Reply to Pat Missin

>Suppose you had a minor triad 10/12/15 - what major sixth would you add to
>make a minor 6th chord?

The same minor triad can also be represented as 1/6:1/5:1/4. I've done this
experiment millions of times, blindfolded, and with a sustaining tone on my
synthesizer, using headphones, I always get 10:12:15:17. It would have been
nicer theoretically if I got 1/6:1/5:1/4:2/7, but no, 10:12:15:17 sounds
right, and 1/6:1/5:1/4:2/7 sounds wrong.

Tuning the strings of my acoustic guitar, assuming I already tuned a
10:12:15, I _do_ end up with 1/6:1/5:1/4:2/7. Amazing, but true. From a
theoretical standpoint, this chord minimizes beating between overtones,
while the 10:12:15:17 exhibits "fusion" or a blending into a single
sensation. Approching this latter chord slowly on the synthesizer, one hears
beating in the low frequencies gradually coming to a halt. This probably has
something to do with eliminating beating between the virtual pitch and the
difference tones. The latter are less pronounced on the acoustic guitar,
which is however rich in overtones.

It is these sorts of experiments that lead me to quarrel with Daniel Wolf
about his use of sine waves, which would invariably lead to the 10:12:15:17
solution, and never to the subharmonic one.

Incidentally, there is another important tuning of the minor 6th chord,
6:7:9:10, but only in 12-equal is this the "same" chord.


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