maj/min stuff (was Re: harmonic entropy continuing)

>BTW, doesn't it make more sense to write these subharmonic chords with the
>identity in reverse order, i.e., the 1/1 7/6 7/5 7/4 as a 1/(7:6:5:4)?

It makes sense if you expect to build chords from the lowest frequency
to the highest. But Partch implies that we should build chords by
increasing their limit rather than their frequency.

>I think that Paul meant that a 2:3, or a 4:6:9 are the same as a
>1/(3:2) and a 1/(9:6:4),

Those would be 9-limit chords.

>Major and minor? Well, if you're talking about otonal and utonal, 3:2 and
>1/2:1/3 are both perfect fifths, and 4:3 and 1/3:1/4 are both perfect
>fourths. It is certainly not the case that the perfect fifth is otonal
>and the perfect fourth is utonal.

Sorry, I did mean otonal/utonal. Yes, otonal and utonal 2:3 create
dyads of the same size, but, like Margo, I consider the 'power chord'
the basic sonority of the 3-limit, since it is saturated. 2:3:4
otonal, 1/(2:3:4) utonal. Using scale degree numbers here was also
a bad choice on my part. Anyway, I do find the difference between
these two "trines" similar to the difference between other saturated
otonal/utonal pairs through the 9-limit.

>>Another thing -- by my proposed definition of minor, all ASS's would be
>>minor.
>
>OK -- what's your proposed definition of minor again?

Any consonance of odd-limit x with significantly less tonalness than the
saturated x-limit otonal sonority.

It's really no big deal, and perhaps we should leave the definition of
minor alone. I simply suggest that the property above can be heard, in
a variety of different consonances, as a _quality_, and that this quality
has something to do with how we percieve music written in the major and
minor modes of the diatonic scale.

I seem to remember reading somebody suggesting that this quality had
to do with the way combination tones work in utonal v. otonal chords.
Same idea.

-Carl