Wandering Tonic in 15TET

Here is a I VIm IIm V7 i progression that I wrote in 15TET, with the tonic
going down a comma (2^1/15) :

15 11 11 8 14
05 05 06 05 08
00 00 02 02 04
--------------- Octave separation
09 11 11 13 14

or, if you prefer

C A A G- C
E E F F- G-
C C D- D- E-
--------------- Octave separation
G A A B- C

In the third bar, F is 4/3, but it goes down to 21/16 in the fourth bar.
What is that called?

Can someone explain to me what I am hearing, and what the other
possibilities are? I have a MIDI file available, if you want it. I intend
to write many progressions like this, examples of wandering and
non-wandering in all the common ET's. I just need some theory help to get
started.

-Kami

** I am a peach tree,
** Blossoming in a deep pit.

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Date: Thu, 27 Feb 1997 15:01:22 -0800
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On Thu, 27 Feb 1997 15:02:22 -0800 John Chalmers
wrote:

>Aristoxenos's (or Cleonides's) parts are still used by the Eastern
>Orthodox Churches to describe their tetrachords, though at one time
>another system of 68 parts to the octave, 28 to the fourth was in use.
>(Savas, Xenakis, Athanasopoulos, Tiby, etc.). I do not know the origin
>of this system, however.

It had two imperfect fourths of 494 cent as tetrachords, connected by
a whole tone of 212 cents. It was not the original intent of the
designer, Abp Chrysanthos, for the imperfect fourths, but mistaken
calculations (building the tetrachord from the whole tone). As Barbour
says regarding Agriola, ("... like many another good man, confused
geometrical with arithmetical proportion" p 152). The tetrachord is
now set at 4/3 and the morion at the 30th root thereof.

Polychronios N. Moniodis
Eastern Michigan University
Ypsilanti, MI


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Date: Fri, 28 Feb 1997 19:01:12 -0800
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