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	22.43
2	44.86	38/37, 39/38
3	67.29	27/26
4	89.72	39/37
5	112.15
6	134.579
7	157.009	23/21
8	179.439	41/37
9	201.869
10	224.299	33/29
11	246.729	15/13
12	269.159
13	291.589	45/38
14	314.019
15	336.449	17/14
16	358.879
17	381.308
18	403.738
19	426.168
20	448.598	22/17
21	471.028
22	493.458
23	515.888	31/23
24	538.318	15/11
25	560.748	29/21
26	583.178	7/5
27	605.607
28	628.037
29	650.467
30	672.897	31/21
31	695.327
32	717.757
33	740.187	23/15
34	762.617	45/29
35	785.047
36	807.477
37	829.907	21/13
38	852.336
39	874.766
40	897.196
41	919.626	17/10
42	942.056
43	964.486
44	986.916	23/13
45	1009.346
46	1031.776
47	1054.206
48	1076.636	41/22
49	1099.065	17/9
50	1121.495	21/11
51	1143.925
52	1166.355
53	1188.785
54	1211.215
55	1233.645
56	1256.075	31/15
57	1278.505	23/11
58	1300.935
59	1323.364
60	1345.794	37/17
61	1368.224
62	1390.654	29/13, 38/17
63	1413.084	43/19
64	1435.514	39/17
65	1457.944
66	1480.374
67	1502.804	31/13
68	1525.234	41/17
69	1547.664	22/9
70	1570.093
71	1592.523
72	1614.953	33/13
73	1637.383
74	1659.813
75	1682.243	37/14
76	1704.673
77	1727.103	19/7
78	1749.533
79	1771.963	39/14
80	1794.393	31/11
81	1816.822
82	1839.252
83	1861.682	41/14
84	1884.112
85	1906.542
86	1928.972
87	1951.402
88	1973.832
89	1996.262
90	2018.692
91	2041.121
92	2063.551
93	2085.981	10/3
94	2108.411
95	2130.841
96	2153.271
97	2175.701
98	2198.131
99	2220.561
100	2242.991
101	2265.421	37/10
102	2287.85
103	2310.28	19/5
104	2332.71
105	2355.14	39/10
106	2377.57
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)