131edt

← 130edt

131edt

132edt →

Prime factorization	131 (prime)
Step size	14.5187 ¢
Octave	83\131edt (1205.06 ¢)
Consistency limit	3
Distinct consistency limit	3

131edt is the equal division of the third harmonic into 131 parts of 14.5187 cents each, corresponding to 82.6520 edo (similar to every third step of 248edo). It is notable for consistency to the no-evens 27-throdd limit. Furthermore, several higher primes, including 29, 31, 37, 43, and 53, lie at close to halfway between 131edt's steps; therefore 262edt, which doubles it, improves representation of a large spectrum of primes, though it loses consistency of a few intervals of 19.

131edt is the 16th no-twos zeta peak EDT, and is the smallest EDT to be purely consistent^{[idiosyncratic term]} in the 27-odd-limit (i.e. maintains no greater than 25% relative error on all odd harmonocs up to and including 27).

Theory

131edt is strong in the 3.5.7.11.13.17.19.23 subgroup, tempering out 1377/1375, 1575/1573, 3591/3575, 4459/4455, 1617/1615 and 6561/6545. Additionally, 131edt tempers out 3213/3211 in the 3.7.13.17.19 subgroup and 2205/2197 in the 3.5.7.13 subgroup. It supports procyon, erigone, hemigone and mebsuta.

Intervals

Steps	Cents	Hekts	Approximate ratios
0	0	0	1/1
1	14.5	9.9
2	29	19.8
3	43.6	29.8	39/38
4	58.1	39.7	30/29
5	72.6	49.6	49/47
6	87.1	59.5	41/39
7	101.6	69.5	35/33
8	116.1	79.4
9	130.7	89.3	41/38
10	145.2	99.2	25/23, 37/34
11	159.7	109.2	45/41
12	174.2	119.1	21/19
13	188.7	129	29/26, 39/35
14	203.3	138.9
15	217.8	148.9	17/15, 42/37
16	232.3	158.8
17	246.8	168.7	15/13
18	261.3	178.6
19	275.9	188.5	27/23, 34/29
20	290.4	198.5	13/11
21	304.9	208.4
22	319.4	218.3
23	333.9	228.2
24	348.4	238.2	11/9
25	363	248.1	37/30
26	377.5	258	41/33, 46/37, 51/41
27	392	267.9
28	406.5	277.9
29	421	287.8	37/29
30	435.6	297.7	9/7
31	450.1	307.6	35/27
32	464.6	317.6	17/13
33	479.1	327.5	29/22, 33/25
34	493.6	337.4
35	508.2	347.3	51/38
36	522.7	357.3	23/17, 50/37
37	537.2	367.2	15/11
38	551.7	377.1
39	566.2	387	43/31
40	580.7	396.9	7/5
41	595.3	406.9
42	609.8	416.8	27/19, 37/26
43	624.3	426.7	33/23
44	638.8	436.6
45	653.3	446.6	51/35
46	667.9	456.5	25/17
47	682.4	466.4
48	696.9	476.3
49	711.4	486.3
50	725.9	496.2	35/23, 38/25
51	740.5	506.1	23/15
52	755	516	17/11
53	769.5	526	39/25
54	784	535.9	11/7
55	798.5	545.8	46/29
56	813	555.7
57	827.6	565.6
58	842.1	575.6
59	856.6	585.5	41/25
60	871.1	595.4
61	885.6	605.3	5/3
62	900.2	615.3	37/22
63	914.7	625.2	39/23
64	929.2	635.1
65	943.7	645	50/29
66	958.2	655	47/27
67	972.8	664.9
68	987.3	674.8	23/13
69	1001.8	684.7	41/23
70	1016.3	694.7	9/5
71	1030.8	704.6	49/27
72	1045.3	714.5
73	1059.9	724.4
74	1074.4	734.4
75	1088.9	744.3
76	1103.4	754.2
77	1117.9	764.1	21/11
78	1132.5	774	25/13
79	1147	784	33/17
80	1161.5	793.9	45/23
81	1176	803.8
82	1190.5	813.7
83	1205.1	823.7
84	1219.6	833.6
85	1234.1	843.5	51/25
86	1248.6	853.4	35/17, 37/18
87	1263.1	863.4
88	1277.6	873.3	23/11
89	1292.2	883.2	19/9
90	1306.7	893.1
91	1321.2	903.1	15/7
92	1335.7	913
93	1350.2	922.9
94	1364.8	932.8	11/5
95	1379.3	942.7	51/23
96	1393.8	952.7	38/17, 47/21
97	1408.3	962.6
98	1422.8	972.5	25/11
99	1437.4	982.4	39/17
100	1451.9	992.4
101	1466.4	1002.3	7/3
102	1480.9	1012.2
103	1495.4	1022.1
104	1509.9	1032.1
105	1524.5	1042	41/17
106	1539	1051.9
107	1553.5	1061.8	27/11
108	1568	1071.8	47/19
109	1582.5	1081.7
110	1597.1	1091.6
111	1611.6	1101.5	33/13
112	1626.1	1111.5	23/9
113	1640.6	1121.4	49/19
114	1655.1	1131.3	13/5
115	1669.7	1141.2
116	1684.2	1151.1	37/14, 45/17
117	1698.7	1161.1
118	1713.2	1171	35/13
119	1727.7	1180.9	19/7
120	1742.2	1190.8	41/15
121	1756.8	1200.8
122	1771.3	1210.7
123	1785.8	1220.6
124	1800.3	1230.5
125	1814.8	1240.5
126	1829.4	1250.4
127	1843.9	1260.3	29/10
128	1858.4	1270.2	38/13
129	1872.9	1280.2
130	1887.4	1290.1
131	1902	1300	3/1

Harmonics

Approximation of prime harmonics in 131edt

Harmonic		2	3	5	7	11	13	17	19	23
Error	Absolute (¢)	+5.06	+0.00	+1.28	-0.48	+1.04	+2.21	+2.38	-1.44	+1.73
	Relative (%)	+34.8	+0.0	+8.8	-3.3	+7.2	+15.2	+16.4	-9.9	+11.9
Steps (reduced)		83 (83)	131 (0)	192 (61)	232 (101)	286 (24)	306 (44)	338 (76)	351 (89)	374 (112)

Approximation of odd harmonics in 131edt

Harmonic		25	27	29	31	33	35	37	39	41	43	45	47	49	51	53
Error	Absolute (¢)	+2.57	+0.00	+6.96	-6.87	+1.04	+0.81	+6.23	+2.21	+2.74	-7.12	+1.28	-1.40	-0.96	+2.38	-6.14
	Relative (%)	+17.7	+0.0	+47.9	-47.3	+7.2	+5.6	+42.9	+15.2	+18.9	-49.1	+8.8	-9.7	-6.6	+16.4	-42.3
Steps (reduced)		384 (122)	393 (0)	402 (9)	409 (16)	417 (24)	424 (31)	431 (38)	437 (44)	443 (50)	448 (55)	454 (61)	459 (66)	464 (71)	469 (76)	473 (80)