source file: mills2.txt
Date: Wed, 26 Feb 1997 18:48:28 -0800

Subject: what's real?

From: Lydia Ayers <layers@cs.ust.hk>

Gary Morrison wrote (a couple of weeks ago):

>   But unlike psychoacoustic aspects, there are some structural aspects of
>the theory of tuning and scales that are pretty much impossible to deny. 
>For example, it's easy to show that it's next to impossible to build a
>scale of two identical tetrachords in most scales of less than 12
>steps/octave.  That has important effects upon the sorts of melodies you
>can realize in that tuning.  

Gary,

Could you please explain why it requires a scale of 12 steps/octave to
built an 8-tone scale?  (i.e., if there are 4 steps in each tetrachord,
there are 8 steps if both tetrachords are identical, although one
of the steps is usually the octave of the first step).

Lydia Ayers


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