The Acoustics of "A0-B0 Mode Matching" in the Violin

It has been found by many experienced violin makers that if a violin is adjusted so as to bring two of its low-frequency modes into close proximity, then players find the result very desirable. The modes in question are a modified Helmholtz air resonance, labelled A0, and a bending mode of the whole body, neck and fingerboard, labelled B0. In this paper a simple model is developed which allows the process of "matching" these two modes to be studied. The model is shown to predict behaviour in good agreement with measurements. Implications are studied, both for instrument makers carrying out this matching, and for possible explanations of the player preference for matched instruments. It is suggested that bowing transients must play a significant role, since effects on steady tones are confined to a very few notes on the instrument.