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	Hekts	Approximate ratios
0	0	0	1/1
1	14.6	10
2	29.3	20
3	43.9	30	41/40
4	58.5	40	30/29, 31/30
5	73.2	50	24/23
6	87.8	60	20/19
7	102.4	70
8	117	80	31/29, 46/43
9	131.7	90	41/38
10	146.3	100	37/34, 49/45
11	160.9	110	34/31, 45/41
12	175.6	120	31/28, 52/47
13	190.2	130	48/43
14	204.8	140	9/8
15	219.5	150	42/37
16	234.1	160
17	248.7	170
18	263.3	180
19	278	190	27/23
20	292.6	200	32/27, 45/38
21	307.2	210	37/31, 43/36, 49/41
22	321.9	220	47/39
23	336.5	230	17/14
24	351.1	240	38/31, 49/40
25	365.8	250	21/17
26	380.4	260
27	395	270
28	409.7	280	19/15
29	424.3	290	23/18
30	438.9	300	49/38
31	453.5	310
32	468.2	320	38/29
33	482.8	330	37/28, 41/31
34	497.4	340	4/3
35	512.1	350	43/32
36	526.7	360	42/31
37	541.3	370	41/30
38	556	380	40/29, 51/37
39	570.6	390	32/23
40	585.2	400
41	599.8	410	41/29
42	614.5	420
43	629.1	430	23/16
44	643.7	440	29/20, 45/31
45	658.4	450
46	673	460	28/19, 31/21
47	687.6	470
48	702.3	480	3/2
49	716.9	490
50	731.5	500	29/19
51	746.2	510
52	760.8	520	45/29
53	775.4	530	36/23
54	790	540	30/19
55	804.7	550	43/27
56	819.3	560
57	833.9	570	34/21
58	848.6	580	31/19, 49/30
59	863.2	590	28/17, 51/31
60	877.8	600
61	892.5	610
62	907.1	620	27/16, 49/29
63	921.7	630	46/27
64	936.3	640
65	951	650
66	965.6	660
67	980.2	670	37/21
68	994.9	680	16/9
69	1009.5	690	43/24
70	1024.1	700	47/26
71	1038.8	710	31/17, 51/28
72	1053.4	720
73	1068	730
74	1082.7	740	43/23
75	1097.3	750
76	1111.9	760	19/10
77	1126.5	770	23/12
78	1141.2	780	29/15
79	1155.8	790
80	1170.4	800
81	1185.1	810
82	1199.7	820	2/1
83	1214.3	830
84	1229	840
85	1243.6	850	41/20
86	1258.2	860	31/15
87	1272.8	870	48/23
88	1287.5	880	40/19
89	1302.1	890
90	1316.7	900
91	1331.4	910	41/19
92	1346	920	37/17
93	1360.6	930
94	1375.3	940	31/14
95	1389.9	950
96	1404.5	960	9/4
97	1419.2	970
98	1433.8	980
99	1448.4	990
100	1463	1000
101	1477.7	1010
102	1492.3	1020	45/19
103	1506.9	1030	43/18
104	1521.6	1040
105	1536.2	1050	17/7
106	1550.8	1060	49/20
107	1565.5	1070	42/17
108	1580.1	1080
109	1594.7	1090
110	1609.3	1100	38/15
111	1624	1110	23/9
112	1638.6	1120	49/19
113	1653.2	1130
114	1667.9	1140
115	1682.5	1150	37/14
116	1697.1	1160	8/3
117	1711.8	1170	43/16
118	1726.4	1180
119	1741	1190	41/15
120	1755.7	1200
121	1770.3	1210
122	1784.9	1220
123	1799.5	1230
124	1814.2	1240
125	1828.8	1250	23/8
126	1843.4	1260	29/10
127	1858.1	1270
128	1872.7	1280
129	1887.3	1290
130	1902	1300	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)