Subject: RE: JI Tuning Resolution

John Loffink pleads:

> Could you give me a rough figure in terms of Hertz/CPS or even beats per
> minute/hour/day/year/millenium? :-)

With high precision, the problem becomes controlling the beats,
as you can never eliminate them. For most compositions, 1 beat
per hour will be good enough. For such slow beating between tones
of 10kHz, you need about 10^7 steps to the octave, or 0.1 millicent
step size. This is the highest precision that can have any real
meaning, and would be restricted to specialist equipment.

This is obviously beyond what any human could produce, because
you'd have to hold the pitch steady for half an hour to be sure
it's in tune. The Midi Tuning Standard covers most realistic
tuning scenarios. We should be lobbying for that to be implemented
fully. If an instrument's designed specifically for JI, it makes
more sense to specify raw frequency ratios and forget cents. It
may be possible to program a synth to adjust the phase to eliminate
beating.

The heading is JI, but I'll mention temperaments anyway. The
fifth in 19-equal is 5.3 cents flat of the 12-equal fifth. This
means there are 5 different meantones that can be accurately
reproduced with cent steps. It would be nicer to have 100 to
choose from, requiring 0.05 cent steps. I reckon on 0.1 cent
steps distinguish all the important meantones. That's all I need.

Enthusiasts for 5-limit JI who really think 53-equal is an
unacceptable compromise obviously need better than 0.15 cent steps.


Come on, does anyone have _quantitative_ data on the inharmonicity
of orchestra instruments? The piano octave is about 2 cents
sharp, so presumably other instruments must be better than this.
By how much?

This is a good reason not to read Helmholtz/Ellis as an exclusive
source. Inharmonicity hadn't been measured that accurately in
those days.

Naked reeds do produce near enough periodic vibrations. That's
how mouth organs work, and other instruments as well. Accordions
sound likely. With clarinets and whatever, the pitch is selected
by the tube. Where chipmunking occurs with wind samples, it's
probably because of the original reed spectrum. I think the
sound source in flutes is truly unpitched, because it's all
turbulence.

Brass instruments really are aperiodic. I read about this since
the last time it came up. The worst tuned partials are the low
ones for a conical tube. Even valve horns rarely play the
fundamental for this reason.


Graham Breed
gbreed@cix.co.uk www.cix.co.uk/~gbreed/