130edt

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130edt

131edt →

Prime factorization	2 × 5 × 13
Step size	14.6304¢
Octave	82\130edt (1199.69¢) (→41\65edt)
Consistency limit	10
Distinct consistency limit	10

130 equal divisions of the tritave, perfect twelfth, or 3rd harmonic (abbreviated 130edt or 130ed3), is a nonoctave tuning system that divides the interval of 3/1 into 130 equal parts of about 14.6 ¢ each. Each step represents a frequency ratio of 3^1/130, or the 130th root of 3.

Intervals

Steps	Cents	Approximate Ratios
0	0	1/1
1	14.63
2	29.261
3	43.891	41/40
4	58.522	30/29, 31/30
5	73.152	24/23
6	87.783	20/19
7	102.413
8	117.043	31/29, 46/43
9	131.674	41/38
10	146.304	37/34, 49/45
11	160.935	34/31, 45/41
12	175.565	31/28, 52/47
13	190.196	48/43
14	204.826	9/8
15	219.456	42/37
16	234.087
17	248.717
18	263.348
19	277.978	27/23
20	292.608	32/27, 45/38
21	307.239	37/31, 43/36, 49/41
22	321.869	47/39
23	336.5	17/14
24	351.13	38/31, 49/40
25	365.761	21/17
26	380.391
27	395.021
28	409.652	19/15
29	424.282	23/18
30	438.913	49/38
31	453.543
32	468.174	38/29
33	482.804	37/28, 41/31
34	497.434	4/3
35	512.065	43/32
36	526.695	42/31
37	541.326	41/30
38	555.956	40/29, 51/37
39	570.587	32/23
40	585.217
41	599.847	41/29
42	614.478
43	629.108	23/16
44	643.739	29/20, 45/31
45	658.369
46	672.999	28/19, 31/21
47	687.63
48	702.26	3/2
49	716.891
50	731.521	29/19
51	746.152
52	760.782	45/29
53	775.412	36/23
54	790.043	30/19
55	804.673	43/27
56	819.304
57	833.934	34/21
58	848.565	31/19, 49/30
59	863.195	28/17, 51/31
60	877.825
61	892.456
62	907.086	27/16, 49/29
63	921.717	46/27
64	936.347
65	950.978
66	965.608
67	980.238	37/21
68	994.869	16/9
69	1009.499	43/24
70	1024.13	47/26
71	1038.76	31/17, 51/28
72	1053.39
73	1068.021
74	1082.651	43/23
75	1097.282
76	1111.912	19/10
77	1126.543	23/12
78	1141.173	29/15
79	1155.803
80	1170.434
81	1185.064
82	1199.695	2/1
83	1214.325
84	1228.956
85	1243.586	41/20
86	1258.216	31/15
87	1272.847	48/23
88	1287.477	40/19
89	1302.108
90	1316.738
91	1331.369	41/19
92	1345.999	37/17
93	1360.629
94	1375.26	31/14
95	1389.89
96	1404.521	9/4
97	1419.151
98	1433.781
99	1448.412
100	1463.042
101	1477.673
102	1492.303	45/19
103	1506.934	43/18
104	1521.564
105	1536.194	17/7
106	1550.825	49/20
107	1565.455	42/17
108	1580.086
109	1594.716
110	1609.347	38/15
111	1623.977	23/9
112	1638.607	49/19
113	1653.238
114	1667.868
115	1682.499	37/14
116	1697.129	8/3
117	1711.76	43/16
118	1726.39
119	1741.02	41/15
120	1755.651
121	1770.281
122	1784.912
123	1799.542
124	1814.172
125	1828.803	23/8
126	1843.433	29/10
127	1858.064
128	1872.694
129	1887.325
130	1901.955	3/1

Harmonics

Approximation of harmonics in 130edt

Harmonic		2	3	4	5	6	7	8	9	10	11	12
Error	Absolute (¢)	-0.31	+0.00	-0.61	-6.53	-0.31	-3.83	-0.92	+0.00	-6.84	+3.72	-0.61
	Relative (%)	-2.1	+0.0	-4.2	-44.7	-2.1	-26.2	-6.3	+0.0	-46.7	+25.4	-4.2
Steps (reduced)		82 (82)	130 (0)	164 (34)	190 (60)	212 (82)	230 (100)	246 (116)	260 (0)	272 (12)	284 (24)	294 (34)

Approximation of harmonics in 130edt

Harmonic		13	14	15	16	17	18	19	20	21	22	23
Error	Absolute (¢)	+7.12	-4.13	-6.53	-1.22	-3.76	-0.31	-6.13	-7.14	-3.83	+3.42	-0.39
	Relative (%)	+48.7	-28.3	-44.7	-8.3	-25.7	-2.1	-41.9	-48.8	-26.2	+23.4	-2.6
Steps (reduced)		304 (44)	312 (52)	320 (60)	328 (68)	335 (75)	342 (82)	348 (88)	354 (94)	360 (100)	366 (106)	371 (111)