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	Hekts	Approximate ratios
0	0	0	1/1
1	16.3	11.1
2	32.5	22.2
3	48.8	33.3	37/36
4	65	44.4	27/26, 28/27
5	81.3	55.6	22/21
6	97.5	66.7	18/17
7	113.8	77.8	31/29, 47/44
8	130	88.9	14/13
9	146.3	100	37/34, 49/45
10	162.6	111.1	45/41
11	178.8	122.2
12	195.1	133.3	47/42
13	211.3	144.4	26/23
14	227.6	155.6
15	243.8	166.7	23/20
16	260.1	177.8	36/31, 43/37
17	276.4	188.9	27/23, 34/29
18	292.6	200
19	308.9	211.1	43/36, 49/41
20	325.1	222.2
21	341.4	233.3	28/23
22	357.6	244.4
23	373.9	255.6	36/29, 41/33
24	390.1	266.7
25	406.4	277.8	24/19, 43/34
26	422.7	288.9	23/18, 37/29
27	438.9	300
28	455.2	311.1	13/10
29	471.4	322.2
30	487.7	333.3
31	503.9	344.4
32	520.2	355.6	27/20
33	536.4	366.7	15/11
34	552.7	377.8
35	569	388.9
36	585.2	400
37	601.5	411.1	17/12
38	617.7	422.2	10/7
39	634	433.3
40	650.2	444.4
41	666.5	455.6
42	682.8	466.7	43/29, 46/31, 49/33
43	699	477.8
44	715.3	488.9
45	731.5	500	29/19
46	747.8	511.1	20/13, 37/24
47	764	522.2	14/9
48	780.3	533.3
49	796.5	544.4	19/12
50	812.8	555.6
51	829.1	566.7	21/13
52	845.3	577.8	44/27
53	861.6	588.9
54	877.8	600
55	894.1	611.1
56	910.3	622.2	22/13
57	926.6	633.3	29/17
58	942.8	644.4	31/18
59	959.1	655.6	40/23, 47/27
60	975.4	666.7
61	991.6	677.8	39/22
62	1007.9	688.9	34/19, 43/24
63	1024.1	700	47/26
64	1040.4	711.1	31/17
65	1056.6	722.2
66	1072.9	733.3	13/7
67	1089.2	744.4
68	1105.4	755.6	36/19
69	1121.7	766.7	44/23
70	1137.9	777.8	27/14
71	1154.2	788.9	37/19, 39/20
72	1170.4	800
73	1186.7	811.1
74	1202.9	822.2
75	1219.2	833.3
76	1235.5	844.4	47/23
77	1251.7	855.6
78	1268	866.7
79	1284.2	877.8	21/10
80	1300.5	888.9	36/17
81	1316.7	900
82	1333	911.1
83	1349.3	922.2
84	1365.5	933.3	11/5
85	1381.8	944.4	20/9
86	1398	955.6
87	1414.3	966.7	43/19
88	1430.5	977.8
89	1446.8	988.9	30/13
90	1463	1000
91	1479.3	1011.1	40/17, 47/20
92	1495.6	1022.2	19/8
93	1511.8	1033.3
94	1528.1	1044.4	29/12
95	1544.3	1055.6
96	1560.6	1066.7
97	1576.8	1077.8
98	1593.1	1088.9
99	1609.3	1100
100	1625.6	1111.1	23/9
101	1641.9	1122.2	31/12
102	1658.1	1133.3
103	1674.4	1144.4
104	1690.6	1155.6
105	1706.9	1166.7
106	1723.1	1177.8	46/17
107	1739.4	1188.9	41/15
108	1755.7	1200
109	1771.9	1211.1	39/14
110	1788.2	1222.2
111	1804.4	1233.3	17/6
112	1820.7	1244.4
113	1836.9	1255.6	26/9
114	1853.2	1266.7
115	1869.4	1277.8
116	1885.7	1288.9
117	1902	1300	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)