RE: Non-octave scales; monkeys banging o

Well, I set up my keyboard to play the Pierce-Bohlen scale with a harmonic
tone having no even partials (i.e., no octaves in the harmonic series). When
I improvised a melody over a drone bass, trying to emphasize the notes that
would theoretically be consonant, I found that 33 steps above the bass
sounded like a resolution while 39 steps above the bass did not. So much for
the theory of tritave equivalence! Clearly there is a lot more equivalence
in 16:1 than in 17:1 or 15:1 or 27:1 -- octave equivalence is a real and
unavoidable phenomenon. My hypothesis is that our virtual pitch sensations
are quite indistinct as to octave register, even though our pure tone
sensations (e.g., formant perception, vowel recognition) may be quite
specific in this regard. The best approximations of the 88CET scale to the
octave are only slightly farther out than those normally used in gamelan
music, so perhaps even your generic inharmonic timbre would allow you to
hear some octave equivalence there. But certainly the tolerability of
out-of-tune, especially of stretched, multiple octaves increases with the
size of the interval -- Yasser showed that a rapid atonal passage played in
a lower register of the piano and doubled in a high register sounded the
same to his subjects when the upper part was played a semitone higher.


Received: from ns.ezh.nl [137.174.112.59] by vbv40.ezh.nl
with SMTP-OpenVMS via TCP/IP; Fri, 9 Aug 1996 15:09 +0200
Received: by ns.ezh.nl; (5.65v3.2/1.3/10May95) id AA09875; Fri, 9 Aug 1996 15:09:11 +0200
Received: from eartha.mills.edu by ns (smtpxd); id XA09873
Received: from by eartha.mills.edu via SMTP (940816.SGI.8.6.9/930416.SGI)
for id GAA24396; Fri, 9 Aug 1996 06:09:08 -0700
Date: Fri, 9 Aug 1996 06:09:08 -0700
Message-Id: <199608091306.JAA01605@cerberus2.Ensoniq.Com>
Errors-To: madole@ella.mills.edu
Reply-To: tuning@eartha.mills.edu
Originator: tuning@eartha.mills.edu
Sender: tuning@eartha.mills.edu