101edt

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101edt

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Prime factorization	101 (prime)
Step size	18.8312¢
Octave	64\101edt (1205.2¢)
Consistency limit	2
Distinct consistency limit	2

101 equal divisions of the tritave, perfect twelfth, or 3rd harmonic (abbreviated 101edt or 101ed3), is a nonoctave tuning system that divides the interval of 3/1 into 101 equal parts of about 18.8⁠ ⁠¢ each. Each step represents a frequency ratio of 3^1/101, or the 101st root of 3. It corresponds to 63.7240edo.

Theory

101edt is strong in the 3.5.7.13 subgroup, tempering out 16875/16807, 2205/2197 and 767637/765625. It supports canopus.

Harmonics

Approximation of harmonics in 101edt

Harmonic		2	3	4	5	6	7	8	9	10	11	12
Error	Absolute (¢)	+5.20	+0.00	-8.43	+0.71	+5.20	+1.97	-3.23	+0.00	+5.91	-8.45	-8.43
	Relative (%)	+27.6	+0.0	-44.8	+3.8	+27.6	+10.4	-17.2	+0.0	+31.4	-44.8	-44.8
Steps (reduced)		64 (64)	101 (0)	127 (26)	148 (47)	165 (64)	179 (78)	191 (90)	202 (0)	212 (10)	220 (18)	228 (26)

Approximation of harmonics in 101edt (continued)

Harmonic		13	14	15	16	17	18	19	20	21	22	23	24
Error	Absolute (¢)	+3.64	+7.16	+0.71	+1.97	-8.83	+5.20	+5.75	-7.72	+1.97	-3.25	-4.88	-3.23
	Relative (%)	+19.4	+38.0	+3.8	+10.4	-46.9	+27.6	+30.5	-41.0	+10.4	-17.2	-25.9	-17.2
Steps (reduced)		236 (34)	243 (41)	249 (47)	255 (53)	260 (58)	266 (64)	271 (69)	275 (73)	280 (78)	284 (82)	288 (86)	292 (90)

Intervals

Steps	Cents	Approximate ratios
0	0	1/1
1	18.8
2	37.7	44/43, 45/44
3	56.5	30/29, 31/30
4	75.3	23/22
5	94.2	19/18, 37/35
6	113
7	131.8	27/25
8	150.6
9	169.5	43/39
10	188.3	29/26, 39/35
11	207.1	44/39
12	226
13	244.8
14	263.6
15	282.5
16	301.3	25/21, 44/37
17	320.1
18	339	45/37
19	357.8	43/35
20	376.6	36/29, 41/33
21	395.5	39/31, 44/35
22	414.3
23	433.1	9/7
24	451.9	13/10
25	470.8
26	489.6
27	508.4
28	527.3	19/14, 42/31
29	546.1	37/27
30	564.9	18/13, 43/31
31	583.8	7/5
32	602.6
33	621.4	43/30
34	640.3	42/29
35	659.1	19/13
36	677.9	34/23, 37/25
37	696.8
38	715.6
39	734.4	29/19
40	753.2	17/11
41	772.1	39/25
42	790.9	30/19
43	809.7
44	828.6	21/13
45	847.4	31/19, 44/27
46	866.2
47	885.1	5/3
48	903.9
49	922.7
50	941.6	31/18
51	960.4
52	979.2	37/21, 44/25
53	998.1
54	1016.9	9/5
55	1035.7
56	1054.5
57	1073.4	13/7
58	1092.2
59	1111	19/10
60	1129.9	25/13
61	1148.7	33/17
62	1167.5
63	1186.4
64	1205.2
65	1224
66	1242.9	39/19, 43/21
67	1261.7	29/14
68	1280.5	44/21
69	1299.4
70	1318.2	15/7
71	1337	13/6
72	1355.8
73	1374.7	31/14, 42/19
74	1393.5
75	1412.3	43/19
76	1431.2
77	1450	30/13
78	1468.8	7/3
79	1487.7
80	1506.5	31/13, 43/18
81	1525.3	29/12, 41/17
82	1544.2
83	1563	37/15
84	1581.8
85	1600.7
86	1619.5
87	1638.3
88	1657.1
89	1676
90	1694.8
91	1713.6	35/13
92	1732.5
93	1751.3
94	1770.1	25/9
95	1789
96	1807.8
97	1826.6
98	1845.5	29/10
99	1864.3	44/15
100	1883.1
101	1902	3/1