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	16.8
2	33.7
3	50.5
4	67.3	27/26
5	84.2	21/20, 43/41
6	101	18/17, 35/33
7	117.8	46/43
8	134.7	40/37
9	151.5
10	168.3	43/39
11	185.1
12	202
13	218.8	42/37
14	235.6	47/41
15	252.5	22/19
16	269.3
17	286.1	46/39
18	303	31/26
19	319.8
20	336.6	17/14
21	353.5	27/22, 38/31
22	370.3	26/21
23	387.1
24	404
25	420.8	37/29
26	437.6
27	454.4	13/10
28	471.3	46/35
29	488.1
30	504.9
31	521.8
32	538.6	15/11
33	555.4	40/29
34	572.3
35	589.1
36	605.9	44/31
37	622.8	43/30
38	639.6	42/29
39	656.4	19/13
40	673.3	31/21
41	690.1
42	706.9
43	723.8	41/27, 44/29
44	740.6	23/15
45	757.4	31/20
46	774.2
47	791.1	30/19
48	807.9
49	824.7	29/18
50	841.6
51	858.4
52	875.2
53	892.1
54	908.9	22/13
55	925.7	29/17
56	942.6	31/18
57	959.4	47/27
58	976.2
59	993.1	39/22
60	1009.9
61	1026.7	38/21, 47/26
62	1043.6
63	1060.4
64	1077.2	41/22
65	1094
66	1110.9	19/10
67	1127.7
68	1144.5
69	1161.4	43/22, 45/23
70	1178.2
71	1195
72	1211.9
73	1228.7
74	1245.5	37/18, 39/19
75	1262.4	29/14
76	1279.2	44/21
77	1296
78	1312.9	47/22
79	1329.7	41/19
80	1346.5	37/17
81	1363.3	11/5
82	1380.2
83	1397
84	1413.8	43/19
85	1430.7
86	1447.5	30/13
87	1464.3
88	1481.2	40/17, 47/20
89	1498
90	1514.8
91	1531.7	46/19
92	1548.5	22/9
93	1565.3	42/17
94	1582.2
95	1599
96	1615.8
97	1632.7
98	1649.5
99	1666.3
100	1683.1	37/14
101	1700
102	1716.8
103	1733.6
104	1750.5
105	1767.3
106	1784.1
107	1801	17/6
108	1817.8	20/7
109	1834.6	26/9
110	1851.5
111	1868.3
112	1885.1
113	1902	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)