19-tone Equal Tetrachords

Several years ago I had the idea of writing out the tetrachords of the
19-tone equal. Anyone can do this for himself, and very probably this
has been done somewhere already, but perhaps it may not be taken amiss
if I here supply them:

1. C C# Db F
2. C C# D F
3. C C# D# F
4. C C# Eb F
5. C C# E F
6. C C# E# F
7. C Db D F
8. C Db D# F
9. C Db Eb F
10. C Db E F
11. C Db Fb F
12. C D D# F
13. C D Eb F
14. C D E F
15. C D Fb F
16. C D# Eb F
17. C D# E F
18. C D# E# F
19. C Eb E F
20. C Eb Fb F
21. C E E# F

Numbers 9, 13 & 14 are diatonic; numbers 8, 10 & 17 are chromatic; the
others are enharmonic (at least one interval of 1/3 tone). These of
course do not comprise all modal possibilities by any means, for which
one must add (at least) the 'augmented tetrachord' such as occurs in the
lydian mode.


SMTPOriginator: tuning@eartha.mills.edu
From: Gregg Gibson
Subject: Mathematics and Tuning
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