117ed4

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117ed4

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Prime factorization	32 × 13
Step size	20.5128¢
Octave	59\117ed4 (1210.26¢)
Twelfth	93\117ed4 (1907.69¢) (→31\39ed4)
Consistency limit	1
Distinct consistency limit	1

117 equal divisions of the 4th harmonic (abbreviated 117ed4) is a nonoctave tuning system that divides the interval of 4/1 into 117 equal parts of about 20.5 ¢ each. Each step represents a frequency ratio of 4^1/117, or the 117th root of 4.

Intervals

Steps	Cents	Approximate Ratios
0	0	1/1
1	20.513
2	41.026
3	61.538	28/27
4	82.051	22/21, 43/41
5	102.564	35/33
6	123.077
7	143.59	25/23
8	164.103
9	184.615
10	205.128
11	225.641	33/29, 49/43
12	246.154
13	266.667
14	287.179	13/11
15	307.692	37/31, 49/41
16	328.205
17	348.718
18	369.231	26/21
19	389.744
20	410.256	19/15
21	430.769
22	451.282
23	471.795
24	492.308
25	512.821	35/26, 39/29
26	533.333	34/25
27	553.846
28	574.359
29	594.872	31/22
30	615.385
31	635.897
32	656.41
33	676.923	34/23, 37/25
34	697.436
35	717.949
36	738.462	23/15
37	758.974
38	779.487
39	800
40	820.513	45/28
41	841.026
42	861.538
43	882.051
44	902.564
45	923.077	29/17, 46/27
46	943.59
47	964.103
48	984.615
49	1005.128	25/14
50	1025.641	47/26
51	1046.154
52	1066.667
53	1087.179
54	1107.692
55	1128.205
56	1148.718	33/17
57	1169.231
58	1189.744
59	1210.256
60	1230.769
61	1251.282	35/17
62	1271.795
63	1292.308	19/9
64	1312.821	47/22
65	1333.333
66	1353.846
67	1374.359	31/14, 42/19
68	1394.872	47/21
69	1415.385	34/15
70	1435.897	39/17
71	1456.41
72	1476.923
73	1497.436
74	1517.949
75	1538.462
76	1558.974
77	1579.487
78	1600
79	1620.513
80	1641.026
81	1661.538
82	1682.051	37/14
83	1702.564
84	1723.077
85	1743.59
86	1764.103
87	1784.615
88	1805.128
89	1825.641
90	1846.154
91	1866.667
92	1887.179
93	1907.692
94	1928.205
95	1948.718
96	1969.231
97	1989.744	41/13
98	2010.256
99	2030.769
100	2051.282
101	2071.795	43/13
102	2092.308
103	2112.821
104	2133.333
105	2153.846
106	2174.359
107	2194.872
108	2215.385
109	2235.897
110	2256.41
111	2276.923	41/11
112	2297.436	49/13
113	2317.949
114	2338.462
115	2358.974	43/11
116	2379.487
117	2400

Harmonics

Approximation of harmonics in 117ed4

Harmonic		2	3	4	5	6	7	8	9	10	11	12
Error	Absolute (¢)	+10.26	+5.74	+0.00	+3.43	-4.52	-4.72	+10.26	-9.04	-6.83	-7.73	+5.74
	Relative (%)	+50.0	+28.0	+0.0	+16.7	-22.0	-23.0	+50.0	-44.1	-33.3	-37.7	+28.0
Steps (reduced)		59 (59)	93 (93)	117 (0)	136 (19)	151 (34)	164 (47)	176 (59)	185 (68)	194 (77)	202 (85)	210 (93)

Approximation of harmonics in 117ed4

Harmonic		13	14	15	16	17	18	19	20	21	22	23
Error	Absolute (¢)	-9.76	+5.53	+9.17	+0.00	-2.39	+1.22	+10.18	+3.43	+1.01	+2.53	+7.62
	Relative (%)	-47.6	+27.0	+44.7	+0.0	-11.7	+5.9	+49.6	+16.7	+4.9	+12.3	+37.2
Steps (reduced)		216 (99)	223 (106)	229 (112)	234 (0)	239 (5)	244 (10)	249 (15)	253 (19)	257 (23)	261 (27)	265 (31)