source file: m1400.txt Date: Wed, 29 Apr 1998 14:25:41 -0400 Subject: RE: Orchestral-Instrument Aperiodicity From: "Paul H. Erlich" >>It looks an awful lot like the true fundamental is an octave below the >>period you have identified. Gary wrote, > That's not terribly likely for three reasons: >1. This note is in the lower register of the bass clarinet. It is not an > overtone. The register key is not down. See my previous post about Benade or Backus and Tuvan throat singing. >2. If you look at the wave earlier in time, you see that the alternating > low-high of that rough slowly starts alternating the other direction, and > in about the same amount of time starts alternating the other way. >There's > something going on that isn't at a subharmonic frequency. Hmm, I wish I had a clearer picture of what you're talking about. I wonder if a double-reed instrument might have some slow phase drift due to slight inequalities between the two reeds, much like a guitar string will vibrate at two slighlty different frequencies if the bridge allows horizontal vibrations to begin at a different point or with different resistance than vertical vibrations. >3. Once again, if it were a component at half the fundamental frequency, we > would have seen the entire wave ooze up and down with that trough. Not necessarily. A physical "subharmonic" is not just a sine wave but is a (weak) true fundamental with any or all (weak) harmonic overtones. In this case, those overtones would be at 3/2, 5/3, 7/2, . . . the primary pitch and could conspire to keep the bulk of the waveform intact. (I'm sure if we knew more about the physics of the situation, this "conspiracy" would turn out to arise in a very natural way, not one that requires any "consciousness" on the part of the instrument).