Critical bandwidth

In message <929351931.2673@onelist.com>, tuning@onelist.com writes
>In acoustics, the term "critical bandwidth" applies to an
>interval of approximately 1/3 octave (pitch-wise; i.e.,
>roughly 400 c.). I know of no instance of it referring to a
>full octave, as the above seems to read. (Am I missing
>something?) The critical
>bandwidth varies a little with frequency. But not that
>much! And the idea that a minor 3rd is the most dissonant
>interval that 2 sines can make seems ridiculous. Why his
>graph appears to show the phenomenon over an octave beats
>me (oops, NPI!). Perhaps he's using it, or some other term,
>differently.

Last yera, as part of my analysis portfolio in my finals of a degree in
music, I wrote an essay called "Modern psycho-acoustics and its impact
on Schenkerian analysis".* Its references included:

W. J. Dowling and D. L. Harwood, Music Cognition, (Orlando, Academic
Press, Inc., 1986), p. 50. and 83.

I interpreted what I found in this interesting book to mean the
following (interpreted for musicians with little knowledge of acoustics
and less of other parts of physics):

"The critical bandwidth is almost constant below about 200 Hz. and
approximates to a constant fraction of the basic frequency above about
500 Hz.

"This means that, in musical terms, from about the top of the treble
stave upward the most dissonant interval* remains constant at somewhat
less than a semitone, while at middle C it is 1.5 semitones, roughly
doubling for each octave downwards from there."

* The complete essay is at http://www.hpsl.demon.co.uk/schenk/

+ I mean between sine waves.

--
Ken Moore
ken@hpsl.demon.co.uk
Web site: http://www.hpsl.demon.co.uk/

Ken Moore [TD219.5]
>"This means that, in musical terms, from about the top of the treble
>stave upward the most dissonant interval* remains constant at somewhat
>less than a semitone, while at middle C it is 1.5 semitones, roughly
>doubling for each octave downwards from there."

From the above it seems that the constant difference is about 23 Hz up
to the high treble (and 4 to 5% difference from there on up). This
frequency is an interesting one because it also occurs in the sense of
sight as roughly the sampling rate (given in one reference as 20 to 25
Hz). I imagine that it some sort of fundamental sampling rate in the
brain and that as it is approached by any frequency in the senses it
would cause unpleasant effects.

I know that I can count repeated phenomena that have up to about 8
repeats per second. It seems that this is related to the same ~23 Hz
sampling rate as 3 samples per cycle are needed to get a fix on the
cycle (two can theoretically do it if you are lucky in hitting the highs
and lows but any phase drift loses it). That seems to also be the
reason for the change over from feeling individual pulses to hearing low
sounds between about 8 and 23 Hz.

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