binaural beats

Thanks, Paul, your reply to Ken Fasano gave an excellent explanation
of the relationship between the "music theory" terms otonal/utonal
and the "physiological" term virtual pitch.

I would like to disagree about a small point, however. You said:

>The reason all that is ascribed to the brain's central pitch processor
is that these "harmonics" can be presented some to one ear, some to the
other, without ever changing the virtual-pitch effect. Roughness
("sensory dissonance" as discussed by Sethares), on the other hand,
occurs only between tones presented to the same ear. This sensory
dissonance accounts for a good deal of the consonance of otonal and
utonal chords formed from complex harmonic tones.

Actually, sensory dissonance (roughness) can be heard when
presented binaurally (one sine at each ear), but the perceived
amplitude of the beating is considerably reduced from when it is
presented monaurally. You can hear this effect on tracks 9 and 10 of
the CD accompanying TTSS. In 9 the two sines are mixed dead center
while in track 10 one is panned to the left and the other to the right.
You can hear the roughness in both cases, but with noticeably
different strengths.

This may be at the heart of why sensory dissonance is so hard to pin
down - its not one phenomenon, but two separate phenomena
entangled with each other. There is the part that occurs in the "ear"
(this is probably due to a nonlinear rectification by the hair cells on
the basilar memnbrane) and there is the part that occurs in the
"higher centers". The former is likely the primary constituent of the
monaural perception, while the latter (very analogous to combination
or difference tones) is the root of the binaural sensation.

There was an excellent paper a while ago (July 1981) in the Am J of
Physics by Don Hall called "The difference between difference tones
and rapid beats" that talked about this at length.

> Actually, sensory dissonance (roughness) can be heard when
> presented binaurally (one sine at each ear), but the perceived
> amplitude of the beating is considerably reduced from when it is
> presented monaurally. You can hear this effect on tracks 9 and 10 of
> the CD accompanying TTSS.

That was an intriguing demonstration from Bill's book. One of many good
reasons to by it!

William Sethares wrote,

>Actually, sensory dissonance (roughness) can be heard when
>presented binaurally (one sine at each ear), but the perceived
>amplitude of the beating is considerably reduced from when it is
>presented monaurally. You can hear this effect on tracks 9 and 10 of
>the CD accompanying TTSS. In 9 the two sines are mixed dead center
>while in track 10 one is panned to the left and the other to the right.

>You can hear the roughness in both cases, but with noticeably
>different strengths.

I was under the impression that roughness and beats were two distinct
phenomena that usually go together. Slow beating, for example, is
normally associated with very little roughness; maximum roughness occurs
at about 25% of the critical bandwidth regardless of the rate of beating
(which will depend on register), and for high-frequency tones separated
by, say, two-thirds of a critical bandwidth, all you have is roughness
-- the beating is just too fast to perceive. I've played with binaural
beats but would you say they are associated with roughness?

>There was an excellent paper a while ago (July 1981) in the Am J of
>Physics by Don Hall called "The difference between difference tones
>and rapid beats" that talked about this at length.

The title of this article is a different confusion that people often
have. People often assume that that any sonic phenomenon with a
frequency in the audible range will produce the tone normally associated
with that frequency. This is not the case, as even a naive mathematical
understanding of wave phenomena will make clear.