We know there is an overtone series, or harmonic series, i.e. if a note A of 440 Hz is being played on a musical instrument, there will also be different amplitudes of sound of 880 Hz (440 Hz * 2), 1320 Hz (440 Hz * 3) etc. emitted at the same time.

But will there be a series of undertones (i.e. 220 Hz, 110 Hz...) emitted too?

I'm asking this question because:

  • I can sometimes hear a note which is an octave lower than what's actually being played on a piano. This can be very significant if this note is in a chord, which can even make me think it's an inversion;
  • In a discussion of the mechanism of the new Taylor V-Class bracing, an explanation which was claimed to be made by Andy Powers, the designer of the bracing, seems to believe the existence of undertones;
  • However, the concept "undertone" is rarely mentioned elsewhere. The wikipedia page believes undertone series can only be produced with unconventional methods.

The answer is 'yes,' with a big "if". If there is something in the instrument which is capable of vibrating at some simple multiple of the tone's wavelength, then it'll happen. As Tim's test showed, playing a note on a piano will produce a little bit of sound at sub8va and other subharmonics.
In general, if you play, say a 440-A, the 110, 220, 880, 1760 A-strings will vibrate in sympathy. Now, the higher pitched strings don't support 440, so they will "dump" energy into their own fundamental. However, the lower-pitched strings do support 440 (as the 2nd, 4th, etc harmonics), so their principle resonance will be at 440. Due to mathematical magic :-), there will be some energy at each string's fundamental, but that's a weak secondary effect.

BTW, lower-brass players can, with a little embouchure hacking, produce subharmonics. It's a matter of forcing a quarter-wave stability on a tube which prefers to be stable at half-wave.

  • My test was on a guitar. Tried it on my studio piano, but vertical strings made it impossible. Must get another grand... – Tim Apr 15 '18 at 11:02

Just done a mini-experiment. On a guitar, when a tiny strip of paper is rested on an open string - let's say the top e, and the bottom E is plucked, the paper gets vibrated off the string. Well-known, as the bottom E produces overtones, one of which is the top e pitch. Worth mentioning that if a bottom F, G etc., is played the paper stays put.

Now, turning the idea on its head, and the paper resting on the bottom, thick E, and plucking the top thin e, that paper falls off!

So yes, undertones must be there - maybe not as strong, as the basic top e is making the bottom E vibrate in sympathy, probably due to the opposite effect.

You can most likely only hear 'undertones' on a piano when the dampers aren't stopping the strings.

  • 2
    "So yes, undertones must be there" - not quite following the logic there - The top e would be able to create sympathetic resonances in the lower E without having any undertones, because the two strings have harmonics in common. – topo Reinstate Monica Mar 12 '18 at 11:48
  • I'm not rubbishing the idea of undertones by the way - the linked article seems to be about what happens when a vibrating system with one set of resonant frequencies (a string) is coupled to another system with another set of frequencies (braced instrument body) - which does seem like it could exhibit complex behaviour. – topo Reinstate Monica Mar 12 '18 at 11:51
  • @topomorto - moot point. Back to the drawing board - or as I call it - a guitar... – Tim Mar 12 '18 at 11:55

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