RE: octave equivalence

>The Bohlen-Pierce tritave unarguably exhibits one kind of
>"tritave equivalence" that is analogous to (one kind of) octave
>equivalence. This is: for a harmonic sound with partials at f,
>2f, 3f, 4f, 5f, 6f, ... and its octave with partials at 2f, 4f, 6f, 8f,
>.. playing the two together adds no new frequency
>information. Similarly, when a sound with only odd partials f,
>3f, 5f, 7f, 9f, ... and its tritave with partials at 3f, 9f, 12f, ...
>playing the two together adds no new frequency information.
>In fact, if you program up the scale, you can hear this kind of
>equivalence.

Western music has always had a very good "tritave" (perfect tweltfth). Even
with a complete harmonic spectrum, the tritave adds no new frequency
information. Why was this never perceived as an equivalence before? The
naive answer is that all our timbres with even partials suggest octaves as
the most direct kind of equivalence. But the fact of the matter is that we
don't hear partials; all we hear is virtual pitches and timbres. Inharmonic
partials are easy to hear and can form the basis of equivalence judgments.
But octave equivalence appears to be a diffent kind of phenomenon entirely.

>Perhaps this is a
>result of our 12-tet octavocentric brainwashing (i.e., cultural
>conditioning).

I doubt it. It seems to be universal, and widespread in the animal kingdom.
People sing, and even speak, in octaves everywhere. I'm going to keep
playing with the P-B and triple P-B scales, but I've failed to make myself
hear tritave equivalence, not for want of trying. I've heard 7-limit
intervals and chords as consonant, though, which motivates most of my
microtonal exploration.


Received: from ns.ezh.nl [137.174.112.59] by vbv40.ezh.nl
with SMTP-OpenVMS via TCP/IP; Fri, 16 Aug 1996 01:20 +0200
Received: by ns.ezh.nl; (5.65v3.2/1.3/10May95) id AA15063; Fri, 16 Aug 1996 01:21:00 +0200
Received: from eartha.mills.edu by ns (smtpxd); id XA15022
Received: from by eartha.mills.edu via SMTP (940816.SGI.8.6.9/930416.SGI)
for id QAA11755; Thu, 15 Aug 1996 16:20:58 -0700
Date: Thu, 15 Aug 1996 16:20:58 -0700
Message-Id: <34960815231943/0005695065PK3EM@MCIMAIL.COM>
Errors-To: madole@ella.mills.edu
Reply-To: tuning@eartha.mills.edu
Originator: tuning@eartha.mills.edu
Sender: tuning@eartha.mills.edu