Re: Digest Number 121

>Last year Paul Erlich pointed out that 4/3 also works
>well in a type of chord alternative-rockers use a lot,
>a "tonic" chord with "dominant 7th" structure, with
>a 4/3 added in: 1/1 - 5/4 - 4/3 - 3/2 - 7/4.

>I wrote a piece based on this idea, using in addition to
>4/3 the rational interpretations Paul discarded: 21/16,
>11/8, and even 43/32.

I don't know if I can be said to have "accepted" 1/1-5/4-4/3-3/2-7/4 and
"discarded" 1/1-5/4-21/16-3/2-7/4. Both chords contain a 21/16 interval
that is best tempered away. Even better than 12-tET for this is
(surprise) 22-tET, due to its better 7/6 and 7/4. Alternative rockers of
the future, take note!

>Haven't tried 13/12 yet, but all this leads me to
>think that the proper lattice metric for these harmonics
>of 3^-1 would connect them also with n^0 [1/1], and,
>measuring from n^0, be shorter than the higher-numbered
>(more-complex) harmonics of n^0 that are nearby in pitch.

So are you starting to lean towards a triangular lattice? (That would
accomplish what you're saying).