Factors influencing the size and shape of f-holes

The f-holes in the body of a violin have evolved to their current shape as the result of generations of trial and error by violin-makers, as reported in a study in the Proceedings of the Royal Society:

Owing to its long-standing prominence in world culture, we find enough archaeological data exist for the violin and its ancestors to quantitatively trace design traits affecting radiated acoustic power at air cavity resonance across many centuries of previously unexplained change. By combining archaeological data with physical analysis, it is found that as sound hole geometry of the violin's ancestors slowly evolved over a period of centuries from simple circular openings of tenth century medieval fitheles to complex f-holes that characterize classical seventeenth–eighteenth century Cremonese violins of the Baroque period, the ratio of inefficient, acoustically inactive to total sound hole area was decimated, making air resonance power efficiency roughly double.

The corresponding evolution rates are found to be consistent with (a) instrument-to-instrument mutations arising within the range of accidental replication fluctuations from craftsmanship limitations and subsequent selection favouring instruments with higher air-resonance power, rather than (b) drastic preconceived design changes from instrument-to-instrument that went beyond errors expected from craftsmanship limitations.

Or, to put it another way...

P∼(r,f)≈jρair(2πf)2(kh02)[v∼air(f)−v∼structure(f)]cosθejkr4πr,

Lots more at the primary link, and in an article in The Economist, via BoingBoing.