101edo

101-EDO divides the octave into 101 equal parts of 11.881 cents each. It can be used to tune the grackle temperament. It is the 26th prime EDO. The 101cd val provides an excellent tuning for witchcraft temperament, falling between the 13 and 15 limit least squares tuning.

5-limit commas

32805/32768 ( [-15 8 1⟩ ), 51018336/48828125 ( [5 13 -11⟩ )

7-limit commas

126/125, 32805/32768, 2430/2401

Some important MOS scales

13 12 13 13 12 13 12 13: 5L3s MOS (Oneirotonic, an 8-tone circulating temperament)

Steps	Cents	Difference from 8edo
13	154.455	+4.455¢
25	297.030	-2.97¢
38	451.485	+1.485¢
51	605.9405	+5.9405¢
63	748.515	-1.485¢
75	891.089	-8.911¢
88	1045.5445	-4.5555¢

9 8 9 8 8 9 8 9 8 9 8 8: 5L7s MOS (Diatonic Pythagorean, a 12-tone circulating temperament)

Steps	Cents	Difference from 12edo
9	106.059	+6.059¢
17	201.980	+1.98¢
26	308.911	+8.911¢
34	403.960	+3.96¢
42	499.010	-.99¢
51	605.9405	+5.9405¢
59	700.990	+.99¢
68	807.921	+7.921¢
76	902.970	+2.97¢
85	1009.901	+9.901¢
93	1104.950	+4.95¢

10 3 10 3 10 3 10 3 10 3 10 3 10 3 10: 8L7s MOS (Opossum)

Steps	Cents
10	118.812
13	154.455
23	273.267
26	308.911
36	427.723
39	463.366
49	582.178
52	617.822
62	736.337
65	772.277
75	891.089
78	926.733
88	1045.5445
91	1081.188

8 5 8 5 8 5 5 8 5 8 5 8 5 8 5 5: 7L9s MOS (Golden Mavila chromatic 1/13-tone)

Steps	Cents
8	95.0495
13	154.455
21	249.505
26	308.911
34	403.960
39	463.366
44	522.772
52	617.822
57	677.228
65	772.277
70	831.683
78	926.733
83	986.139
91	1081.188
96	1045.545

4 3 3 4 3 3 4 3 4 3 3 4 3 3 4 3 3 4 3 4 3 3 4 3 3 4 3 3 4 3: 11L19s MOS (Improper Sensi-30, a 30-tone circulating temperament)

Steps	Cents	Difference from 30edo
4	47.525	+7.525¢
7	83.168	+3.168¢
10	118.812	-1.188¢
14	166.336	+6.336¢
17	201.980	+1.98¢
20	237.624	+7.624¢
24	285.1485	+5.1485¢
27	320.792	+.792¢
31	368.317	+8.317¢
34	403.960	+3.96¢
37	439.604	-.396¢
41	487.129	+7.129¢
44	527.772	+7.772¢
47	558.416	+8.416¢
51	605.9405	+5.9405¢
54	641.584	+1.584¢
57	677.228	+7.228¢
61	724.7525	+4.7525¢
64	760.396	+.396¢
68	807.921	+7.921¢
71	843.564	+3.564¢
74	879.218	-.792¢
78	926.733	+6.733¢
81	962.376	+2.376¢
84	998.020	-1.98¢
88	1045.5445	+5.5445¢
91	1081.188	+1.188¢
94	1116.842	-3.158¢
98	1164.3564	+4.356¢

7 7 7 7 1 7 7 7 7 7 1 7 7 7 7 7 1: 14L3s MOS (Anti-Ketradektriatoh)

Steps	Cents
7	83.168
14	166.337
21	249.505
22	261.386
29	344.554
36	427.723
43	510.891
50	594.059
57	677.278
58	689.119
65	772.287
72	855.446
79	938.614
86	1021.782
93	1104.950
100	1188.119

Since 101edo has a step of 11.881 cents, it also allows one to use its MOS scales as circulating temperaments. It is the first edo which truly allows one to use an 80 tone or larger MOS scale as a circulating temperament or allows one to use an MOS scale with 50 or more large steps as a circulating temperament.

Circulating temperaments in 101edo

Tones	Pattern	L:s
5	1L 4s	21:20
6	5L 1s	17:16
7	3L 4s	15:14
8	5L 3s	13:12
9	2L 7s	12:11
10	1L 9s	11:10
11	2L 9s	10:9
12	5L 7s	9:8
13	10L 3s	8:7
14	3L 11s
15	11L 4s	7:6
16	5L 11s
17	16L 1s	6:5
18	11L 7s
19	6L 13s
20	1L 19s
21	17L 4s	5:4
22	13L 9s
23	9L 14s
24	5L 19s
25	1L 24s
26	23L 3s	4:3
27	20L 7s
28	17L 11s
29	14L 15s
30	11L 19s
31	8L 23s
32	5L 27s
33	2L 31s
34	33L 1s	3:2
35	31L 4s
36	29L 7s
37	27L 10s
38	25L 13s
39	23L 16s
40	21L 19s
41	19L 22s
42	17L 25s
43	15L 28s
44	13L 31s
45	11L 34s
46	9L 37s
47	7L 40s
48	5L 43s
49	3L 49s
50	1L 49s
51	50L 1s	2:1
52	49L 3s
53	48L 5s
54	47L 7s
55	46L 9s
56	45L 11s
57	44L 13s
58	43L 15s
59	42L 17s
60	41L 19s
61	40L 21s
62	39L 23s
63	38L 25s
64	37L 27s
65	36L 29s
66	35L 31s
67	34L 33s
68	33L 35s
69	32L 37s
70	31L 39s
71	30L 41s
72	29L 43s
73	28L 45s
74	27L 47s
75	26L 49s
76	25L 51s
77	24L 53s
78	23L 55s
79	22L 57s
80	21L 59s

Links

The Ellis duodene in 101-equal