Re: [tuning] Alternative Tuning and How We Hear

From: Paul H. Erlich <PERLICH@ACADIAN-ASSET.COM>
> http://www.ultranet.com/~wrg/wrg/music/scales/0.shtml
>
> This good site also explains the difference between harmonic tuning and
just
> tuning

I'm sorry, but I can't buy this distinction between "harmonic" and "just".
Any tuning based on whole number ratios can be described in terms of either
a harmonic (or, for that matter, subharmonic) series or on an n-dimensional
lattice; both tunings are just, both are "harmonic", and the useful term
"limit" is missing from this page.

I've observed that distinctions of this sort can often mislead beginners
into thinking of such terms as rigid, absolute classifications (e.g. there
are some out there for whom just intonation can only be Partch's 43 tone
gamut at 1/1=392 Hz). Music theory can be both intellectually lively and
musically useful -- for listeners, performers, composers alike -- but
scarcely so when applied prescriptively and inflexibly. What is harmful to
a musician in learning more than one way of describing a collection of
tones?

Daniel Wolf wrote,

>I'm sorry, but I can't buy this distinction between "harmonic" and "just".
>Any tuning based on whole number ratios can be described in terms of either
>a harmonic (or, for that matter, subharmonic) series or on an n-dimensional
>lattice; both tunings are just, both are "harmonic", and the useful term
>"limit" is missing from this page.

True, but in many cases only one or the other description is perceptually
relevant. For example, when a ratio like 405:256 arises in a just tuning
(say, an extended sruti system), it has nothing to do with hearing the 405th
harmonic directly. Likewise, in tunings like La Monte Young's sine wave
complexes, very large primes are useful only because combination tones (and
perhaps periodicity) formed with other large primes reinforce a common
fundamental, an effect which would be impossible if these primes defined
lattice axes on which multiple ratios appeared.

>What is harmful to
>a musician in learning more than one way of describing a collection of
>tones?

Nothing at all; however, when the mathematics used is not perceptually
relevant, we are in danger of both creating music divorced from sonic
reality, and of scaring away musicians with too much mathematics (I know, I
should talk . . . :).