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.

Intervals

Steps	Cents	Approximate ratios
0	0	1/1
1	18.831
2	37.662	44/43, 45/44
3	56.494	30/29, 31/30
4	75.325	23/22
5	94.156	19/18, 37/35
6	112.987
7	131.819	27/25
8	150.65
9	169.481	43/39
10	188.312	29/26, 39/35
11	207.144	44/39
12	225.975
13	244.806
14	263.637
15	282.469
16	301.3	25/21, 44/37
17	320.131
18	338.962	45/37
19	357.794	43/35
20	376.625	36/29, 41/33
21	395.456	39/31, 44/35
22	414.287
23	433.118	9/7
24	451.95	13/10
25	470.781
26	489.612
27	508.443
28	527.275	19/14, 42/31
29	546.106	37/27
30	564.937	18/13, 43/31
31	583.768	7/5
32	602.6
33	621.431	43/30
34	640.262	42/29
35	659.093	19/13
36	677.925	34/23, 37/25
37	696.756
38	715.587
39	734.418	29/19
40	753.25	17/11
41	772.081	39/25
42	790.912	30/19
43	809.743
44	828.574	21/13
45	847.406	31/19, 44/27
46	866.237
47	885.068	5/3
48	903.899
49	922.731
50	941.562	31/18
51	960.393
52	979.224	37/21, 44/25
53	998.056
54	1016.887	9/5
55	1035.718
56	1054.549
57	1073.381	13/7
58	1092.212
59	1111.043	19/10
60	1129.874	25/13
61	1148.705	33/17
62	1167.537
63	1186.368
64	1205.199
65	1224.03
66	1242.862	39/19, 43/21
67	1261.693	29/14
68	1280.524	44/21
69	1299.355
70	1318.187	15/7
71	1337.018	13/6
72	1355.849
73	1374.68	31/14, 42/19
74	1393.512
75	1412.343	43/19
76	1431.174
77	1450.005	30/13
78	1468.837	7/3
79	1487.668
80	1506.499	31/13, 43/18
81	1525.33	29/12, 41/17
82	1544.161
83	1562.993	37/15
84	1581.824
85	1600.655
86	1619.486
87	1638.318
88	1657.149
89	1675.98
90	1694.811
91	1713.643	35/13
92	1732.474
93	1751.305
94	1770.136	25/9
95	1788.968
96	1807.799
97	1826.63
98	1845.461	29/10
99	1864.293	44/15
100	1883.124
101	1901.955	3/1

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

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