arquitectura  del instrumento regida por una clave única. 

This discussion about the geometry of the violin has been started for a long time. I propose this system for design from scratch. Tell me what you think. The absence of marks, both in folded templates, used to transfer the contour silhouettes to the molds, as in the molds, makes us have to assume the geometry used to draw them. There are many theories about it. For ancient instruments, prior to the XVI, it is almost certain that the curves were drawn to measure. But since the appearance of the first violins and family, I believe that my theory has a certain entity, since the template that I propose allows the drawing of aerial curves and serves to provide and measure the entire instrument. Dürer's instruction on the form of Drawing that spiral was published in 1525 and the first violins appeared years later. I understand that the purpose of these folded templates was, above all, to achieve perfect symmetry. The purpose of the system that I propose is the achievement of an instrument architecture governed by a unique key.








Edited by Joaquín Fonollosa

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