Re: 11/8 vs. 7/5

>I disagree and stick with the model. 11/8 by itself doesn't quite cut
>it.

And 11/6 does? I think I can tune the 11/8 dyad by ear about as well as
the 7/5 dyad, for whatever that's worth. The 7/5 sounds more consonant,
maybe...

>In an otonal chord, though, it definitely does cut it, but as you
>know I haven't been able to formulate a harmonic entropy model for
>chords of more than two notes.

Yes, and this is on my top-3-most-wanted list. I don't understand the
dyadic model well enough to be of much help. Did you think about the 3D
diamond? Anyhow, I really think harmonic entropy is tha bomb. Thanks for
coming up with it, Paul!

C.

Carl, where are you? Want to hear from you about you piece on May 23rd

Johnny

>>I disagree and stick with the model. 11/8 by itself doesn't quite cut
>>it.

Carl Lumma wrote,

>And 11/6 does?

I never claimed much importance for local minima of harmonic entropy,
but if you're swweping continuously through intervals, 11/6 might be a
little easier to catch.

>>In an otonal chord, though, it definitely does cut it, but as you
>>know I haven't been able to formulate a harmonic entropy model for
>>chords of more than two notes.

>Yes, and this is on my top-3-most-wanted list. I don't understand the
>dyadic model well enough to be of much help. Did you think about the
3D
>diamond?

The difficulty with a 3-note harmonic entropy measure is that a
particular ratio may not be in lowest terms by itself but each member of
the ratio may form a lowest-terms ratio with the third note. That means
that any set of mutually exclusive regions, one for each JI triad, that
covers the plane would have to be very weirdly shaped. The triads
themselves form a fractal-like structure on the plane.

>Anyhow, I really think harmonic entropy is tha bomb. Thanks for
>coming up with it, Paul!

You're welcome, but you should really thank van Eck for writing _J. S.
Bach's Critique of Pure Music_, where I got the Farey series + Gaussian
model from (I only corrected one error). And thank Yale for having that
book in their library, and for offering an Information Theory course
while I was a senior, which is where I learned to use the probabilistic
definition of entropy. All I really did was apply the latter to the
former, and you can thank "Herb" for giving me that idea (oops, I better
not run for President now). I've been sending Joe Monzo some graphs of
harmonic entropy that he'll put on his website.