262edt

← 261edt

262edt

263edt →

Prime factorization	2 × 131
Step size	7.25937¢
Octave	165\262edt (1197.8¢)
Consistency limit	2
Distinct consistency limit	2

262EDT is the equal division of the third harmonic into 262 parts of 7.2594 cents each, corresponding to 165.3036 edo (similar to every third step of 496edo). It doubles 131edt, which is consistent to the no-evens 25-throdd limit, and is contorted with it to the no-twos 23-limit, but it improves the representation of a number of higher primes so that 262edt is consistent to the entire no-evens 53-throdd limit with the exception of only 9 inconsistent interval pairs (19/13, 19/17, 25/19, 41/19, 41/37, 47/17, 47/25, 47/41, and 49/41), all of which are still within 60% of a step off.

Intervals

Steps	Cents	Approximate Ratios
0	0	1/1
1	7.259
2	14.519
3	21.778	78/77, 82/81
4	29.037
5	36.297
6	43.556
7	50.816	35/34
8	58.075	30/29
9	65.334	27/26
10	72.594	49/47
11	79.853	22/21
12	87.112	41/39, 81/77
13	94.372	19/18
14	101.631	35/33
15	108.891	33/31, 49/46, 82/77
16	116.15	31/29, 46/43
17	123.409	29/27
18	130.669	55/51
19	137.928
20	145.187	62/57
21	152.447
22	159.706	34/31, 57/52
23	166.966
24	174.225	52/47
25	181.484
26	188.744	29/26
27	196.003
28	203.262
29	210.522	35/31
30	217.781
31	225.04
32	232.3
33	239.559	31/27, 54/47
34	246.819
35	254.078	22/19
36	261.337	50/43, 57/49
37	268.597
38	275.856	34/29
39	283.115
40	290.375
41	297.634
42	304.894	31/26, 68/57
43	312.153
44	319.412
45	326.672
46	333.931	57/47
47	341.19
48	348.45
49	355.709	43/35, 70/57
50	362.969	37/30
51	370.228	26/21
52	377.487	46/37, 51/41
53	384.747
54	392.006	69/55
55	399.265	34/27
56	406.525	43/34
57	413.784	47/37
58	421.043	37/29
59	428.303
60	435.562	9/7
61	442.822
62	450.081	35/27
63	457.34
64	464.6	17/13
65	471.859
66	479.118	62/47
67	486.378	49/37
68	493.637
69	500.897
70	508.156	55/41
71	515.415	35/26, 66/49
72	522.675	23/17
73	529.934
74	537.193	15/11
75	544.453	63/46
76	551.712
77	558.972	29/21
78	566.231	43/31
79	573.49
80	580.75
81	588.009	66/47
82	595.268	55/39
83	602.528
84	609.787
85	617.046	10/7
86	624.306	33/23
87	631.565
88	638.825	68/47
89	646.084
90	653.343
91	660.603	63/43
92	667.862	25/17
93	675.121
94	682.381	43/29
95	689.64	70/47
96	696.9
97	704.159
98	711.418
99	718.678	50/33
100	725.937
101	733.196
102	740.456	23/15
103	747.715	57/37, 77/50
104	754.975
105	762.234
106	769.493	39/25
107	776.753	47/30
108	784.012
109	791.271	30/19
110	798.531	46/29, 65/41
111	805.79	43/27
112	813.049
113	820.309
114	827.568	50/31
115	834.828	34/21, 81/50
116	842.087
117	849.346	49/30
118	856.606	41/25
119	863.865
120	871.124	43/26
121	878.384
122	885.643
123	892.903	62/37
124	900.162	37/22
125	907.421	49/29
126	914.681	39/23
127	921.94	46/27, 63/37
128	929.199	77/45
129	936.459
130	943.718	50/29
131	950.978
132	958.237
133	965.496
134	972.756
135	980.015	37/21, 81/46
136	987.274	23/13
137	994.534
138	1001.793	66/37
139	1009.052	77/43
140	1016.312
141	1023.571
142	1030.831	78/43
143	1038.09	82/45
144	1045.349	75/41
145	1052.609
146	1059.868
147	1067.127	50/27, 63/34
148	1074.387
149	1081.646
150	1088.906
151	1096.165	81/43
152	1103.424	70/37
153	1110.684	19/10
154	1117.943	82/43
155	1125.202
156	1132.462	25/13
157	1139.721
158	1146.98
159	1154.24	37/19
160	1161.499	45/23
161	1168.759
162	1176.018
163	1183.277
164	1190.537
165	1197.796
166	1205.055
167	1212.315
168	1219.574
169	1226.834
170	1234.093	51/25
171	1241.352	43/21
172	1248.612
173	1255.871
174	1263.13
175	1270.39
176	1277.649	23/11
177	1284.909	21/10
178	1292.168
179	1299.427
180	1306.687
181	1313.946	47/22
182	1321.205
183	1328.465
184	1335.724
185	1342.983	63/29
186	1350.243
187	1357.502	46/21
188	1364.762	11/5
189	1372.021
190	1379.28	51/23
191	1386.54	49/22, 78/35
192	1393.799
193	1401.058
194	1408.318
195	1415.577	77/34
196	1422.837
197	1430.096
198	1437.355	39/17
199	1444.615
200	1451.874	81/35
201	1459.133
202	1466.393	7/3
203	1473.652	82/35
204	1480.912
205	1488.171
206	1495.43
207	1502.69	81/34
208	1509.949	55/23
209	1517.208
210	1524.468	41/17
211	1531.727	63/26
212	1538.986
213	1546.246
214	1553.505
215	1560.765
216	1568.024	47/19
217	1575.283	77/31, 82/33
218	1582.543
219	1589.802
220	1597.061	78/31
221	1604.321
222	1611.58
223	1618.84
224	1626.099
225	1633.358
226	1640.618	49/19
227	1647.877	57/22
228	1655.136
229	1662.396	47/18, 81/31
230	1669.655
231	1676.915
232	1684.174	82/31
233	1691.433
234	1698.693
235	1705.952
236	1713.211	78/29
237	1720.471
238	1727.73
239	1734.989
240	1742.249	52/19
241	1749.508
242	1756.768
243	1764.027
244	1771.286
245	1778.546	81/29
246	1785.805
247	1793.064	31/11
248	1800.324
249	1807.583	54/19
250	1814.843	77/27
251	1822.102	63/22
252	1829.361
253	1836.621	26/9
254	1843.88	29/10
255	1851.139
256	1858.399
257	1865.658
258	1872.918
259	1880.177	77/26
260	1887.436
261	1894.696
262	1901.955	3/1

Harmonics

Approximation of prime harmonics in 262edt

Harmonic		2	3	5	7	11	13	17	19	23
Error	Absolute (¢)	-2.20	+0.00	+1.28	-0.48	+1.04	+2.21	+2.38	-1.44	+1.73
	Relative (%)	-30.4	+0.0	+17.7	-6.6	+14.4	+30.4	+32.8	-19.8	+23.9
Steps (reduced)		165 (165)	262 (0)	384 (122)	464 (202)	572 (48)	612 (88)	676 (152)	702 (178)	748 (224)

Approximation of odd harmonics in 262edt

Harmonic		25	27	29	31	33	35	37	39	41	43	45	47	49	51	53
Error	Absolute (¢)	+2.57	+0.00	-0.30	+0.39	+1.04	+0.81	-1.03	+2.21	+2.74	+0.14	+1.28	-1.40	-0.96	+2.38	+1.12
	Relative (%)	+35.4	+0.0	-4.2	+5.4	+14.4	+11.1	-14.1	+30.4	+37.7	+1.9	+17.7	-19.4	-13.2	+32.8	+15.4
Steps (reduced)		768 (244)	786 (0)	803 (17)	819 (33)	834 (48)	848 (62)	861 (75)	874 (88)	886 (100)	897 (111)	908 (122)	918 (132)	928 (142)	938 (152)	947 (161)