107ed11

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107ed11

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Prime factorization	107 (prime)
Step size	38.7974 ¢
Octave	31\107ed11 (1202.72 ¢)
Twelfth	49\107ed11 (1901.07 ¢) (semiconvergent)
Consistency limit	12
Distinct consistency limit	9

107 equal divisions of the 11th harmonic (abbreviated 107ed11) is a nonoctave tuning system that divides the interval of 11/1 into 107 equal parts of about 38.8 ¢ each. Each step represents a frequency ratio of 11^1/107, or the 107th root of 11.

Theory

107ed11 is related to 31edo, but with the 7/1 rather than the 2/1 being just. The octave is slightly stretched (about 2.7182 ¢, which is almost exactly e cents). Like 31edo, 107ed11 is consistent through the 12-integer-limit.

Harmonics

Approximation of harmonics in 87ed7

Harmonic		2	3	4	5	6	7	8	9	10	11	12
Error	Absolute (¢)	+0.4	-4.6	+0.8	+1.7	-4.2	+0.0	+1.2	-9.1	+2.1	-8.0	-3.8
	Relative (%)	+1.0	-11.8	+2.0	+4.3	-10.8	+0.0	+3.0	-23.6	+5.3	-20.8	-9.8
Steps (reduced)		31 (31)	49 (49)	62 (62)	72 (72)	80 (80)	87 (0)	93 (6)	98 (11)	103 (16)	107 (20)	111 (24)

Approximation of harmonics in 87ed7 (continued)

Harmonic		13	14	15	16	17	18	19	20	21	22	23	24
Error	Absolute (¢)	+12.5	+0.4	-2.9	+1.5	+12.8	-8.8	+13.8	+2.5	-4.6	-7.7	-7.2	-3.4
	Relative (%)	+32.3	+1.0	-7.5	+4.0	+32.9	-22.6	+35.7	+6.3	-11.8	-19.8	-18.5	-8.8
Steps (reduced)		115 (28)	118 (31)	121 (34)	124 (37)	127 (40)	129 (42)	132 (45)	134 (47)	136 (49)	138 (51)	140 (53)	142 (55)

Subsets and supersets

Since 87 factors into primes as 3 × 29, 87ed7 contains 3ed7 and 29ed7 as subset ed7's.

Intervals

Steps	Cents	Approximate ratios
0	0	1/1
1	38.8	43/42, 44/43, 45/44, 46/45
2	77.6	23/22, 45/43
3	116.4	31/29, 46/43
4	155.2	35/32
5	194	19/17, 28/25
6	232.8	8/7
7	271.6
8	310.4
9	349.2	11/9
10	388	5/4
11	426.8	32/25, 41/32
12	465.6	17/13
13	504.4
14	543.2	26/19
15	582	7/5
16	620.8
17	659.6	41/28
18	698.4
19	737.1	26/17
20	775.9	36/23
21	814.7	8/5
22	853.5	18/11
23	892.3
24	931.1	12/7
25	969.9	7/4
26	1008.7	34/19, 43/24
27	1047.5	11/6
28	1086.3	15/8
29	1125.1	23/12, 44/23
30	1163.9	45/23
31	1202.7
32	1241.5	41/20, 43/21
33	1280.3	44/21
34	1319.1	15/7
35	1357.9	46/21
36	1396.7
37	1435.5	39/17
38	1474.3
39	1513.1
40	1551.9
41	1590.7
42	1629.5	41/16
43	1668.3
44	1707.1
45	1745.9
46	1784.7	14/5
47	1823.5	43/15
48	1862.3	41/14, 44/15
49	1901.1	3/1
50	1939.9	46/15
51	1978.7
52	2017.5
53	2056.3
54	2095.1
55	2133.9	24/7
56	2172.7
57	2211.4	43/12
58	2250.2	11/3
59	2289	15/4
60	2327.8	23/6
61	2366.6
62	2405.4
63	2444.2	41/10
64	2483	21/5
65	2521.8
66	2560.6
67	2599.4
68	2638.2
69	2677
70	2715.8	24/5
71	2754.6
72	2793.4
73	2832.2
74	2871	21/4
75	2909.8	43/8
76	2948.6
77	2987.4
78	3026.2	23/4
79	3065
80	3103.8	6/1
81	3142.6	43/7
82	3181.4	44/7
83	3220.2	45/7
84	3259	46/7
85	3297.8
86	3336.6
87	3375.4
88	3414.2
89	3453
90	3491.8
91	3530.6
92	3569.4
93	3608.2
94	3647
95	3685.7	42/5
96	3724.5	43/5
97	3763.3	44/5
98	3802.1	9/1
99	3840.9	46/5
100	3879.7
101	3918.5
102	3957.3
103	3996.1
104	4034.9
105	4073.7
106	4112.5	43/4
107	4151.3	11/1

See also

• 18edf – relative edf
• 31edo – relative edo
• 49edt – relative edt
• 72ed5 – relative ed5
• 80ed6 – relative ed6
• 87ed7 – relative ed17
• 111ed12 – relative ed12
• 39cET