107ed4

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107ed4

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Prime factorization	107 (prime)
Step size	22.4299¢
Octave	54\107ed4 (1211.21¢)
Twelfth	85\107ed4 (1906.54¢)
Consistency limit	1
Distinct consistency limit	1

107 equal divisions of the 4th harmonic (abbreviated 107ed4) is a nonoctave tuning system that divides the interval of 4/1 into 107 equal parts of about 22.4 ¢ each. Each step represents a frequency ratio of 4^1/107, or the 107th root of 4.

Intervals

Steps	Cents	Approximate ratios
0	0	1/1
1	22.4
2	44.9	38/37, 39/38
3	67.3	27/26
4	89.7	39/37
5	112.1
6	134.6
7	157	23/21
8	179.4	41/37
9	201.9
10	224.3	33/29
11	246.7	15/13
12	269.2
13	291.6	45/38
14	314
15	336.4	17/14
16	358.9
17	381.3
18	403.7
19	426.2
20	448.6	22/17
21	471
22	493.5
23	515.9	31/23
24	538.3	15/11
25	560.7	29/21
26	583.2	7/5
27	605.6
28	628
29	650.5
30	672.9	31/21
31	695.3
32	717.8
33	740.2	23/15
34	762.6	45/29
35	785
36	807.5
37	829.9	21/13
38	852.3
39	874.8
40	897.2
41	919.6	17/10
42	942.1
43	964.5
44	986.9	23/13
45	1009.3
46	1031.8
47	1054.2
48	1076.6	41/22
49	1099.1	17/9
50	1121.5	21/11
51	1143.9
52	1166.4
53	1188.8
54	1211.2
55	1233.6
56	1256.1	31/15
57	1278.5	23/11
58	1300.9
59	1323.4
60	1345.8	37/17
61	1368.2
62	1390.7	29/13, 38/17
63	1413.1	43/19
64	1435.5	39/17
65	1457.9
66	1480.4
67	1502.8	31/13
68	1525.2	41/17
69	1547.7	22/9
70	1570.1
71	1592.5
72	1615	33/13
73	1637.4
74	1659.8
75	1682.2	37/14
76	1704.7
77	1727.1	19/7
78	1749.5
79	1772	39/14
80	1794.4	31/11
81	1816.8
82	1839.3
83	1861.7	41/14
84	1884.1
85	1906.5
86	1929
87	1951.4
88	1973.8
89	1996.3
90	2018.7
91	2041.1
92	2063.6
93	2086	10/3
94	2108.4
95	2130.8
96	2153.3
97	2175.7
98	2198.1
99	2220.6
100	2243
101	2265.4	37/10
102	2287.9
103	2310.3	19/5
104	2332.7
105	2355.1	39/10
106	2377.6
107	2400

Harmonics

Approximation of harmonics in 107ed4

Harmonic		2	3	4	5	6	7	8	9	10	11	12
Error	Absolute (¢)	+11.21	+4.59	+0.00	-5.01	-6.63	-4.34	+11.21	+9.17	+6.21	-1.79	+4.59
	Relative (%)	+50.0	+20.5	+0.0	-22.3	-29.5	-19.3	+50.0	+40.9	+27.7	-8.0	+20.5
Steps (reduced)		54 (54)	85 (85)	107 (0)	124 (17)	138 (31)	150 (43)	161 (54)	170 (63)	178 (71)	185 (78)	192 (85)

Approximation of harmonics in 107ed4

Harmonic		13	14	15	16	17	18	19	20	21	22	23
Error	Absolute (¢)	+0.59	+6.88	-0.42	+0.00	+7.19	-2.04	-5.92	-5.01	+0.25	+9.43	-0.24
	Relative (%)	+2.6	+30.7	-1.9	+0.0	+32.1	-9.1	-26.4	-22.3	+1.1	+42.0	-1.1
Steps (reduced)		198 (91)	204 (97)	209 (102)	214 (0)	219 (5)	223 (9)	227 (13)	231 (17)	235 (21)	239 (25)	242 (28)