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By cascading tube resonators of different cross section areas, it is possible to have a lot of control over the filtering of the sound, e.g. vowels in human voice can be approximated by cascading only a small number of tubes. Below are some examples to approximate 'a' and 'i' sounds:

enter image description hereenter image description here

Is it possible to do something similar using different soundboard designs, so that the same effects can be created with string instruments on a soundboard, rather than using tube resonators on a wind instrument, or is such a control of frequency filtering not possible on soundboards?

  • I guess I should ask: why would you want this kind of filtering on a soundboard? You do get some anyway, I mean in terms of some frequencies corresponding to resonances, which helps make the sound of one violin different from another. But having a soundboard that somehow selectively amplified frequencies with the Q of Helmholz resonators would make for a rather peculiar sound, perhaps something like autotune. As alephzero said in his answer, that's precisely what instrument makers strive not to do: they try to make all frequencies as equal as possible. – Scott Wallace May 6 '17 at 14:01
  • @ScottWallace The reason I would want this kind of filtering is not for designing a conventional or better-sounding instrument, but the curiosity about the possibilities. More specifically, this leads to the question whether it is possible to make a string instrument that produces vowel-like sounds (like vowels in human speech as in the above drawings), or if this kind of application is only possible with tubes. Doesn't need to be perfect, peculiar effects are fine as long as formants can be formed. When you refer to these autotune-like sounds, do you mean the wolf tones you mentioned earlier? – ali May 6 '17 at 14:44
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    Hey ali. I think you need to check out the work of the recently deceased Hans Reichel. He made bowed instruments with very strong formants that sound the closest, in my opinion, to vowel sounds of any instrument. Here's a sample: youtube.com/watch?v=j8dG8adbOXQ – Scott Wallace May 6 '17 at 15:00
  • @ScottWallace This is amazing! – ali May 6 '17 at 15:06
  • Yeah, he created some very cool sounds. Cheers from sunny Vienna, Scott – Scott Wallace May 6 '17 at 15:44
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The resonances of a single narrow tube are simple and well separated. The frequencies are all multiples of the fundamental frequency. Joining several tubes end-to-end does not introduce more resonances, compared with separate tubes, though it does change the resonant frequencies.

For most instruments with soundboards, the soundboard itself is two-dimensional, often has a complex shape, and often has ribs or other features to strengthen it. Even for a simple rectangular plate, the resonant frequencies are proportional to (m^2/a^2 + n^2/b^2)^0.5 where a and b are the lengths of the sides of the plate, and m and n are integers 1,2,3,...

For a square plate, this gives frequencies proportional to

1.00, 1.58, 2.00, 2.23, 2.54, 2.91, 3.00, 3.16, 3.53, 3.60, 3.80, 4.00, 4.12, etc.

and the higher frequencies are even more closely spaced.

These resonances are much more complicated than a pipe. In fact soundboards are usually intended not to have distinct resonances, but to resonate uniformly at any frequency.

This shows the measured response curve of a piano soundboard, over the frequency range 0 to 5 KHz - taken from https://www.isma-isaac.be/past/conf/isma2010/proceedings/papers/isma2010_0202.pdf (which has more experimental data).

enter image description here

  • "In fact soundboards are usually intended not to have distinct resonances, but to resonate uniformly at any frequency." - Is this still true for possible experimental soundboards with complex shapes such as ones with branching areas, varying narrow and wide parts, etc.? In other words, does the two-dimensionality is a limiting factor for the purpose of creating the mentioned vowel-like sounds or is possible but only makes it much more complicated to do? – ali May 5 '17 at 12:32
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Actually, frequency filtering happens quite frequently on soundboards: it's called a "wolf tone". But wolf tones usually only resonate to one or at most a couple of tones harmonically related. I guess you could build a soundboard like a steel drum, with many differently tuned areas. I don't know if anyone's ever tried it. But nothing like having, say, 12 Helmholz resonators, is possible with normal soundboard construction.

  • Wolf tones can be caused by resonances of the air inside the body of the instrument, not of the soundboard itself. That is often the cause for cellos, where it is a common problem, especially if the "wolf" matches the frequency of one of the notes in the musical temperament being used. – user19146 May 5 '17 at 12:07
  • This is true, but in my experience, wolf tone problems caused by soundboard resonance are more frequent. – Scott Wallace May 5 '17 at 12:52

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