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5

Being EXACTLY 1/5 is a coincidence (see Carl Witthoft answer). But the musical instrument size (or generally everything made to produce sound) is pretty much related to the wavelength of the sounds it produces. The laws of physics dictate that you cannot efficiently radiate sound (or any other waves, say, electromagnetic waves) using something much less than ...


12

It is a coincidence, because there is no simple relation between the wavelength of sound in air, and the wavelength in the structure of the instrument (either in the wood or the strings). The fact which is critical to the sound of a violin is the lowest vibration frequency of the air inside the body, which is about an octave higher than the lowest note. ...


5

Yes, it's coincidence, mostly. Consider that 200 years ago A was maybe 415 Hz, not 440 or 444 Hz. It is "mostly" true that there's no real value to a resonant chamber more than 1/4 wave of the lowest tone desired, but there's also a lot of art bordering on black magic to create a body which produces a "pleasant" resonant strength at all wavelengths (...


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