Reply to Robert Valentine

Robert Valentine wrote,

>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.

I absolutely agree with these and they are perfect illustrations of what I
was trying to say:

>> Certainly one will find [ratios of higher powers of low primes] 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.

So we are agreeing!

>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".

That's because there is an additional note sounding, so your "strong pocket"
at the 3/2 of 3/2 is really nothing more than a pocket at 3/2 for the
interval formed with the additional note.

>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".

Well, that point I would contest, since in these examples you could voice
the chords differently and the "correct" notes would not longer be
octave-equivalent to overtones of the lowest note.