21edt

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21edt

22edt →

Prime factorization	3 × 7
Step size	90.5693 ¢
Octave	13\21edt (1177.4 ¢)
Consistency limit	4
Distinct consistency limit	4

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.