113edt

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113edt

114edt →

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	Hekts	Approximate ratios
0	0	0	1/1
1	16.8	11.5
2	33.7	23
3	50.5	34.5
4	67.3	46	27/26
5	84.2	57.5	21/20, 43/41
6	101	69	18/17, 35/33
7	117.8	80.5	46/43
8	134.7	92	40/37
9	151.5	103.5
10	168.3	115	43/39
11	185.1	126.5
12	202	138.1
13	218.8	149.6	42/37
14	235.6	161.1	47/41
15	252.5	172.6	22/19
16	269.3	184.1
17	286.1	195.6	46/39
18	303	207.1	31/26
19	319.8	218.6
20	336.6	230.1	17/14
21	353.5	241.6	27/22, 38/31
22	370.3	253.1	26/21
23	387.1	264.6
24	404	276.1
25	420.8	287.6	37/29
26	437.6	299.1
27	454.4	310.6	13/10
28	471.3	322.1	46/35
29	488.1	333.6
30	504.9	345.1
31	521.8	356.6
32	538.6	368.1	15/11
33	555.4	379.6	40/29
34	572.3	391.2
35	589.1	402.7
36	605.9	414.2	44/31
37	622.8	425.7	43/30
38	639.6	437.2	42/29
39	656.4	448.7	19/13
40	673.3	460.2	31/21
41	690.1	471.7
42	706.9	483.2
43	723.8	494.7	41/27, 44/29
44	740.6	506.2	23/15
45	757.4	517.7	31/20
46	774.2	529.2
47	791.1	540.7	30/19
48	807.9	552.2
49	824.7	563.7	29/18
50	841.6	575.2
51	858.4	586.7
52	875.2	598.2
53	892.1	609.7
54	908.9	621.2	22/13
55	925.7	632.7	29/17
56	942.6	644.2	31/18
57	959.4	655.8	47/27
58	976.2	667.3
59	993.1	678.8	39/22
60	1009.9	690.3
61	1026.7	701.8	38/21, 47/26
62	1043.6	713.3
63	1060.4	724.8
64	1077.2	736.3	41/22
65	1094	747.8
66	1110.9	759.3	19/10
67	1127.7	770.8
68	1144.5	782.3
69	1161.4	793.8	43/22, 45/23
70	1178.2	805.3
71	1195	816.8
72	1211.9	828.3
73	1228.7	839.8
74	1245.5	851.3	37/18, 39/19
75	1262.4	862.8	29/14
76	1279.2	874.3	44/21
77	1296	885.8
78	1312.9	897.3	47/22
79	1329.7	908.8	41/19
80	1346.5	920.4	37/17
81	1363.3	931.9	11/5
82	1380.2	943.4
83	1397	954.9
84	1413.8	966.4	43/19
85	1430.7	977.9
86	1447.5	989.4	30/13
87	1464.3	1000.9
88	1481.2	1012.4	40/17, 47/20
89	1498	1023.9
90	1514.8	1035.4
91	1531.7	1046.9	46/19
92	1548.5	1058.4	22/9
93	1565.3	1069.9	42/17
94	1582.2	1081.4
95	1599	1092.9
96	1615.8	1104.4
97	1632.7	1115.9
98	1649.5	1127.4
99	1666.3	1138.9
100	1683.1	1150.4	37/14
101	1700	1161.9
102	1716.8	1173.5
103	1733.6	1185
104	1750.5	1196.5
105	1767.3	1208
106	1784.1	1219.5
107	1801	1231	17/6
108	1817.8	1242.5	20/7
109	1834.6	1254	26/9
110	1851.5	1265.5
111	1868.3	1277
112	1885.1	1288.5
113	1902	1300	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)