Re: [tuning] Digest Number 1109

Quoth Paul Erlich:

"But Daniel, Dan Stearns and I were talking about a case where this intervals
are not voiced particularly high. In a high register, the central pitch
processor has less uncertainty, and the harmonic entropy model predicts, as you
say, that 9:7 is more concordant than 11:8 which is a bit more concordant than
11:9 -- and this agrees with my perceptions too. But in a lower register, a
greater uncertainty is in effect, and Dan Stearns' and my perceptions, as well
as the harmonic entropy model, predict that 11:9 is the most concordant of these
three intervals. Care to comment?"

My perception in the lower register is that the consonance ranking remains
intact, but that tolerance takes over and intervals within the tolerance range
are heard as out-of-tune versions of simpler ratios. So, with a lower tone below
ca. 175Hz 9:7 has slips into the 5:4 interval class and is heard as an
out-of-tune 5:4, similarly, with the lower tone below 200 Hz or so, the 11:8
gets heard as an out-of-tune 7:5, while 11/9 is optimally positioned so that it
is heard as neither 5:4 or 6:5, at least through the lowest optimal voicing of a
6:5.

DJW

Daniel Wolf wrote,

>My perception in the lower register is that the consonance ranking remains
>intact

Oh well. Our perceptions certainly differ here.