source file: m1418.txt
Date: Sat, 16 May 1998 15:35:56 -0700 (PDT)

Subject: Re: tetrachords (Digest 1417 Topic 4)

From: Mark Nowitzky <nowitzky@alum.mit.edu>

Hey hey, Haverstick!

At 04:49 PM 5/16/98 -0400, you wrote (Digest 1417 Topic 4):
>From: Aline Surman <stick@uswest.net>
>Subject: tetrachords
>
>Here's a question which I was originally going to post privately to 
>Chalmers, but thought I'd air it out here for maximum response; why are 
>scales formed by tetrachords in the first place? I've read about them for 
>many years, and all of a sudden I realized that I don't know the 
>fundamental reason behind their origin. Any thoughts are surely 
>appreciated....thanks...Hstick

I've tripped on tetrachord explanations myself.  The explanation usually
goes "a little something like this":

        A tetrachord is four notes; e.g., "C D E F".
        Now, repeat that sequence starting at "G",
        put 'em together and you get a major scale.
        "C D E F, G A B C".

Now to what always bugged me.  In "justly intoned" scales, along with
"semitones", 16/15 interval, there's that distinction between "major tones",
9/8 interval, and "minor tones", 10/9 interval.  C major is USUALLY:

        C 9/8 D 10/9 E 16/15 F 9/8 G 10/9 A 9/8 B 16/15 C

The two "tetrachords" are not the same!  For example, there's a major tone
between C and D, but a minor tone between G and A.

Apparently this issue bugged Helmholtz and/or Ellis too, 'cuz there's a
footnote about it in "On the Sensations of Tone" (English translation of 4th
German edition, p. 255 bottom, for those of you reading along).

--Mark
+------------------------------------------------------+
| Mark Nowitzky                                        |
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