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	Hekts	Approximate ratios
0	0	0	1/1
1	18.8	12.9
2	37.7	25.7	44/43, 45/44
3	56.5	38.6	30/29, 31/30
4	75.3	51.5	23/22
5	94.2	64.4	19/18, 37/35
6	113	77.2
7	131.8	90.1	27/25
8	150.6	103
9	169.5	115.8	43/39
10	188.3	128.7	29/26, 39/35
11	207.1	141.6	44/39
12	226	154.5
13	244.8	167.3
14	263.6	180.2
15	282.5	193.1
16	301.3	205.9	25/21, 44/37
17	320.1	218.8
18	339	231.7	45/37
19	357.8	244.6	43/35
20	376.6	257.4	36/29, 41/33
21	395.5	270.3	39/31, 44/35
22	414.3	283.2
23	433.1	296	9/7
24	451.9	308.9	13/10
25	470.8	321.8
26	489.6	334.7
27	508.4	347.5
28	527.3	360.4	19/14, 42/31
29	546.1	373.3	37/27
30	564.9	386.1	18/13, 43/31
31	583.8	399	7/5
32	602.6	411.9
33	621.4	424.8	43/30
34	640.3	437.6	42/29
35	659.1	450.5	19/13
36	677.9	463.4	34/23, 37/25
37	696.8	476.2
38	715.6	489.1
39	734.4	502	29/19
40	753.2	514.9	17/11
41	772.1	527.7	39/25
42	790.9	540.6	30/19
43	809.7	553.5
44	828.6	566.3	21/13
45	847.4	579.2	31/19, 44/27
46	866.2	592.1
47	885.1	605	5/3
48	903.9	617.8
49	922.7	630.7
50	941.6	643.6	31/18
51	960.4	656.4
52	979.2	669.3	37/21, 44/25
53	998.1	682.2
54	1016.9	695	9/5
55	1035.7	707.9
56	1054.5	720.8
57	1073.4	733.7	13/7
58	1092.2	746.5
59	1111	759.4	19/10
60	1129.9	772.3	25/13
61	1148.7	785.1	33/17
62	1167.5	798
63	1186.4	810.9
64	1205.2	823.8
65	1224	836.6
66	1242.9	849.5	39/19, 43/21
67	1261.7	862.4	29/14
68	1280.5	875.2	44/21
69	1299.4	888.1
70	1318.2	901	15/7
71	1337	913.9	13/6
72	1355.8	926.7
73	1374.7	939.6	31/14, 42/19
74	1393.5	952.5
75	1412.3	965.3	43/19
76	1431.2	978.2
77	1450	991.1	30/13
78	1468.8	1004	7/3
79	1487.7	1016.8
80	1506.5	1029.7	31/13, 43/18
81	1525.3	1042.6	29/12, 41/17
82	1544.2	1055.4
83	1563	1068.3	37/15
84	1581.8	1081.2
85	1600.7	1094.1
86	1619.5	1106.9
87	1638.3	1119.8
88	1657.1	1132.7
89	1676	1145.5
90	1694.8	1158.4
91	1713.6	1171.3	35/13
92	1732.5	1184.2
93	1751.3	1197
94	1770.1	1209.9	25/9
95	1789	1222.8
96	1807.8	1235.6
97	1826.6	1248.5
98	1845.5	1261.4	29/10
99	1864.3	1274.3	44/15
100	1883.1	1287.1
101	1902	1300	3/1