OCTAVE FALSEHOODS

>On octave invariance, it has just occurred to me that, in LCM
>terms, the octave has a property that no other ratio shares.
>That is two notes that differ only by octaves can be mixed
>without making the length of the resulting "interference" pattern
>longer than the waveform of the lowest note.

Other ratios indeed have this property: 3:1, 5:1, 6:1, etc.

>If you mix two notes of wavelength 1 and 8, the wavelength of the
>resulting pattern is still 8, but if you mix two notes of
>wavelength 2 and 3, the resulting pattern has a wavelength of 6.

Two notes of wavelength 1 and 3 combine to form a wavelength of 3.

>[two notes] one of which has a frequency at a power-of-two of the other, the
lower one
>will cross the zero point only at points at which the higher one is crossing
>as well.

This is only true assuming the notes are exactly in phase. Changing the
phase won't change the sound of the interval. If they are in phase,
though, you can replace "power-of-two" with "integer multiple" and the
statement is still true. So 3:1, 5:1, 6:1, etc. are just as good as 2:1,
4:1, 8:1, etc.


Sorry people, there is no theoretical justification for octave
equivalence. Maybe my comments above explain why many who feel that
octave equivalence is brainwashing try to replace it with 3:1
equivalence. I believe, though, that octave equivalence is an innate,
inborn phenomenon, and I would be interested to know if that claim about
the cochlea going around once per octave is true.

Received: from ns.ezh.nl [137.174.112.59] by vbv40.ezh.nl
with SMTP-OpenVMS via TCP/IP; Wed, 2 Jul 1997 18:52 +0200
Received: by ns.ezh.nl; (5.65v3.2/1.3/10May95) id AA11650; Wed, 2 Jul 1997 18:53:05 +0200
Date: Wed, 2 Jul 1997 18:53:05 +0200
Received: from ella.mills.edu by ns (smtpxd); id XA11656
Received: (qmail 16478 invoked from network); 2 Jul 1997 16:51:32 -0000
Received: from localhost (HELO ella.mills.edu) (127.0.0.1)
by localhost with SMTP; 2 Jul 1997 16:51:32 -0000
Message-Id:
Errors-To: madole@mills.edu
Reply-To: tuning@eartha.mills.edu
Originator: tuning@eartha.mills.edu
Sender: tuning@eartha.mills.edu