source file: m1398.txt
Date: Mon, 27 Apr 1998 14:08:04 -0400

Subject: Re: JI Tuning Resolution

From: wauchope@AIC.NRL.Navy.Mil

David First wrote:
> Ultimately, you have to use your ears. If you hear beating/phasing
> between a given pair of frequencies, then something's off. 

My approach is that if you can hear a beat of about 0.5 Hz, then you
can in fact hear the underlying pure interval which is doing the phase
shifting, so the harmonic objective has not been compromised.  Indeed,
synth players sometimes intentionally detune a pair of oscillators so
they'd slowly phase shift and create a "fat" sound that is richer and
less boring than a single oscillator.  Beating faster than 0.5 Hz
becomes less desirable, however, and beyond vibrato rates begins
introducing actual dissonance.

Some time back I did some audio experiments to determine the extent to
which I could actually discriminate beating in just intervals.
Listening to rather loud synthesized sawtooth waves through headphones
at about 440Hz, I found that the limit of my discrimination was at the
19 limit -- for example I could manage to tune a 19/13 by eliminating
beats, but not a 21/13.  So to my ear, a 21/13 a few tenths of a cent
sharp or flat makes no distinguishable difference in terms of consonance,
but does (just barely) for a 19/13.

Figuring that the 19th partial of A440 will beat at 0.5 Hz if detuned
by 0.1 cent, that becomes my desired accuracy for the goal of avoiding
audible dissonance in a conventional pitch range.  I can imagine
musics that would want precision beyond that for particular effects
such as very sustained chords with rock-solid lack of phase shifting,
but that's another issue than dissonance.

Ken Wauchope