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, and their complements), all of which are still within 60% of a step off.

Intervals

Steps	Cents	Hekts	Approximate ratios
0	0	0	1/1
1	7.26	4.96
2	14.52	9.92
3	21.78	14.89	78/77, 82/81
4	29.04	19.85
5	36.3	24.81
6	43.56	29.77
7	50.82	34.73	35/34
8	58.07	39.69	30/29
9	65.33	44.66	27/26
10	72.59	49.62	49/47
11	79.85	54.58	22/21
12	87.11	59.54	41/39, 81/77
13	94.37	64.5	19/18
14	101.63	69.47	35/33
15	108.89	74.43	33/31, 49/46, 82/77
16	116.15	79.39	31/29, 46/43
17	123.41	84.35	29/27
18	130.67	89.31	55/51
19	137.93	94.27
20	145.19	99.24	62/57
21	152.45	104.2
22	159.71	109.16	34/31, 57/52
23	166.97	114.12
24	174.22	119.08	52/47
25	181.48	124.05
26	188.74	129.01	29/26
27	196	133.97
28	203.26	138.93
29	210.52	143.89	35/31
30	217.78	148.85
31	225.04	153.82
32	232.3	158.78
33	239.56	163.74	31/27, 54/47
34	246.82	168.7
35	254.08	173.66	22/19
36	261.34	178.63	50/43, 57/49
37	268.6	183.59
38	275.86	188.55	34/29
39	283.12	193.51
40	290.37	198.47
41	297.63	203.44
42	304.89	208.4	31/26, 68/57
43	312.15	213.36
44	319.41	218.32
45	326.67	223.28
46	333.93	228.24	57/47
47	341.19	233.21
48	348.45	238.17
49	355.71	243.13	43/35, 70/57
50	362.97	248.09	37/30
51	370.23	253.05	26/21
52	377.49	258.02	46/37, 51/41
53	384.75	262.98
54	392.01	267.94	69/55
55	399.27	272.9	34/27
56	406.52	277.86	43/34
57	413.78	282.82	47/37
58	421.04	287.79	37/29
59	428.3	292.75
60	435.56	297.71	9/7
61	442.82	302.67
62	450.08	307.63	35/27
63	457.34	312.6
64	464.6	317.56	17/13
65	471.86	322.52
66	479.12	327.48	62/47
67	486.38	332.44	49/37
68	493.64	337.4
69	500.9	342.37
70	508.16	347.33	55/41
71	515.42	352.29	35/26, 66/49
72	522.67	357.25	23/17
73	529.93	362.21
74	537.19	367.18	15/11
75	544.45	372.14	63/46
76	551.71	377.1
77	558.97	382.06	29/21
78	566.23	387.02	43/31
79	573.49	391.98
80	580.75	396.95
81	588.01	401.91	66/47
82	595.27	406.87	55/39
83	602.53	411.83
84	609.79	416.79
85	617.05	421.76	10/7
86	624.31	426.72	33/23
87	631.57	431.68
88	638.82	436.64	68/47
89	646.08	441.6
90	653.34	446.56
91	660.6	451.53	63/43
92	667.86	456.49	25/17
93	675.12	461.45
94	682.38	466.41	43/29
95	689.64	471.37	70/47
96	696.9	476.34
97	704.16	481.3
98	711.42	486.26
99	718.68	491.22	50/33
100	725.94	496.18
101	733.2	501.15
102	740.46	506.11	23/15
103	747.72	511.07	57/37, 77/50
104	754.97	516.03
105	762.23	520.99
106	769.49	525.95	39/25
107	776.75	530.92	47/30
108	784.01	535.88
109	791.27	540.84	30/19
110	798.53	545.8	46/29, 65/41
111	805.79	550.76	43/27
112	813.05	555.73
113	820.31	560.69
114	827.57	565.65	50/31
115	834.83	570.61	34/21, 81/50
116	842.09	575.57
117	849.35	580.53	49/30
118	856.61	585.5	41/25
119	863.87	590.46
120	871.12	595.42	43/26
121	878.38	600.38
122	885.64	605.34
123	892.9	610.31	62/37
124	900.16	615.27	37/22
125	907.42	620.23	49/29
126	914.68	625.19	39/23
127	921.94	630.15	46/27, 63/37
128	929.2	635.11	77/45
129	936.46	640.08
130	943.72	645.04	50/29
131	950.98	650
132	958.24	654.96
133	965.5	659.92
134	972.76	664.89
135	980.01	669.85	37/21, 81/46
136	987.27	674.81	23/13
137	994.53	679.77
138	1001.79	684.73	66/37
139	1009.05	689.69	77/43
140	1016.31	694.66
141	1023.57	699.62
142	1030.83	704.58	78/43
143	1038.09	709.54	82/45
144	1045.35	714.5	75/41
145	1052.61	719.47
146	1059.87	724.43
147	1067.13	729.39	50/27, 63/34
148	1074.39	734.35
149	1081.65	739.31
150	1088.91	744.27
151	1096.16	749.24	81/43
152	1103.42	754.2	70/37
153	1110.68	759.16	19/10
154	1117.94	764.12	82/43
155	1125.2	769.08
156	1132.46	774.05	25/13
157	1139.72	779.01
158	1146.98	783.97
159	1154.24	788.93	37/19
160	1161.5	793.89	45/23
161	1168.76	798.85
162	1176.02	803.82
163	1183.28	808.78
164	1190.54	813.74
165	1197.8	818.7
166	1205.06	823.66
167	1212.31	828.63
168	1219.57	833.59
169	1226.83	838.55
170	1234.09	843.51	51/25
171	1241.35	848.47	43/21
172	1248.61	853.44
173	1255.87	858.4
174	1263.13	863.36
175	1270.39	868.32
176	1277.65	873.28	23/11
177	1284.91	878.24	21/10
178	1292.17	883.21
179	1299.43	888.17
180	1306.69	893.13
181	1313.95	898.09	47/22
182	1321.21	903.05
183	1328.46	908.02
184	1335.72	912.98
185	1342.98	917.94	63/29
186	1350.24	922.9
187	1357.5	927.86	46/21
188	1364.76	932.82	11/5
189	1372.02	937.79
190	1379.28	942.75	51/23
191	1386.54	947.71	49/22, 78/35
192	1393.8	952.67
193	1401.06	957.63
194	1408.32	962.6
195	1415.58	967.56	77/34
196	1422.84	972.52
197	1430.1	977.48
198	1437.36	982.44	39/17
199	1444.61	987.4
200	1451.87	992.37	81/35
201	1459.13	997.33
202	1466.39	1002.29	7/3
203	1473.65	1007.25	82/35
204	1480.91	1012.21
205	1488.17	1017.18
206	1495.43	1022.14
207	1502.69	1027.1	81/34
208	1509.95	1032.06	55/23
209	1517.21	1037.02
210	1524.47	1041.98	41/17
211	1531.73	1046.95	63/26
212	1538.99	1051.91
213	1546.25	1056.87
214	1553.51	1061.83
215	1560.76	1066.79
216	1568.02	1071.76	47/19
217	1575.28	1076.72	77/31, 82/33
218	1582.54	1081.68
219	1589.8	1086.64
220	1597.06	1091.6	78/31
221	1604.32	1096.56
222	1611.58	1101.53
223	1618.84	1106.49
224	1626.1	1111.45
225	1633.36	1116.41
226	1640.62	1121.37	49/19
227	1647.88	1126.34	57/22
228	1655.14	1131.3
229	1662.4	1136.26	47/18, 81/31
230	1669.66	1141.22
231	1676.91	1146.18
232	1684.17	1151.15	82/31
233	1691.43	1156.11
234	1698.69	1161.07
235	1705.95	1166.03
236	1713.21	1170.99	78/29
237	1720.47	1175.95
238	1727.73	1180.92
239	1734.99	1185.88
240	1742.25	1190.84	52/19
241	1749.51	1195.8
242	1756.77	1200.76
243	1764.03	1205.73
244	1771.29	1210.69
245	1778.55	1215.65	81/29
246	1785.81	1220.61
247	1793.06	1225.57	31/11
248	1800.32	1230.53
249	1807.58	1235.5	54/19
250	1814.84	1240.46	77/27
251	1822.1	1245.42	63/22
252	1829.36	1250.38
253	1836.62	1255.34	26/9
254	1843.88	1260.31	29/10
255	1851.14	1265.27
256	1858.4	1270.23
257	1865.66	1275.19
258	1872.92	1280.15
259	1880.18	1285.11	77/26
260	1887.44	1290.08
261	1894.7	1295.04
262	1901.96	1300	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)