To pursuie my previous post
Ratio, proportion or unit fraction are used indistinctly to mean specific relations internal to the violin. In this sense, they are distinguished from our casual measures which are ratios to an external reference (meter).
We all know the ratio 4/5 which often links the lower bout to the upper bout or the fraction 1/7 proposed by Sacconi to set the bass bar. But we do not know anything about the origin of this ratio and fraction. When other values appear like 13/16 rather than 4/5 (Nicolo Amati and Strad) or fractions 1/4 and 1/5 to set the viols bass bars, one remains without convincing explanations. David Burguess can post on MN "may be" or "why" and he is right because there exist according to the violins that one measures, dozens this occasional relations of which one can quite reasonably think like David does that, "if one search them one finds them ".
In Fine, finding "proportions" in a violin seems to mean nothing but apparently casual internal relationships. Nothing very interesting here for me. This wise observation has long kept me away from the subject (until a severe and persistent insomnia decides otherwise).
The ancient texts are filled with these "occasional" proportions without accessible meaning. Thus, the proportions of the ancient temples do not correspond or that very partially to the recommendations of Vitruvius, the Lute of Arnault de Zwolle seems to have existed only in his imagination etc.. ..
In the 1970s Richard Tobin publishes "the Canon Polykleitos" and then come from other publications in the 1990s Louis Frey publishes "Architectural Data and Hypothesis on Pre-Euclidean Mathematics" and Pierre Gros "" Irrational Number and Perfect Number at Vitruvius " ), recognized commentator of Vitruvius with whom I come into epistolary contact (no email at this time) and who adroitly advises me.These publications defend the idea that the proportional sections and their approximations provide a plausible explanation to the origin "ratio".
Take our previous example, the fraction 1/7, this measurement is taken from the center of the instrument which is to say that the width is divided into 14 and that the bass bar is positioned by 6 parts on one side and 8 parts of the other. This division corresponds to a section 3-4 (6-8), a fourth. It's starting to get more interesting...
The fourth is one of the possible approximations of a proportional section called "harmonic". The two approximations that "frame" 3-4 are 2-3 and 5-7. The measure becomes predictable 2-3 and 5-7 are two possible alternatives of 3-4 and "cerise sur le gâteau" (icing on the cake), the average of the difference between 2-3 and 3-4 gives you the avrage thickness of the bass bar which otherwise corresponds to what is called the "Pythagorean tone".
So, we went from a simple measurement injunction to a reasoned knowledge. That's a lot more exciting, (at least for me).
After a few sleepless nights I published a book in 2006 "Treaty of violin making, the violin and the art of measurement" in which I continued and I hope thorough, the works of my predecessors. The book is based on the analysis of a technical plan of a string instrument, a lute. The document (middle XV ° C) is known but I revisit its interpretation. Zwolle gives some simple relations like tthe settings of the bridge and sound hole. But it appears that these few indications of "relative measures" (ratio) are however contradictory. The important thing is that I demonstrate that these contradictions can be explained by the use of approximations of the proportional sections. (I don't receive to date any critic about the validity of my demonstration but I have to admit that, unfortunately, these 30 pages are rather tricky to grasp for many)
In conclusion, the lute of Zwolle is not a drawing in the sense we understand it but an "exempla", that is to say, a teaching medium on the way to take measurements.
Wow! doors open, what happens if I apply this teaching to the form of the violin ? It happens that many things are rationally explained that the connection between a 4/5 and 13/16 becomes clear, it happens that sense arrives in the system.
Sorry to have been a bit long but it was a complement to my previous post on the interest of talking about "relative measure" instead of "proportion".