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	20.5
2	41
3	61.5	28/27
4	82.1	22/21, 43/41
5	102.6	35/33
6	123.1
7	143.6	25/23
8	164.1
9	184.6
10	205.1
11	225.6	33/29, 49/43
12	246.2
13	266.7
14	287.2	13/11
15	307.7	37/31, 49/41
16	328.2
17	348.7
18	369.2	26/21
19	389.7
20	410.3	19/15
21	430.8
22	451.3
23	471.8
24	492.3
25	512.8	35/26, 39/29
26	533.3	34/25
27	553.8
28	574.4
29	594.9	31/22
30	615.4
31	635.9
32	656.4
33	676.9	34/23, 37/25
34	697.4
35	717.9
36	738.5	23/15
37	759
38	779.5
39	800
40	820.5	45/28
41	841
42	861.5
43	882.1
44	902.6
45	923.1	29/17, 46/27
46	943.6
47	964.1
48	984.6
49	1005.1	25/14
50	1025.6	47/26
51	1046.2
52	1066.7
53	1087.2
54	1107.7
55	1128.2
56	1148.7	33/17
57	1169.2
58	1189.7
59	1210.3
60	1230.8
61	1251.3	35/17
62	1271.8
63	1292.3	19/9
64	1312.8	47/22
65	1333.3
66	1353.8
67	1374.4	31/14, 42/19
68	1394.9	47/21
69	1415.4	34/15
70	1435.9	39/17
71	1456.4
72	1476.9
73	1497.4
74	1517.9
75	1538.5
76	1559
77	1579.5
78	1600
79	1620.5
80	1641
81	1661.5
82	1682.1	37/14
83	1702.6
84	1723.1
85	1743.6
86	1764.1
87	1784.6
88	1805.1
89	1825.6
90	1846.2
91	1866.7
92	1887.2
93	1907.7
94	1928.2
95	1948.7
96	1969.2
97	1989.7	41/13
98	2010.3
99	2030.8
100	2051.3
101	2071.8	43/13
102	2092.3
103	2112.8
104	2133.3
105	2153.8
106	2174.4
107	2194.9
108	2215.4
109	2235.9
110	2256.4
111	2276.9	41/11
112	2297.4	49/13
113	2317.9
114	2338.5
115	2359	43/11
116	2379.5
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)