101ed7

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101ed7

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Prime factorization	101 (prime)
Step size	33.3547 ¢
Octave	36\101ed7 (1200.77 ¢)
Twelfth	57\101ed7 (1901.22 ¢)
Consistency limit	8
Distinct consistency limit	8

101 divisions of the seventh harmonic (101ed7) is related to 36edo (sixth-tone tuning), but with the 7/1 rather than the 2/1 being just. The octave is about 1.2347 cents stretched and the step size is about 33.3547 cents. It is consistent to the 8-integer-limit. This tuning tempers out the syntonic comma.

Lookalikes: 21edf, 36edo, 57edt, 93ed6

Intervals

Steps	Cents	Approximate ratios
0	0	1/1
1	33.4
2	66.7	27/26
3	100.1	18/17
4	133.4	41/38
5	166.8	43/39
6	200.1	37/33
7	233.5	8/7
8	266.8	7/6
9	300.2	44/37
10	333.5
11	366.9	21/17
12	400.3	29/23, 34/27
13	433.6	9/7
14	467	38/29
15	500.3	4/3
16	533.7
17	567	43/31
18	600.4	41/29
19	633.7
20	667.1
21	700.4	3/2
22	733.8	26/17, 29/19
23	767.2	14/9
24	800.5	27/17
25	833.9	34/21
26	867.2	38/23
27	900.6	32/19, 37/22
28	933.9	12/7
29	967.3	7/4
30	1000.6	41/23
31	1034
32	1067.4
33	1100.7	17/9
34	1134.1
35	1167.4
36	1200.8	2/1
37	1234.1
38	1267.5	27/13
39	1300.8	36/17
40	1334.2
41	1367.5
42	1400.9
43	1434.3
44	1467.6	7/3
45	1501
46	1534.3	17/7
47	1567.7	42/17
48	1601
49	1634.4	18/7
50	1667.7
51	1701.1
52	1734.4
53	1767.8
54	1801.2	17/6
55	1834.5	26/9
56	1867.9
57	1901.2	3/1
58	1934.6
59	1967.9
60	2001.3
61	2034.6
62	2068
63	2101.3	37/11
64	2134.7	24/7
65	2168.1	7/2
66	2201.4
67	2234.8
68	2268.1
69	2301.5	34/9
70	2334.8	27/7
71	2368.2
72	2401.5	4/1
73	2434.9
74	2468.2
75	2501.6
76	2535
77	2568.3
78	2601.7	9/2
79	2635
80	2668.4	14/3
81	2701.7
82	2735.1	34/7
83	2768.4
84	2801.8
85	2835.2	36/7
86	2868.5	21/4
87	2901.9
88	2935.2
89	2968.6
90	3001.9	17/3
91	3035.3
92	3068.6
93	3102	6/1
94	3135.3
95	3168.7
96	3202.1
97	3235.4
98	3268.8
99	3302.1
100	3335.5
101	3368.8	7/1

Harmonics

Approximation of prime harmonics in 101ed7

Harmonic		2	3	5	7	11	13	17	19	23	29	31
Error	Absolute (¢)	+0.8	-0.7	+15.5	+0.0	-15.3	-4.4	-1.8	+5.8	+8.5	+7.5	-7.9
	Relative (%)	+2.3	-2.2	+46.4	+0.0	-46.0	-13.0	-5.4	+17.3	+25.6	+22.5	-23.7
Steps (reduced)		36 (36)	57 (57)	84 (84)	101 (0)	124 (23)	133 (32)	147 (46)	153 (52)	163 (62)	175 (74)	178 (77)

Approximation of prime harmonics in 101ed7

Harmonic		37	41	43	47	53	59	61	67	71	73	79
Error	Absolute (¢)	-14.0	+8.4	-7.3	+5.4	-2.4	+12.0	-12.3	-8.0	-8.3	+10.3	+7.0
	Relative (%)	-42.0	+25.2	-22.0	+16.3	-7.3	+36.1	-37.0	-23.9	-24.9	+30.9	+20.9
Steps (reduced)		187 (86)	193 (92)	195 (94)	200 (99)	206 (4)	212 (10)	213 (11)	218 (16)	221 (19)	223 (21)	227 (25)

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