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Reply to Neil from Paul

🔗Manuel.Op.de.Coul@ezh.nl (Manuel Op de Coul)

2/13/1997 2:10:19 PM
From: PAULE

Neil,

If the harmonic series is really your model for tuning, but you want equal
temperament, it seems odd that you concentrate on 19- and 34- (and have
lauded 53-) equal. 19 consistently represents the harmonic series only
through the 9th harmonic (though in your music, you tend to use the
diatonic, rather than harmonic, dom7th), and 34 consistently represents the
harmonic series only through the 5th harmonic. Equal tunings with similar
accuracies to 19 and 34, but which represent the harmonic series
consistently through the 11th harmonic, are 22 and 31, respectively.

I assume that, not being a Harry Partch fan, you don't get anything out of
ratios of 7, 9, and 11. That's fine. Maybe your model for tuning is the
harmonic series only through the 5th harmonic (plus octave equivalence).
That's fine too. Someone else's model may be the diatonic scale with no
commas and smooth 5-limit triads, they would choose 19- or 31- or 50-tET.
Someone else might like 5-limit triads and huge commas; 15-equal is for
them. Someone else might like diatonic scales with thirds tuned 7:6 and 9:7;
they would love 22. (I have other reasons for loving it.) Another person
might like to combine two different diatonic scales, taking consonant triads
from either and consonant 7-limit additions from the other. 26-equal is for
them. Someone else might want to strecth as far up the harmonic series as
possible; they could go all the way through the 15th harmonic quite
accurately with 41.

Then there are those who don't like equal temperament, or don't like simple
ratios (i.e., they like dissonance), or both, or have other specific
desiderata. As long as these goals are perceptibly beautiful, and not merely
mathematically beautiful, they will gravitate towards some tuning over
others. Equal temperament is great for transposition, for "punning," and
fretted instruments, but some want no deviation from just ratios, while
others want to control these deviations compositionally. I believe that
dissonance can be beautiful, but as almost any tuning has plenty of
dissonances available, I find it important to find tunings where this
dissonance can be contrasted with consonance. However, others may wish to
find simple pitch structures lacking in tonality of any sort; Blackwood as
singled out 11-equal as "the most effective for random dissonance" -- far
better than 12-tone serialism would be 11-tone serialism!

I'm just rambling here, but the point is that if we declare a tuning "best,"
especially in some cross-cultural sense, we are going to make life pretty
boring for future composers, and impossible for performers of traditional
music around the world (if 12-equal hasn't already done so). As for magic
and healing and Creatorship, these are things which presumably escape
scientific inquiry anyway so we'd be better off not trying to analyze or
prescribe frameworks for them.

-Paul

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