117edt

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117edt

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Prime factorization	32 × 13
Step size	16.256¢
Octave	74\117edt (1202.95¢)
Consistency limit	4
Distinct consistency limit	4

117 equal divisions of the tritave, perfect twelfth, or 3rd harmonic (abbreviated 117edt or 117ed3), is a nonoctave tuning system that divides the interval of 3/1 into 117 equal parts of about 16.3 ¢ each. Each step represents a frequency ratio of 3^1/117, or the 117th root of 3.

Intervals

Steps	Cents	Approximate Ratios
0	0	1/1
1	16.256
2	32.512
3	48.768	37/36
4	65.024	27/26, 28/27
5	81.28	22/21
6	97.536	18/17
7	113.792	31/29, 47/44
8	130.048	14/13
9	146.304	37/34, 49/45
10	162.56	45/41
11	178.816
12	195.072	47/42
13	211.328	26/23
14	227.584
15	243.84	23/20
16	260.096	36/31, 43/37
17	276.352	27/23, 34/29
18	292.608
19	308.864	43/36, 49/41
20	325.121
21	341.377	28/23
22	357.633
23	373.889	36/29, 41/33
24	390.145
25	406.401	24/19, 43/34
26	422.657	23/18, 37/29
27	438.913
28	455.169	13/10
29	471.425
30	487.681
31	503.937
32	520.193	27/20
33	536.449	15/11
34	552.705
35	568.961
36	585.217
37	601.473	17/12
38	617.729	10/7
39	633.985
40	650.241
41	666.497
42	682.753	43/29, 46/31, 49/33
43	699.009
44	715.265
45	731.521	29/19
46	747.777	20/13, 37/24
47	764.033	14/9
48	780.289
49	796.545	19/12
50	812.801
51	829.057	21/13
52	845.313	44/27
53	861.569
54	877.825
55	894.081
56	910.337	22/13
57	926.593	29/17
58	942.849	31/18
59	959.106	40/23, 47/27
60	975.362
61	991.618	39/22
62	1007.874	34/19, 43/24
63	1024.13	47/26
64	1040.386	31/17
65	1056.642
66	1072.898	13/7
67	1089.154
68	1105.41	36/19
69	1121.666	44/23
70	1137.922	27/14
71	1154.178	37/19, 39/20
72	1170.434
73	1186.69
74	1202.946
75	1219.202
76	1235.458	47/23
77	1251.714
78	1267.97
79	1284.226	21/10
80	1300.482	36/17
81	1316.738
82	1332.994
83	1349.25
84	1365.506	11/5
85	1381.762	20/9
86	1398.018
87	1414.274	43/19
88	1430.53
89	1446.786	30/13
90	1463.042
91	1479.298	40/17, 47/20
92	1495.554	19/8
93	1511.81
94	1528.066	29/12
95	1544.322
96	1560.578
97	1576.834
98	1593.091
99	1609.347
100	1625.603	23/9
101	1641.859	31/12
102	1658.115
103	1674.371
104	1690.627
105	1706.883
106	1723.139	46/17
107	1739.395	41/15
108	1755.651
109	1771.907	39/14
110	1788.163
111	1804.419	17/6
112	1820.675
113	1836.931	26/9
114	1853.187
115	1869.443
116	1885.699
117	1901.955	3/1

Harmonics

Approximation of harmonics in 117edt

Harmonic		2	3	4	5	6	7	8	9	10	11	12
Error	Absolute (¢)	+2.95	+0.00	+5.89	-6.53	+2.95	-3.83	-7.42	+0.00	-3.59	-6.03	+5.89
	Relative (%)	+18.1	+0.0	+36.2	-40.2	+18.1	-23.6	-45.6	+0.0	-22.1	-37.1	+36.2
Steps (reduced)		74 (74)	117 (0)	148 (31)	171 (54)	191 (74)	207 (90)	221 (104)	234 (0)	245 (11)	255 (21)	265 (31)

Approximation of harmonics in 117edt

Harmonic		13	14	15	16	17	18	19	20	21	22	23
Error	Absolute (¢)	-2.63	-0.88	-6.53	-4.47	+4.36	+2.95	+6.88	-0.64	-3.83	-3.09	+1.24
	Relative (%)	-16.2	-5.4	-40.2	-27.5	+26.8	+18.1	+42.3	-3.9	-23.6	-19.0	+7.6
Steps (reduced)		273 (39)	281 (47)	288 (54)	295 (61)	302 (68)	308 (74)	314 (80)	319 (85)	324 (90)	329 (95)	334 (100)