All proper modes of ET

On Brian's request I have written a computer program for finding 5-,
6-, 7-, 8-, and 9-note modes of equal temperaments with fifths less
than 21 cents away from 3/2 and the fifth degree relatively prime to
the number of notes.
I have restricted the list to proper and strictly proper modes and
didn't go beyond 31- to 53-tET as Brian wanted, because that would
yield a very very long list. The ET's are: 5, 7, 12, 17, 19, 22, 26,
27, 29 and 31.
Most of the cyclic and inversely identical modes were left out, but
not all because otherwise the program would need to run a fortnight.
This is the file, compressed by 83% to 84 Kb:
ftp://ella.mills.edu/ccm/tuning/papers/modes5-9.zip

These are the results of 7 and 12. The strictly proper modes are
indicated with an asterisk.
A mode is called proper when all intervals of an interval class are
not smaller than those of lower interval classes. It is called
strictly proper when all intervals of an interval class are larger
than the ones of lower classes.

Number of notes: 7
Selection of 5:
1 1 2 1 2
Selection of 6:
1 1 1 1 1 2
Selection of 7:
* 1 1 1 1 1 1 1

Number of notes: 12
Selection of 5:
1 2 3 3 3
1 3 2 2 4
1 3 2 3 3
1 3 3 1 4
1 3 3 2 3
1 3 3 3 2
1 4 1 3 3
1 4 2 2 3
2 1 3 3 3
2 2 2 2 4
2 2 2 3 3
2 2 2 4 2
2 2 3 1 4
* 2 2 3 2 3
2 2 3 3 2
2 2 4 1 3
2 2 4 2 2
2 3 1 3 3
2 3 1 4 2
* 2 3 2 2 3
* 2 3 2 3 2
2 3 3 1 3
2 3 3 2 2
Selection of 6:
1 2 2 2 2 3
1 2 2 2 3 2
1 2 2 3 1 3
1 2 2 3 2 2
1 2 3 1 2 3
1 2 3 1 3 2
1 2 3 2 1 3
1 2 3 2 2 2
1 3 1 2 2 3
1 3 1 2 3 2
* 1 3 1 3 1 3
1 3 1 3 2 2
1 3 2 1 2 3
1 3 2 1 3 2
1 3 2 2 1 3
1 3 2 2 2 2
2 1 2 2 2 3
2 1 2 2 3 2
2 1 2 3 1 3
2 1 2 3 2 2
2 1 3 1 2 3
2 1 3 1 3 2
2 1 3 2 1 3
2 1 3 2 2 2
2 2 1 2 2 3
2 2 1 2 3 2
2 2 1 3 1 3
2 2 1 3 2 2
2 2 2 1 2 3
2 2 2 1 3 2
2 2 2 2 1 3
* 2 2 2 2 2 2
Selection of 7:
1 1 2 2 2 2 2
1 2 1 2 2 1 3
1 2 1 2 2 2 2
1 2 1 3 1 2 2
1 2 2 1 2 1 3
1 2 2 1 2 2 2
1 2 2 1 3 1 2
1 2 2 2 1 2 2
1 2 2 2 2 1 2
Selection of 8:
1 1 2 1 2 1 2 2
1 1 2 1 2 2 1 2
1 1 2 2 1 1 2 2
1 1 2 2 1 2 1 2
1 2 1 1 2 1 2 2
1 2 1 1 2 2 1 2
1 2 1 2 1 1 2 2
* 1 2 1 2 1 2 1 2
Selection of 9:
1 1 1 2 1 1 2 1 2
1 1 1 2 1 2 1 1 2
1 1 2 1 1 1 2 1 2
1 1 2 1 1 2 1 1 2

Manuel Op de Coul coul@ezh.nl

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