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 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

Approximation of prime harmonics in 101edo

Harmonic		3	5	7	11	13	17	19	23	29	31	37
Error	Absolute (¢)	-0.96	+5.77	+5.43	-4.78	+3.04	+1.98	-0.48	+1.43	+4.09	-4.44	-1.84
	Relative (%)	-8.1	+48.5	+45.7	-40.3	+25.6	+16.6	-4.1	+12.0	+34.4	-37.4	-15.5
Steps (reduced)		160 (59)	235 (33)	284 (82)	349 (46)	374 (71)	413 (9)	429 (25)	457 (53)	491 (87)	500 (96)	526 (21)

Intervals

Degree	Cents
0	0.000
1	11.881
2	23.762
3	35.644
4	47.525
5	59.406
6	71.287
7	83.168
8	95.050
9	106.931
10	118.812
11	130.693
12	142.574
13	154.455
14	166.337
15	178.218
16	190.099
17	201.980
18	213.861
19	225.743
20	237.624
21	249.505
22	261.386
23	273.267
24	285.149
25	297.030
26	308.911
27	320.792
28	332.673
29	344.554
30	356.436
31	368.317
32	380.198
33	392.079
34	403.960
35	415.842
36	427.723
37	439.604
38	451.485
39	463.366
40	475.248
41	487.129
42	499.010
43	510.891
44	522.772
45	534.653
46	546.535
47	558.416
48	570.297
49	582.178
50	594.059
...	...

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]}