RE: Reply to Pat Missin

Note that I don't agree with James Tenney here, nor am I appealing to
authority, but the assymmetry is strong enough to cause exaggerated
responses an obviously careful listener. Even Daniel and Little Wolf
preferred 10 12 15 17 to /12 /10 /8 /7, despite the smaller numbers in the
latter.*** Only in changing the comparison to 17 20 24 30 vs. /7 /6 /5 /4
does the subharmonic version win out.

The real test, Daniel, is to start with a just minor triad in sine waves,
and then, without looking at the numbers, and starting far away from the
target pitch, try to tune a fourth sine wave to the /7 or 17 purely by ear.
If you can do the former with anywhere near the accuracy with which you can
do the latter, I'll eat my hat.

***Yes, in tuning the added major sixth to the 17 above a minor triad 10 12
15, two double difference tones will stop beating: the 2 and the 5. But a
true test of symmetry would be whether you and your little one also think
/17 /15 /12 /10 is more consonant than 7 8 10 12.

If you think I'm posting a lot, be glad I'm in digest mode! Have a nice
weekend.


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