157edt

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157edt

158edt →

Prime factorization	157 (prime)
Step size	12.1144 ¢
Octave	99\157edt (1199.32 ¢)
Consistency limit	12
Distinct consistency limit	12

Division of the third harmonic into 157 equal parts (157EDT) is related to 99edo, but with the 3/1 rather than the 2/1 being just. The octave is about 0.6781 cents compressed and the step size is about 12.1144 cents. It is consistent to the 12-integer-limit. In comparison, 99edo is only consistent up to the 10-integer-limit. 157edt is notable for it's excellent 5/3, as a convergent to log₃(5), and can be used effectively both with and without twos.

Intervals

Steps	Cents	Hekts	Approximate ratios
0	0	0	1/1
1	12.1	8.3
2	24.2	16.6
3	36.3	24.8	47/46, 48/47, 49/48, 50/49
4	48.5	33.1	36/35, 37/36
5	60.6	41.4	29/28, 57/55
6	72.7	49.7	24/23, 49/47
7	84.8	58	21/20
8	96.9	66.2	37/35, 55/52
9	109	74.5	33/31, 49/46
10	121.1	82.8	44/41
11	133.3	91.1	27/25
12	145.4	99.4	25/23, 37/34
13	157.5	107.6	23/21, 57/52
14	169.6	115.9	32/29, 43/39, 54/49
15	181.7	124.2	10/9
16	193.8	132.5	19/17, 47/42
17	205.9	140.8
18	218.1	149	17/15, 42/37
19	230.2	157.3	8/7
20	242.3	165.6	23/20
21	254.4	173.9	22/19, 51/44
22	266.5	182.2	7/6
23	278.6	190.4	27/23, 47/40
24	290.7	198.7	58/49
25	302.9	207	25/21, 56/47
26	315	215.3	6/5
27	327.1	223.6	29/24
28	339.2	231.8	28/23, 45/37
29	351.3	240.1	38/31, 49/40
30	363.4	248.4	37/30, 58/47
31	375.5	256.7	36/29, 41/33, 46/37
32	387.7	265	5/4
33	399.8	273.2	34/27
34	411.9	281.5	33/26, 52/41
35	424	289.8	23/18
36	436.1	298.1	9/7
37	448.2	306.4	35/27, 57/44
38	460.3	314.6	30/23, 47/36
39	472.5	322.9	46/35
40	484.6	331.2	41/31, 45/34
41	496.7	339.5	4/3
42	508.8	347.8	51/38, 55/41
43	520.9	356.1	27/20, 50/37
44	533	364.3	34/25, 49/36
45	545.1	372.6	37/27
46	557.3	380.9	40/29
47	569.4	389.2	25/18, 57/41
48	581.5	397.5	7/5
49	593.6	405.7	31/22
50	605.7	414	44/31
51	617.8	422.3	10/7
52	629.9	430.6	36/25
53	642.1	438.9	29/20, 42/29
54	654.2	447.1	35/24, 54/37
55	666.3	455.4	25/17, 47/32
56	678.4	463.7	37/25
57	690.5	472
58	702.6	480.3	3/2
59	714.7	488.5
60	726.9	496.8	35/23
61	739	505.1	23/15, 49/32
62	751.1	513.4	54/35
63	763.2	521.7
64	775.3	529.9	36/23
65	787.4	538.2	41/26, 52/33
66	799.5	546.5	27/17, 46/29
67	811.7	554.8
68	823.8	563.1	37/23
69	835.9	571.3	47/29
70	848	579.6	31/19, 49/30
71	860.1	587.9	23/14
72	872.2	596.2	43/26, 48/29
73	884.3	604.5	5/3
74	896.5	612.7	47/28, 52/31
75	908.6	621	49/29
76	920.7	629.3
77	932.8	637.6	12/7
78	944.9	645.9	19/11
79	957	654.1	33/19, 40/23
80	969.1	662.4	7/4
81	981.3	670.7	37/21
82	993.4	679	55/31
83	1005.5	687.3
84	1017.6	695.5	9/5
85	1029.7	703.8	29/16
86	1041.8	712.1	42/23
87	1053.9	720.4	57/31
88	1066.1	728.7	37/20, 50/27
89	1078.2	736.9	41/22
90	1090.3	745.2
91	1102.4	753.5	17/9
92	1114.5	761.8	40/21
93	1126.6	770.1	23/12
94	1138.8	778.3	56/29
95	1150.9	786.6	35/18
96	1163	794.9	45/23, 47/24
97	1175.1	803.2
98	1187.2	811.5
99	1199.3	819.7	2/1
100	1211.4	828
101	1223.6	836.3
102	1235.7	844.6	49/24, 51/25
103	1247.8	852.9	37/18
104	1259.9	861.1	29/14
105	1272	869.4	25/12
106	1284.1	877.7	21/10
107	1296.2	886	55/26
108	1308.4	894.3	49/23
109	1320.5	902.5	15/7
110	1332.6	910.8	41/19, 54/25
111	1344.7	919.1	50/23
112	1356.8	927.4	46/21
113	1368.9	935.7
114	1381	943.9	20/9
115	1393.2	952.2	38/17
116	1405.3	960.5	9/4
117	1417.4	968.8	34/15
118	1429.5	977.1
119	1441.6	985.4	23/10
120	1453.7	993.6	44/19
121	1465.8	1001.9	7/3
122	1478	1010.2	47/20, 54/23
123	1490.1	1018.5	26/11
124	1502.2	1026.8	50/21
125	1514.3	1035	12/5
126	1526.4	1043.3	29/12
127	1538.5	1051.6
128	1550.6	1059.9	49/20
129	1562.8	1068.2	37/15
130	1574.9	1076.4
131	1587	1084.7	5/2
132	1599.1	1093
133	1611.2	1101.3
134	1623.3	1109.6	23/9
135	1635.4	1117.8	18/7
136	1647.6	1126.1	44/17, 57/22
137	1659.7	1134.4
138	1671.8	1142.7	21/8
139	1683.9	1151	37/14, 45/17
140	1696	1159.2
141	1708.1	1167.5	51/19
142	1720.2	1175.8	27/10
143	1732.4	1184.1	49/18
144	1744.5	1192.4	52/19
145	1756.6	1200.6
146	1768.7	1208.9	25/9
147	1780.8	1217.2
148	1792.9	1225.5	31/11
149	1805	1233.8
150	1817.2	1242	20/7
151	1829.3	1250.3	23/8
152	1841.4	1258.6	55/19
153	1853.5	1266.9	35/12
154	1865.6	1275.2	47/16
155	1877.7	1283.4
156	1889.8	1291.7
157	1902	1300	3/1

Harmonics

Approximation of harmonics in 157edt

Harmonic		2	3	4	5	6	7	8	9	10	11	12
Error	Absolute (¢)	-0.68	+0.00	-1.36	-0.01	-0.68	-1.03	-2.03	+0.00	-0.69	+3.91	-1.36
	Relative (%)	-5.6	+0.0	-11.2	-0.1	-5.6	-8.5	-16.8	+0.0	-5.7	+32.3	-11.2
Steps (reduced)		99 (99)	157 (0)	198 (41)	230 (73)	256 (99)	278 (121)	297 (140)	314 (0)	329 (15)	343 (29)	355 (41)

Approximation of harmonics in 157edt

Harmonic		13	14	15	16	17	18	19	20	21	22	23
Error	Absolute (¢)	+5.44	-1.71	-0.01	-2.71	+1.36	-0.68	+2.63	-1.37	-1.03	+3.23	-1.04
	Relative (%)	+44.9	-14.1	-0.1	-22.4	+11.2	-5.6	+21.7	-11.3	-8.5	+26.7	-8.6
Steps (reduced)		367 (53)	377 (63)	387 (73)	396 (82)	405 (91)	413 (99)	421 (107)	428 (114)	435 (121)	442 (128)	448 (134)

See also

• 99edo
• 58edf