21edt

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21 Equal Divisions of the Tritave

Degrees Cents hekts Approximate Ratio
0 1/1
1 90.569 61.905 21/20, 135/128
2 181.139 123.81 10/9
3 271.708 185.714 7/6
4 362.277 247.619 16/13
5 452.846 309.524 13/10
6 543.416 371.429 15/11, 11/8
7 633.985 433.333 13/9
8 724.554 495.238 35/23
9 815.124 557.143 8/5
10 905.693 619.048 27/16
11 996.262 680.952 16/9
12 1086.831 742.857 15/8
13 1177.401 804.762 69/35
14 1267.97 866.667 27/13
15 1358.539 928.571 11/5 (11/10 plus an octave), 24/11 (12/11 plus an octave)
16 1449.109 990.476 30/13 (15/13 plus an octave)
17 1539.678 1052.381 39/16
18 1630.247 1114.286 18/7 (9/7 plus an octave)
19 1720.816 1076.19 27/10
20 1811.386 1238.095 20/7, 128/45
21 1901.955 1300 3/1

21edt contains 6 intervals from 7edt and 2 intervals from 3edt, meaning that it introduces 12 new intervals not available in lower edt's. These new intervals allow for construction of strange chords like 9:10:13:16:22:27:30...

21edt contains a 7L7s MOS similar to Whitewood, which I call Ivory. It has a period of 1/7 of the tritave and the generator is one step. The major scale is LsLsLsLsLsLsLs, and the minor scale is sLsLsLsLsLsLsL.

21edt also contains a 4L5s MOS similar to BP, with a 4:1 ratio of large to small; quite exaggerated from the optimal 2:1. Although the 7/3 is a little off, the 4L+5s BP scale is pretty. However, one of the star scales in 21edt is the 3L+6s (ssLssLssL and modes thereof) which is very harmonically rich, the cornerstone of which is the approximate 9:13:19 chord (which is just the 3edt essentially tempered chord).

Not the best approximations but all within 20 cents: it has 5th (+20c), 7th(-16c), 10th (+2c), 11th (+15c), 13th (-3c), 17th (-14c), 23rd (+6 c), and 37th (-2c) harmonics. For a lower division of the tritave that's quite a constellation! The chord is a little out of tune but it works, you can really sink into it.