source file: m1394.txt
Date: Fri, 24 Apr 1998 07:10:37 -0500 (CDT)

Subject: RE: JI Tuning Resolution

From: mr88cet@texas.net (Gary Morrison)

Just to make sure that this discussion is not getting too far off the
original topic, let me paraphrase my original suggestion:  If you go to a
synthesizer manufacturer asking for tuning resolution on the order of a few
tenths of a single cent, it would probably be wise to ask yourself whether
the tones you're realizing with it are even that close to being periodic.

   Now Paul here is calling into question my belief that typical orchestral
instruments have deviations from purely harmonic vibrations.  These
deviations, best I can tell, are extremely slight, but almost certainly
much more than a few tenths of a cent.  I have not, however, specifically
measured them;  I have only observed them to exist.

   Now back to your regularly-scheduled discussion.




>I'm afraid I have to disqualify the oscilloscope here. The oscilloscope
>will have a certain finite sampling time and the period of the waveform,
>varying slighlty as it does, will never be precisely matched to this
>sampling time.

   I don't know what you're getting at by introducing sampling into this,
but you certainly don't need a digitizing oscilloscope to see this.  A
plain, boring ol' analog scope will show it just fine.

   If you zoom it in on a single period of the tone, you see the peaks and
troughs of the vibration bobbing up and down, and sometimes moving around
too.  Regardless of what you attribute that to, it's certainly not a
strictly periodic wave.  But if you change the time per division so as to
zoom out to show 10 or so cycles, you can see that the bobbing up and down
of the peaks and troughs follows a regular progression from one cycle to
the next.  Sometimes you can even actually see a peak moving through the
lower frequency components.

   This, by the way occurs on fundamental-mode pitches as well as
"overblown" pitches, so it can't be due to a subharmonic.





>If you study the mechanics of
>a 1-component driver, such as a bow, reed, or lips, you will understand
>that regardless of the extent to which the resonant modes of vibration
>of the instrument deviate from a harmonic series, the driving mechanism
>will force the waveform to become periodic,

   Would you apply that to a flute, for example?

   It sounds like you're suggesting that lips, or a reed for example, can
only vibrate periodically.  I personally am aware of no evidence to that
effect.  They certainly don't have the physical characteristics of a system
that vibrates only in harmonics, notably a mechanical transmission line.





>> . . . JI does what it does more in the lower harmonics
>>than the upper ones
>I think Harry Partch would disagree with you there.

   That of course is why I said "to the degree that JI does what it
does...":  To include the possibility that that degree might be zero.  Or
very high.

   In other words, I was not expressing an opinion along those lines;  just
stating that if that were true, then the fact that the lower harmonics are
closer to harmonic than the would be relevant.