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I'll stick to the viola example, though I've heard similar arguments made about the double bass.

I've seen the following reasoning: the viola is tuned one fifth lower than the violin. A perfect fifth means a frequency ratio of 3:2, which means a wavelength ratio of 2:3, which (if we assume that the violin has the perfect size for its pitch) means what the viola should be one and a half times as big as the violin. Normally, it's smaller than that, which means it's too small.

My problem with this explanation is that the ranges of the two instruments mostly overlap. If the viola's body is too small to play e.g. the D3 note properly, then surely the violin, whose body is even smaller, must be even less suitable for producing the same pitch.

What am I missing?

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    I think at least the strings need consideration. If they are heavier, the pitch should be lower without the length changing. That why the four strings are different in pitch despite being the same length. I imagine viola strings are heavier than violin. Mar 22 at 18:29
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    Playability concerns also limit the size of the bass: you can't get much bigger and still finger and bow. Well, not without some very inventive measures. Mar 22 at 18:45
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    The problem with your problem is that the actual problem is about the part where the ranges don't overlap. It is about the inadequacy of the scale to the lowest notes produced by the viola, which the violin doesn't produce at all.
    – user207421
    Mar 23 at 7:04
  • @user207421 your answer implies that the C string behaves differently than the other strings. I haven't ever tried it myself, but after a quick search, I've found many posts that confirm that, e.g. at reddit.com/r/Viola/comments/ysh727 the top comment says: "the C string has a very different bow response than anything on the violin, and is different from the upper three strings of the viola".
    – zabolekar
    Mar 23 at 9:54
  • The Hutchins versions are an exception they're the right size for their range but their bodies are thinner Apr 11 at 3:24

2 Answers 2

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A violin doesn't resonate to just ONE particular pitch. The wood and the air in the body cavity certainly have resonant peaks, but there are lots of them, and a good violin is designed so that any one resonance doesn't predominate.

We COULD design a viola 1.5 times as big as a violin, but it probably wouldn't fit under the chin too well! It won't necessarily reproduce the same resonance plot as a violin. Why should it? It isn't a violin, it's a viola, with its own characteristic sound.

A similar, but not identical, question is discussed here: Why do lower pitched string instruments have a larger body?

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The explanation of instrument size with relation to pitch is mostly relevant for the lowest notes it plays, not as much for overlapping notes. Also instrument size goes hand in hand with instrument scale length, the distance of the open vibrating string. That is also a big factor in the sound an instrument produces.

Assuming the size in approximate body length of the violin (~360mm) was conceived perfectly hundreds of years ago then yes, scientifically the body length of a viola is small (~432mm as opposed to ~540mm) for the lowest pitch it produces based on the 1.5x model for an instrument a P5 lower. I and some others believe the low notes on a viola do lack some depth and power due to its size. The reason for its size is ease of playing since it was designed to be held like a violin and this was also conceived and decided hundreds of years ago. Fortunately we have the cellos in quartets and chamber groups, not to mention cellos and basses in orchestras to beef up the low end in the music.

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