101edo

← 100edo

101edo

102edo →

Prime factorization	101 (prime)
Step size	11.8812¢
Fifth	59\101 (700.99¢)
Semitones (A1:m2)	9:8 (106.9¢ : 95.05¢)
Consistency limit	3
Distinct consistency limit	3

101 equal divisions of the octave (abbreviated 101edo or 101ed2), also called 101-tone equal temperament (101tet) or 101 equal temperament (101et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 101 equal parts of about 11.9 ¢ each. Each step represents a frequency ratio of 2^1/101, or the 101st root of 2.

101edo 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.

Theory

5-limit commas

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

7-limit commas

126/125, 32805/32768, 2430/2401

Approximation of prime harmonics in 101edo

Harmonic		2	3	5	7	11	13	17	19	23	29	31
Error	absolute (¢)	+0.00	-0.96	+5.77	+5.43	-4.78	+3.04	+1.98	-0.48	+1.43	+4.09	-4.44
	relative (%)	+0	-8	+49	+46	-40	+26	+17	-4	+12	+34	-37
Steps (reduced)		101 (0)	160 (59)	235 (33)	284 (82)	349 (46)	374 (71)	413 (9)	429 (25)	457 (53)	491 (87)	500 (96)

Intervals

Steps	Cents	Ups and downs notation	Approximate ratios
0	0	D	1/1
1	11.8812	^D, v7Eb
2	23.7624	^^D, v6Eb	64/63, 78/77
3	35.6436	^3D, v5Eb	50/49, 55/54, 56/55
4	47.5248	^4D, v4Eb	40/39
5	59.4059	^5D, v3Eb
6	71.2871	^6D, vvEb
7	83.1683	^7D, vEb	21/20, 81/77
8	95.0495	^8D, Eb	55/52
9	106.931	D#, v8E
10	118.812	^D#, v7E	15/14, 77/72
11	130.693	^^D#, v6E	14/13
12	142.574	^3D#, v5E	13/12
13	154.455	^4D#, v4E	12/11
14	166.337	^5D#, v3E
15	178.218	^6D#, vvE
16	190.099	^7D#, vE
17	201.98	E	9/8
18	213.861	^E, v7F
19	225.743	^^E, v6F
20	237.624	^3E, v5F	55/48, 63/55
21	249.505	^4E, v4F	15/13, 52/45
22	261.386	^5E, v3F	64/55, 65/56
23	273.267	^6E, vvF
24	285.149	^7E, vF
25	297.03	F	32/27
26	308.911	^F, v7Gb
27	320.792	^^F, v6Gb	77/64
28	332.673	^3F, v5Gb	63/52
29	344.554	^4F, v4Gb	11/9, 39/32
30	356.436	^5F, v3Gb	16/13, 27/22
31	368.317	^6F, vvGb	26/21
32	380.198	^7F, vGb	56/45
33	392.079	^8F, Gb
34	403.96	F#, v8G	81/64
35	415.842	^F#, v7G	80/63
36	427.723	^^F#, v6G	77/60
37	439.604	^3F#, v5G
38	451.485	^4F#, v4G	13/10
39	463.366	^5F#, v3G	55/42, 72/55
40	475.248	^6F#, vvG	21/16
41	487.129	^7F#, vG	65/49
42	499.01	G	4/3
43	510.891	^G, v7Ab
44	522.772	^^G, v6Ab
45	534.653	^3G, v5Ab
46	546.535	^4G, v4Ab
47	558.416	^5G, v3Ab
48	570.297	^6G, vvAb	39/28
49	582.178	^7G, vAb	7/5
50	594.059	^8G, Ab	45/32, 55/39
51	605.941	G#, v8A	64/45, 78/55
52	617.822	^G#, v7A	10/7, 77/54
53	629.703	^^G#, v6A	56/39
54	641.584	^3G#, v5A
55	653.465	^4G#, v4A
56	665.347	^5G#, v3A
57	677.228	^6G#, vvA	77/52
58	689.109	^7G#, vA
59	700.99	A	3/2
60	712.871	^A, v7Bb
61	724.752	^^A, v6Bb	32/21
62	736.634	^3A, v5Bb	55/36, 75/49
63	748.515	^4A, v4Bb	20/13
64	760.396	^5A, v3Bb	65/42
65	772.277	^6A, vvBb
66	784.158	^7A, vBb	63/40
67	796.04	^8A, Bb
68	807.921	A#, v8B
69	819.802	^A#, v7B	45/28, 77/48
70	831.683	^^A#, v6B	21/13
71	843.564	^3A#, v5B	13/8, 44/27
72	855.446	^4A#, v4B	18/11, 64/39
73	867.327	^5A#, v3B
74	879.208	^6A#, vvB
75	891.089	^7A#, vB
76	902.97	B	27/16
77	914.851	^B, v7C
78	926.733	^^B, v6C	77/45
79	938.614	^3B, v5C	55/32
80	950.495	^4B, v4C	26/15, 45/26
81	962.376	^5B, v3C
82	974.257	^6B, vvC
83	986.139	^7B, vC
84	998.02	C	16/9
85	1009.9	^C, v7Db
86	1021.78	^^C, v6Db
87	1033.66	^3C, v5Db
88	1045.54	^4C, v4Db	11/6
89	1057.43	^5C, v3Db	24/13, 81/44
90	1069.31	^6C, vvDb	13/7
91	1081.19	^7C, vDb	28/15
92	1093.07	^8C, Db
93	1104.95	C#, v8D
94	1116.83	^C#, v7D	40/21
95	1128.71	^^C#, v6D
96	1140.59	^3C#, v5D
97	1152.48	^4C#, v4D	39/20
98	1164.36	^5C#, v3D	49/25, 55/28
99	1176.24	^6C#, vvD	63/32, 77/39
100	1188.12	^7C#, vD
101	1200	D	2/1

Some important MOS scales

25 13 25 25 13: 3L2s MOS (Pentatonic)

Steps	Cents
25	297.030
38	451.485
63	748.515
88	1045.545

17 17 8 17 17 17 8: 5L2s MOS (Diatonic Pythagorean)

Steps	Cents
17	201.980
34	403.960
42	499.010
59	700.990
76	902.970
93	1104.950

13 13 13 13 13 13 13 10: 7L1s MOS (Grumpy Octatonic)

Steps	Cents
13	154.455
26	308.911
39	463.366
52	617.822
65	772.277
78	926.733
91	1081.188

13 13 13 5 13 13 13 13 5: 7L2s MOS (Superdiatonic 1/13-tone 13;5 relation)

Steps	Cents
13	154.455
26	308.911
39	463.366
44	522.772
57	677.228
70	831.683
83	986.139
96	1045.545

10 10 7 10 10 10 7 10 10 10 7: 8L3s MOS (Improper Sensi-11)

Steps	Cents
10	118.812
20	237.624
27	320.792
37	439.604
47	558.416
57	677.228
64	760.396
74	879.218
84	998.020
94	1116.842

7 7 7 8 7 7 7 7 8 7 7 7 7 8: 3L11s MOS (Anti-Ketradektriatoh)

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

Links

The Ellis duodene in 101-equal ^{[dead link]}