Re: Digest Number 391

> >Whether my thinking is based on overtones, prime or odd
> >limits, 3/2^n has a very strong pocket.
>
> I don't know what you mean. I have seen no evidence in any psychoacoustic
> model of consonance, whether based on roughness, harmonic entropy, or
> combination tones, to suggest that ratios of higher powers of low primes
> could be more consonant that ratios of lower numbers based on higher primes.
> Certainly one will find the former in many chords built mainly of consonant
> intervals, but if you compare the intervals themselves, and really try to
> listen for "objective" dissonance, I think you'll find that I'm right.
>

I won't say I know enough at this point. In the situation we were
discussing, with chords and scales, I was referring to something that
has come up lately in a few threads, that of the ratios between ALL the
simultaneous terms.

27/16 in isolation may well be perceived as a sharp 5/3. In the
context of
C D G
1/1 9/8 3/2

I think the "fifth of the fifth of the fifth" will be perceived
rather than a mistuned 5/3 (mistuned to become more harmonious!).

My guess is that sounding 27/16 with

C D G
1/1 10/9 3/2

the 10/9 will be perceived as the 'wrong' note.

Similarly in

C D G A
1/1 9/8 3/2 5/3

I think the 5/3 will be perceived as flat.

Perhaps these are contrived examples (and I'll have to give them a
listen), or perhaps you can just add up all the lower limit intervals
and say "well 10/9 fails 'cuz it lunches the 4/3". What I believe they
show is my belief that the strong pocket at 3/2 (shown in your graphs)
can (somehow) carry over into a strong pocket on the "3/2 of 3/2". Not
too new a batch of knowledge, I've discovered Pythagorean tuning.

The other point is that in all these cases, what I believe will be
the perceived as "correct note" is also the "overtone series note".
This may or may not be important. I was surprised in playing with
the altered dominant scales that there was a 'rightness' in having
the b9 and #9 represented as 17 and 19 where I would have wanted
6/5 or 7/6 for the #9 to tune with a 9/5 or 7/4 seventh.

thanks.

Bob Valentine