67ed5

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Division of the 5th harmonic into 67 equal parts (67ed5) is related to 29 edo, but with the 5/1 rather than the 2/1 being just. The octave is about 6.0164 cents stretched and the step size is about 41.5868 cents. The patent val has a generally sharp tendency for harmonics up to 28. Unlike 29edo, it is only consistent up to the 8-integer-limit, with discrepancy for the 9th harmonic.

degree cents value corresponding
JI intervals
comments
0 0.0000 exact 1/1
1 41.5868
2 83.1735 22/21, 21/20
3 124.7603 3375/3136
4 166.3471 11/10
5 207.9339 150/133
6 249.5206 800/693, 231/200
7 291.1074 45/38
8 332.6942 40/33
9 374.2809 4455/3584
10 415.8677 80/63, 14/11
11 457.4545
12 499.0413 4/3
13 540.6280
14 582.2148 7/5
15 623.8016 1125/784
16 665.3883 22/15, 147/100
17 706.9751 200/133 pseudo-3/2
18 748.5619 77/50
19 790.1487 30/19
20 831.7354 160/99
21 873.3222 63/38
22 914.9090 95/56, 56/33
23 956.4958
24 998.0825 16/9, 57/32
25 1039.6693
26 1081.2561 28/15
27 1122.8428 375/196
28 1164.4296 49/25
29 1206.0164 800/399, 225/112 pseudo-octave
30 1247.6032 154/75
31 1289.1899 40/19
32 1330.7767 640/297
33 1372.3635 495/224, 42/19
34 1413.9502 95/42, 224/99
35 1455.5370 297/128
36 1497.1238 19/8
37 1538.7106 375/154
38 1580.2973 112/45, 399/160 pseudo-5/2
39 1621.8841 125/49
40 1663.4709 196/75
41 1705.0576 75/28
42 1746.6444
43 1788.2312 160/57, 45/16
44 1829.8180
45 1871.4047 165/56, 56/19
46 1912.9915 190/63
47 1954.5783 99/32
48 1996.1650 19/6
49 2037.7518 250/77
50 2079.3386 133/40 pseudo-10/3
51 2120.9254 500/147, 75/22
52 2162.5121 784/225
53 2204.0989 25/7
54 2245.6857
55 2287.2725 15/4
56 2328.8592
57 2370.4460 55/14, 63/16
58 2412.0328 3584/891
59 2453.6195 33/8
60 2495.2063 38/9
61 2536.7931 1000/231, 693/160
62 2578.3799 133/30
63 2619.9666 50/11
64 2661.5534 3136/675
65 2703.1402 100/21
66 2744.7269
67 2786.3137 exact 5/1 just major third plus two octaves

67ed5 as a generator

67ed5 can also be thought of as a generator of the 2.3.5.7.11.19 subgroup temperament which tempers out 441/440, 513/512, 4000/3993, and 10125/10108, which is a cluster temperament with 29 clusters of notes in an octave. The small chroma interval between adjacent notes in each cluster is very versatile, representing 205821/204800 ~ 210/209 ~ 225/224 ~ 7448/7425 ~ 361/360 ~ 400/399 ~ 1375/1372 ~ 200704/200475 all tempered together. This temperament is supported by 29edo, 202edo, and 231edo.