Re: harmonic entropy (Graham Breed)

>Hold the geometric mean of the frequencies of the two notes constant, and
>entropy is proportional to the geometric mean of the numerator and
>denominator. This is a product or LCM rule.
>
>So, Paul, are you happy with this or do we have to start that row again?

Erlich once gave the example of 15:8 vs. 6:5 against the geometric mean.
The 6/5 is supposed to be more consonant, but the (n*d) for each is the
same, as the 5 has simply switched sides of the fraction.

>As large intervals do appear to be less consonant, the denominator rule

Aha! The issue of large intervals comes again. I will follow Keenan and
call this "span".

It is true that with a large enough span, you can play almost anything and
it won't be dissonant. So in a way, span decreases dissonance. But, these
large dyads are also more difficult to difficult to tune accurately, which
suggests an increase.

Maybe the answer is that consonance and dissonance aren't mutually
exclusive opposites -- In the case of large dyads, maybe we should say that
the dissonance decreases, and so does the consonance!

Carl

Carl Lumma wrote,

>Erlich once gave the example of 15:8 vs. 6:5 against the geometric
mean.
>The 6/5 is supposed to be more consonant, but the (n*d) for each is the
>same, as the 5 has simply switched sides of the fraction.

Graham means to include factors of 2 here so my objection doesn't apply
in his case. It only applies to octave-equivalent formulations.

>I don't remember what Paul said about this. But Graham's post seemed
to
>indicate that they consider dissonance to _increase_ with span.
[...]
>Hmm. The way I read it, Graham and Erlich were saying wide dyads had
high
>dissonance. This does not fit the definition of dissonance that we've
been
>using. So I suggested that maybe they meant wide dyads had low
consonance.

You must have read it wrong. I, at least, have been saying that wide
dyads have low dissonance.

[Erlich, TD 122-21:]
>
> Carl Lumma wrote,
>
> >Erlich once gave the example of 15:8 vs. 6:5 against the geometric
mean.
> >The 6/5 is supposed to be more consonant, but the (n*d) for each is
the
> >same, as the 5 has simply switched sides of the fraction.
>
> Graham means to include factors of 2 here so my objection doesn't apply
> in his case. It only applies to octave-equivalent formulations.
>
> >I don't remember what Paul said about this. But Graham's post seemed
to
> >indicate that they consider dissonance to _increase_ with span. [...]
> >Hmm. The way I read it, Graham and Erlich were saying wide dyads had
high
> >dissonance. This does not fit the definition of dissonance that we've
been
> >using. So I suggested that maybe they meant wide dyads had low
consonance.
>
> You must have read it wrong. I, at least, have been saying that wide
> dyads have low dissonance.
>

This is exactly why I said I thought Graham
mis-wrote "larger" when he meant "larger-number".
My recollection is that it *did* sound like he was
saying that wide dyads have high dissonance.

Graham.........?????????

-monz
|\=/|.-"""-. Joseph L. Monzo...................monz@juno.com
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