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The Qm(3) family

🔗Gene W Smith <genewardsmith@juno.com>

6/14/2002 6:33:20 PM

Since seven 7s, two 9s and a 5 keep cropping up as step sizes for a 72-et
scale, I decided to look at the lot. Four stood out in the 11-limit, one
of which was Qm(3), which was distinguished by the fact that more of its
harmony was lower limit. The other three scales can be considered
11-limit siblings of Qm(3). The numbers for various odd limits are as
usual number of intervals and number of triads; all scales had an
11-limit connectivity of 6.

[0, 7, 14, 21, 30, 37, 44, 51, 60, 67] [7, 7, 7, 9, 7, 7, 7, 9, 7, 5]

3: 6 0
5: 13 4
7: 25 18
9: 29 31
11: 35 53

[0, 7, 14, 21, 30, 37, 44, 49, 56, 63] [7, 7, 7, 9, 7, 7, 5, 7, 7, 9]

3: 6 0
5: 15 6
7: 27 22
9: 31 36
11: 35 52

[0, 7, 14, 21, 30, 37, 46, 53, 60, 67] [7, 7, 7, 9, 7, 9, 7, 7, 7, 5]

3: 4 0
5: 11 4
7: 21 12
9: 27 26
11: 35 52

[0, 7, 14, 21, 30, 37, 44, 53, 60, 67] [7, 7, 7, 9, 7, 7, 9, 7, 7, 5]

3: 5 0
5: 14 5
7: 25 18
9: 30 33
11: 35 51