113edt

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113edt

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Prime factorization	113 (prime)
Step size	16.8315¢
Octave	71\113edt (1195.03¢)
Consistency limit	2
Distinct consistency limit	2

113 equal divisions of the tritave, perfect twelfth, or 3rd harmonic (abbreviated 113edt or 113ed3), is a nonoctave tuning system that divides the interval of 3/1 into 113 equal parts of about 16.8 ¢ each. Each step represents a frequency ratio of 3^1/113, or the 113th root of 3.

Intervals

Steps	Cents	Approximate Ratios
0	0	1/1
1	16.831
2	33.663
3	50.494
4	67.326	27/26
5	84.157	21/20, 43/41
6	100.989	18/17, 35/33
7	117.82	46/43
8	134.652	40/37
9	151.483
10	168.315	43/39
11	185.146
12	201.978
13	218.809	42/37
14	235.64	47/41
15	252.472	22/19
16	269.303
17	286.135	46/39
18	302.966	31/26
19	319.798
20	336.629	17/14
21	353.461	27/22, 38/31
22	370.292	26/21
23	387.124
24	403.955
25	420.787	37/29
26	437.618
27	454.449	13/10
28	471.281	46/35
29	488.112
30	504.944
31	521.775
32	538.607	15/11
33	555.438	40/29
34	572.27
35	589.101
36	605.933	44/31
37	622.764	43/30
38	639.595	42/29
39	656.427	19/13
40	673.258	31/21
41	690.09
42	706.921
43	723.753	41/27, 44/29
44	740.584	23/15
45	757.416	31/20
46	774.247
47	791.079	30/19
48	807.91
49	824.742	29/18
50	841.573
51	858.404
52	875.236
53	892.067
54	908.899	22/13
55	925.73	29/17
56	942.562	31/18
57	959.393	47/27
58	976.225
59	993.056	39/22
60	1009.888
61	1026.719	38/21, 47/26
62	1043.551
63	1060.382
64	1077.213	41/22
65	1094.045
66	1110.876	19/10
67	1127.708
68	1144.539
69	1161.371	43/22, 45/23
70	1178.202
71	1195.034
72	1211.865
73	1228.697
74	1245.528	37/18, 39/19
75	1262.36	29/14
76	1279.191	44/21
77	1296.022
78	1312.854	47/22
79	1329.685	41/19
80	1346.517	37/17
81	1363.348	11/5
82	1380.18
83	1397.011
84	1413.843	43/19
85	1430.674
86	1447.506	30/13
87	1464.337
88	1481.168	40/17, 47/20
89	1498
90	1514.831
91	1531.663	46/19
92	1548.494	22/9
93	1565.326	42/17
94	1582.157
95	1598.989
96	1615.82
97	1632.652
98	1649.483
99	1666.315
100	1683.146	37/14
101	1699.977
102	1716.809
103	1733.64
104	1750.472
105	1767.303
106	1784.135
107	1800.966	17/6
108	1817.798	20/7
109	1834.629	26/9
110	1851.461
111	1868.292
112	1885.124
113	1901.955	3/1

Harmonics

Approximation of harmonics in 113edt

Harmonic		2	3	4	5	6	7	8	9	10	11	12
Error	Absolute (¢)	-4.97	+0.00	+6.90	+7.71	-4.97	-2.53	+1.93	+0.00	+2.74	+6.05	+6.90
	Relative (%)	-29.5	+0.0	+41.0	+45.8	-29.5	-15.1	+11.5	+0.0	+16.3	+36.0	+41.0
Steps (reduced)		71 (71)	113 (0)	143 (30)	166 (53)	184 (71)	200 (87)	214 (101)	226 (0)	237 (11)	247 (21)	256 (30)

Approximation of harmonics in 113edt

Harmonic		13	14	15	16	17	18	19	20	21	22	23
Error	Absolute (¢)	+2.98	-7.50	+7.71	-3.03	-7.00	-4.97	+2.42	-2.22	-2.53	+1.09	+8.29
	Relative (%)	+17.7	-44.6	+45.8	-18.0	-41.6	-29.5	+14.4	-13.2	-15.1	+6.5	+49.2
Steps (reduced)		264 (38)	271 (45)	279 (53)	285 (59)	291 (65)	297 (71)	303 (77)	308 (82)	313 (87)	318 (92)	323 (97)