Tuning asymmetrically braced guitars : Analytical models and MATLAB code

Abstract

This is supplementary material to the full paper "Sound tuning in asymmetrically braced guitars - a lesson by Faustino Conde", to be referenced to.

Asymmetric bracing promises multiple resonances to appear between A0 and A1 (in the range between 150 Hz and 350 Hz) and therefore a full tone with a prominent fundamentals for every semitone in mentioned range. However, this is only achievable with knowledgeable tuning. Asymmetric bracing also promises modulation and therefore a lively tone, and it promises radiation efficiency, as outlined in the associated paper.

The tuning parameters are: a measure of asymmetry - expressed in the difference of spring properties of the braces a measure of the bridge overhang, that is how much does the bridge reach beyond the working point of the braces a measure of coupling between the top plate and the back plate a measure of how much the top and the back plate are 'tuned apart'

The prediction only applies for mentioned range of the so-called signature modes. Measurements from a well-conditioned guitar from Faustino Conde confirm the findings in terms of frequency and intensity, which explain why the four-fold resonances are found in this guitar whereas in other guitars there are only one or two such resonances.

There are several analytical models (see attached pfd). The most complete model constists of three DEs and covers all aspects of mutual coupling. However, it is only solvable by numerical methods. For this purpose, the MATLAB code is provided. Simplier models only cover the mutual couling partially but allow for analytical solutions.

MATLAB code Faustino_Conde_asymmetrical_bracing_frequencies.m searches numerically related frequencies. MATLAB code Faustino_Conde_asymmetrical_bracing_intensities.m determines related intensities via executed DEs. Code is tested under MATLAB R2011a.