RE: 1%

>>According to Goldstein, the precision with which frequency information is
>>transmitted to the brain's central pitch processor is between 0.6% and 1.2%
>>within a certain optimal frequency range. Goldstein, J. L. 1973. "An
>>optimum processor theory for the central formation of the pitch of complex
>>tones." J. Acoust. Soc. Amer. Vol. 54 p. 1499. The roughness component is
>>somewhat more permissive as to mistuning, but a 1% standard deviation would
>>cause the
>>accuracy to fall below 1/2 at around the point where benign beating begins
>>to gives way to the roughness effects of the critical band.

>..Just wondering what this means. It deals with mistuning plus or minus
>0.3% - 0.6% of a dyad's logorithmic size? No? What then? And what does
>it say can percieve about an interval so mistuned?

No, 0.6% means a frequency change of 0.6%. Basically Goldstein dealt
with the way complex tone pitch (virtual pitch) was inferred from sets
of pure tones which departed by various amounts from an exact harmonic
series. His experimental results were very well fit by a model with only
one parameter, sigma, which could vary from listener to listener.
Essentially the model states that the listener will interpret the set of
pure tones as a certain virtual pitch if the pure tones have an rms
deviation less than sigma from a harmonic series above that virtual
pitch. As the deviations are increased further, the ear shifts to a
different, lower virtual pitch, whose harmonics better fit the pure
>tones (this is a very rough description).

I improved the bottom of my web page entitled "'The' Dominant Seventh
Chord", thanks to feedback I've received; notably:

1) Thanks to Graham Breed for the idea of showing both chords (and making
one red) instead of showing just the Gdom7 chord.
2) Thanks to Joseph Monzo for suggesting I add a diagram for the
equal-tempered version.
3) Thanks to Andrew Kaye for the "blind" test idea.

The web page is (still) located at

http://www.pacificnet.net/~nowitzky/justint/dom7.htm

--Mark

P.S.: What a way to spend Memorial Day weekend. Well, at least I haven't
eaten any hot dogs (yet).
+------------------------------------------------------+
| Mark Nowitzky |
| email: nowitzky@alum.mit.edu AIM: Nowitzky |
| www: http://www.pacificnet.net/~nowitzky |
| "If you haven't visited Mark Nowitzky's home |
| page recently, you haven't missed much..." |
+------------------------------------------------------+