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	16.3
2	32.5
3	48.8	37/36
4	65	27/26, 28/27
5	81.3	22/21
6	97.5	18/17
7	113.8	31/29, 47/44
8	130	14/13
9	146.3	37/34, 49/45
10	162.6	45/41
11	178.8
12	195.1	47/42
13	211.3	26/23
14	227.6
15	243.8	23/20
16	260.1	36/31, 43/37
17	276.4	27/23, 34/29
18	292.6
19	308.9	43/36, 49/41
20	325.1
21	341.4	28/23
22	357.6
23	373.9	36/29, 41/33
24	390.1
25	406.4	24/19, 43/34
26	422.7	23/18, 37/29
27	438.9
28	455.2	13/10
29	471.4
30	487.7
31	503.9
32	520.2	27/20
33	536.4	15/11
34	552.7
35	569
36	585.2
37	601.5	17/12
38	617.7	10/7
39	634
40	650.2
41	666.5
42	682.8	43/29, 46/31, 49/33
43	699
44	715.3
45	731.5	29/19
46	747.8	20/13, 37/24
47	764	14/9
48	780.3
49	796.5	19/12
50	812.8
51	829.1	21/13
52	845.3	44/27
53	861.6
54	877.8
55	894.1
56	910.3	22/13
57	926.6	29/17
58	942.8	31/18
59	959.1	40/23, 47/27
60	975.4
61	991.6	39/22
62	1007.9	34/19, 43/24
63	1024.1	47/26
64	1040.4	31/17
65	1056.6
66	1072.9	13/7
67	1089.2
68	1105.4	36/19
69	1121.7	44/23
70	1137.9	27/14
71	1154.2	37/19, 39/20
72	1170.4
73	1186.7
74	1202.9
75	1219.2
76	1235.5	47/23
77	1251.7
78	1268
79	1284.2	21/10
80	1300.5	36/17
81	1316.7
82	1333
83	1349.3
84	1365.5	11/5
85	1381.8	20/9
86	1398
87	1414.3	43/19
88	1430.5
89	1446.8	30/13
90	1463
91	1479.3	40/17, 47/20
92	1495.6	19/8
93	1511.8
94	1528.1	29/12
95	1544.3
96	1560.6
97	1576.8
98	1593.1
99	1609.3
100	1625.6	23/9
101	1641.9	31/12
102	1658.1
103	1674.4
104	1690.6
105	1706.9
106	1723.1	46/17
107	1739.4	41/15
108	1755.7
109	1771.9	39/14
110	1788.2
111	1804.4	17/6
112	1820.7
113	1836.9	26/9
114	1853.2
115	1869.4
116	1885.7
117	1902	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)