Figure 1.

Acoustic air-resonance power efficiency grows as sound hole shape evolves over centuries through the violin's European ancestors to the violin. (a) Change in radiated acoustic air-resonance power for an elastic instrument W^air-elastic (equation (4.5)), rigid instrument W^air-rigid (equation (4.2)) and infinite rigid sound hole bearing wall W^wall (equation (4.1)) as a function of sound hole shape, where percentage change is measured from the circular sound hole shape. (b) Air-resonance frequency for elastic instrument f^air-elastic (equation (4.4)) and rigid instrument f^air-rigid (equation (4.3)) as a function of sound hole shape, normalized by f^air-elastic for the circular opening (i). (c) Conductance C (equation (2.3)) and perimeter length L for different sound hole shapes of fixed sound-hole area, normalized to be unity for the circular opening (i). Shape overlap occurred between nearby centuries. Only sound hole shape is changed and all other parameters are held fixed and equal to those of the 1703 ‘Emiliani’ Stradivari violin [30]. The conductance of the two interacting sound holes for each instrument is determined from equation (2.3). Data sources are provided in the electronic supplementary material, §5.