source file: m1393.txt
Date: Thu, 23 Apr 1998 08:01:41 -0500 (CDT)

Subject: RE: JI Tuning Resolution

From: mr88cet@texas.net (Gary Morrison)

>Last time we had this discussion, we agreed (I thought) that bowed
>strings, winds, and brass instruments had exact integer harmonics for as
>long as they sustain a consistent tone.

   Bowed strings could be a prominent exception, but I doubt if anybody
could convincingly make that case for most any other orchestral instrument.
It's almost trivial to demonstrate that that's not true of winds in
general:  All you have to so is play them onto an oscilloscope;  in many
cases, you can quite clearly see the higher harmonics "walking" through the
oscillogram.

   Now bowed strings, since they have very exact nodal points (at least in
the cases of bridges and frets) that may not be true.  The nodal point at
the reed end of a typical wind pipe is inherently much more elastic in
nature though.  (Air-pressure node that is; air-velocity antinode.)

   But in the case of the comparatively imprecise nodal-point that a
finger-pad provides in unfretted strings, I wouldn't be surprised at all if
different overtones vary in exactly where they conclude the node is.  I
don't recall any specifics in this regard, but could investigate.

   Also, having worked a lot with sampled tones looped on a single
vibration, which obviously renders them exactly harmonic, I can certainly
attest to the fact that the timbre changes slightly when it drops into
looping.  And that timbre changes in a manner consistent with overtone
detuning.

   Now bear in mind that I'm talking about very small deviations from exact
harmonics here - probably, just as an estimate, on the order of 2-4 cents
or so.  So when we start demanding tuning accuracy on the order of tenths
of a single cent, they start becoming significant.

   Again though, as I aluded in my earlier message, these deviations from
exact harmonics are much smaller in the lower harmonics than in the higher
ones.  To the degree that JI does what it does more in the lower harmonics
than the upper ones, perhaps that makes this consideration a small one.