Your experiment

Dave:

I am a bit pressed for time (we fly to the States for four weeks on
Saturday), but I initially did the test with fixed upper tones. The series
with identical d's did not have the uniform sense of consonance I found
with those with fixed lower tones. In addition, the choice of the upper
tone was always limited by the fact that eventually you had pitches at the
bottom of the audible range or below, and then one had modulation effects.
If the bottom frequency is fixed, one does not have this restriction
(indeed, from past experiences, you can go into ultra sound and still
maintain some of the consonance sensations).

My tests were admittedly not as thorough as those with fixed lower tones,
and I do have a trained musician's bias towards hearing from the bottom up,
but my fondness for the subharmonic does mitigate this prejudice somewhat
and I would be surprised if a lengthier study showed a contrary result.

If you like, please forward this to the list.
Best

Daniel

Dan Wolf wrote:
>I am a bit pressed for time (we fly to the States for four weeks on
>Saturday), but I initially did the test with fixed upper tones. The series
>with identical d's did not have the uniform sense of consonance I found
>with those with fixed lower tones.

I would expect you to find uniform consonance with identical n's in this
case. Is that out of the question?

>In addition, the choice of the upper
>tone was always limited by the fact that eventually you had pitches at the
>bottom of the audible range or below, and then one had modulation effects.

Sure, but We're not so interested in those really wide intervals anyway.
I'd suggest upper frequencies of 400, 600 and 800Hz.

>If the bottom frequency is fixed, one does not have this restriction
>(indeed, from past experiences, you can go into ultra sound and still
>maintain some of the consonance sensations).
>
>My tests were admittedly not as thorough as those with fixed lower tones,
>and I do have a trained musician's bias towards hearing from the bottom up,
>but my fondness for the subharmonic does mitigate this prejudice somewhat
>and I would be surprised if a lengthier study showed a contrary result.
>
>If you like, please forward this to the list.

Done.

Safe journey,
-- Dave Keenan
http://dkeenan.com

Dave:

While packing last night, I had dyads playing from the series with the
upper tone fixed at 400 and 800 Hz. There is a general decrease in
dissonance as n gets larger (and the freq of the lower tone decreases). The
uniformity just isn't there that there is for a fixed lower tone. I'm
fairly convinced that consonance is the same for all intervals sharing d
when the frequency of d is fixed and the interval is wider than the
roughness curve.

Best wishes,

Daniel