158edt

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158edt

159edt →

Prime factorization	2 × 79
Step size	12.0377 ¢
Octave	100\158edt (1203.77 ¢) (→ 50\79edt)
Consistency limit	3
Distinct consistency limit	3

158 equal divisions of the tritave, perfect twelfth, or 3rd harmonic (abbreviated 158edt or 158ed3), is a nonoctave tuning system that divides the interval of 3/1 into 158 equal parts of about 12 ¢ each. Each step represents a frequency ratio of 3^1/158, or the 158th root of 3.

Intervals

Steps	Cents	Hekts	Approximate ratios
0	0	0	1/1
1	12	8.2
2	24.1	16.5
3	36.1	24.7	47/46
4	48.2	32.9
5	60.2	41.1
6	72.2	49.4	49/47
7	84.3	57.6	21/20
8	96.3	65.8	37/35
9	108.3	74.1	33/31, 49/46
10	120.4	82.3
11	132.4	90.5	41/38
12	144.5	98.7
13	156.5	107	23/21
14	168.5	115.2	43/39, 54/49
15	180.6	123.4
16	192.6	131.6	19/17
17	204.6	139.9
18	216.7	148.1	17/15
19	228.7	156.3
20	240.8	164.6	23/20, 54/47
21	252.8	172.8
22	264.8	181
23	276.9	189.2	27/23
24	288.9	197.5	13/11
25	300.9	205.7
26	313	213.9
27	325	222.2	35/29, 41/34
28	337.1	230.4
29	349.1	238.6
30	361.1	246.8
31	373.2	255.1
32	385.2	263.3
33	397.2	271.5	39/31
34	409.3	279.7	19/15
35	421.3	288	37/29
36	433.4	296.2
37	445.4	304.4
38	457.4	312.7	43/33
39	469.5	320.9
40	481.5	329.1
41	493.5	337.3
42	505.6	345.6
43	517.6	353.8	31/23, 58/43
44	529.7	362
45	541.7	370.3	41/30
46	553.7	378.5
47	565.8	386.7	43/31
48	577.8	394.9
49	589.8	403.2
50	601.9	411.4	58/41
51	613.9	419.6
52	626	427.8	33/23
53	638	436.1	13/9
54	650	444.3
55	662.1	452.5
56	674.1	460.8	31/21
57	686.1	469	55/37, 58/39
58	698.2	477.2
59	710.2	485.4
60	722.3	493.7	41/27
61	734.3	501.9
62	746.3	510.1	20/13
63	758.4	518.4	31/20
64	770.4	526.6
65	782.4	534.8	11/7
66	794.5	543
67	806.5	551.3	43/27
68	818.6	559.5
69	830.6	567.7	21/13
70	842.6	575.9
71	854.7	584.2
72	866.7	592.4	33/20
73	878.8	600.6
74	890.8	608.9
75	902.8	617.1
76	914.9	625.3	39/23
77	926.9	633.5
78	938.9	641.8
79	951	650
80	963	658.2
81	975.1	666.5	58/33
82	987.1	674.7	23/13
83	999.1	682.9
84	1011.2	691.1
85	1023.2	699.4
86	1035.2	707.6	20/11
87	1047.3	715.8
88	1059.3	724.1
89	1071.4	732.3	13/7
90	1083.4	740.5	43/23, 58/31
91	1095.4	748.7
92	1107.5	757	55/29
93	1119.5	765.2	21/11
94	1131.5	773.4
95	1143.6	781.6
96	1155.6	789.9	39/20
97	1167.7	798.1
98	1179.7	806.3
99	1191.7	814.6
100	1203.8	822.8
101	1215.8	831
102	1227.8	839.2
103	1239.9	847.5	43/21
104	1251.9	855.7
105	1264	863.9	27/13
106	1276	872.2	23/11
107	1288	880.4
108	1300.1	888.6
109	1312.1	896.8
110	1324.1	905.1	43/20, 58/27
111	1336.2	913.3
112	1348.2	921.5
113	1360.3	929.7
114	1372.3	938
115	1384.3	946.2
116	1396.4	954.4
117	1408.4	962.7
118	1420.4	970.9
119	1432.5	979.1
120	1444.5	987.3
121	1456.6	995.6
122	1468.6	1003.8
123	1480.6	1012	47/20
124	1492.7	1020.3	45/19
125	1504.7	1028.5	31/13
126	1516.7	1036.7
127	1528.8	1044.9
128	1540.8	1053.2
129	1552.9	1061.4
130	1564.9	1069.6
131	1576.9	1077.8
132	1589	1086.1
133	1601	1094.3	58/23
134	1613.1	1102.5	33/13
135	1625.1	1110.8	23/9
136	1637.1	1119
137	1649.2	1127.2
138	1661.2	1135.4	47/18
139	1673.2	1143.7
140	1685.3	1151.9	45/17
141	1697.3	1160.1
142	1709.4	1168.4	51/19
143	1721.4	1176.6
144	1733.4	1184.8	49/18
145	1745.5	1193
146	1757.5	1201.3	58/21
147	1769.5	1209.5
148	1781.6	1217.7
149	1793.6	1225.9	31/11
150	1805.7	1234.2
151	1817.7	1242.4	20/7
152	1829.7	1250.6
153	1841.8	1258.9
154	1853.8	1267.1
155	1865.8	1275.3
156	1877.9	1283.5
157	1889.9	1291.8
158	1902	1300	3/1

Harmonics

Approximation of harmonics in 158edt

Harmonic		2	3	4	5	6	7	8	9	10	11	12
Error	Absolute (¢)	+3.77	+0.00	-4.50	-5.61	+3.77	+1.73	-0.73	+0.00	-1.84	+1.69	-4.50
	Relative (%)	+31.3	+0.0	-37.4	-46.6	+31.3	+14.3	-6.1	+0.0	-15.3	+14.0	-37.4
Steps (reduced)		100 (100)	158 (0)	199 (41)	231 (73)	258 (100)	280 (122)	299 (141)	316 (0)	331 (15)	345 (29)	357 (41)

Approximation of harmonics in 158edt

Harmonic		13	14	15	16	17	18	19	20	21	22	23
Error	Absolute (¢)	+1.38	+5.50	-5.61	+3.04	-5.62	+3.77	-5.57	+1.93	+1.73	+5.45	+0.72
	Relative (%)	+11.5	+45.7	-46.6	+25.2	-46.7	+31.3	-46.3	+16.0	+14.3	+45.3	+6.0
Steps (reduced)		369 (53)	380 (64)	389 (73)	399 (83)	407 (91)	416 (100)	423 (107)	431 (115)	438 (122)	445 (129)	451 (135)