Since the "Kertsopoulos mathematical model of the classical guitar" is posted above, please find below the "Kertsopoulos geometrical progression of the classical guitar".
geometrical progression-KertsopoulosG.JPG
This "geometrical progression" shows step by step the initial lines that are the basis for the "mathematical model" that evolves and continue step by step to the final "geometrical structure" that defines the final "mathematical model".
The "geometrical progression" supports the "mathematical model", which contains both simple and intricate mathematical proportions and ratios, as well as constructional approximations and dependencies of an interesting historical and acoustical context also.
It can be seen, that the whole essence of the guitar’s shape and context is directly related to the ratios and relations existing in the physical behavior of sound as expressed by the harmonic spectrum, the specific tuning of the instrument, the ideal behavior of strings and the diatonic system.
This multi-interconnection relation combined with the acoustical function of the perimeter-outline, creating “standing wave zones” (see below fig's 3e, 3f, 3g and 3h - Fig's 3a to 3d avoid standing wave formation):
standing waves.jpg
Also, specific enhancement of preferred resonant frequencies of the chamber and control of the “wolf tone” production, gives satisfying answers to so many questions put forward by many in the past.
Questions of the nature:
1) What determines the location and size of the sound hole and the bridge?
2) Why this shape?
3) What is the real magic about the 65-cm scale length? (32.5 x 2 = 65 -
32.5 is the violin's ideal string length).
4) What is the aesthetic but also acoustically ideal curvature of the outline?
5) Why does every experiment link back in a mysterious way to the center of tradition, that center being mainly Antonio de Torres?
6) Why did Hauser and so many other luthiers copy instinctively and through experience obtained in construction the work of Antonio de Torres?
7) Why this mathematical model is found in the work of Antonio de Torres initially and afterwards in the guitars of the Ramirez family throughout their history and also in Hauser's work but not in any other guitar made by any luthier before 1982? After 1982 (Greek publication at IHOS) and 1983 where the mathematical model was presented internationally at Musik Messe Frankfurt in Feb. 5-9, 1983 and published internationally by Das Musikinstrument in the English and German languages, many luthiers and guitar companies started to use it successfully. At the press conference in Musik Messe in 1983, Maestro Jose Ramirez III stated:
"...after this presentation made by Mr. Kertsopoulos better guitars will be built all over the world...".
Below is the dedication of Maestro Jose Ramirez III to this specific work.
Mr Ramirez dedication with translation-small.jpg
Il signor Kertsopoulos fece una brillante esposizione su tutti i calcoli matematici necessari per ottenere un disegno della cassa della chitarra (curve, intaglio, bocca, dimensioni ecc.), perfetta, in base a rigore scientifico, partendo da qualsiasi lunghezza di diapason…
Edizioni Suvini Zerboni., 1983, Page 46
Translated: Mr. Kertsopoulos made a brilliant exposition of all the mathematical calculations necessary to obtain a drawing of the body of the guitar (curves, carving, soundhole, dimensions, etc.) perfect, based on scientific rigor, starting from any length of string scale…
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