source file: m1410.txt
Date: Sat, 9 May 1998 16:02:06 -0500 (CDT)

Subject: Brass Aharmonicity and Other Vibrational Sources

From: mr88cet@texas.net (Gary Morrison)

>> I maintain that any systematic inharmonicity in brass instruments, which
>> is either nonexistent or extremely small, has little or nothing to do
>> with the failure of the resonant modes of the instrument to form an
>> exact harmonic series.

   I'm inclined to agree, based upon experimental evidence.  All of the
brass waveforms I've looked at have been exceptionally periodic.

   And as Paul pointed out, by all accounts I'm aware of, the
aharmonicities in brasses, bowed strings, most woodwinds are at a minimum
extremely slight.  (That even includes the observations I mentioned early
on in this conversation that a more comprehensive review proved to be much
more rare than I realized.)

   Please understand that I don't have any specific experimental results to
substantiate the following conjectures:  It would not surprise me if the
rare cases of apparently systematic fluctuations in overtone structure I've
noticed could in fact actually be periodic amplitude fluctuations of
various harmonics attributable to unrelated vibratory systems.  Examples of
such an unrelated vibratory system might perhaps include mechanisms like:
1.  Slight, low-frequency vibrations in the looser parts of a wind-instrument
    embouchure (like perhaps cheeks, or possibly even vocal chords very slightly
    "flapping in the breeze" so to speak).
2.  Parasitic vibrational modes in strings, like longitudinal or tortional
    vibrations.
3.  Parasitic vibrations in other fragments of string in a stringed instrument,
    like the short string fragments between the bridge and tailpiece.
4.  Possibly (although these would have to be very quiet to say the least!)
    parasitic resonances in other parts of an instrument like the material of
    the walls of a wind instrument vibrating.
5.  Possibly bow hairs vibrating slightly (although that seems unlikely since
    they don't have much mass).  It is, however, very easy to see that the bow
    itself can bounce subtly, or sometimes even not-too-subtly.  That, however,
    generates mostly a volume wobble that seems to affect all harmonics about
    equally.