9edt

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The 9 equal division of 3, the tritave, divides it into 9 equal steps of size 211.328 cents each. It has a decent 7 and an excellent 13, but a 5 which is 39 cents flat; if octaves were added and it was a sixth, it would count as a neutral sixth. The corresponding interval for 5/3 is 845 cents, which is a neutral sixth between 8/5 and 5/3, which is really more of a 13/8, though this is allegedly a no-twos tuning. On the 3.7.13 subgroup it tempers out 351/343 and 2197/2187. 9edt is the third no-twos zeta peak edt.

Following 4edt, this is the next "Lambda" (BP related) equal division of the tritave; in a certain sense analogous to 7edo in diatonic music.

This scale is also related to 17edo by which it may be approximated by playing every third step (the 17edo non-octave whole-tone scale), the discrepancy is only about four cents when it gets to 3/1.

Steps Size Comparable intervals
(in ¢) in hekts
0 1/1
1 211.328 144.444 9/8 (204)
2 422.657 288.889 9/7 (435)
3 633.985 433.333 13/9 (637)
4 845.313 577.778 13/8 (841), 5/3 (884), 8/5 (814)
5 1056.642 722.222 9/5 (1018), 11/6 (1049)
6 1267.970 866.667 27/13 (1265)
7 1479.298 1011.111 7/3 (1467)
8 1690.627 1155.556 8/3 (1698)
9 1901.955 1300 3/1