133edt

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133edt

134edt →

Prime factorization	7 × 19
Step size	14.3004¢
Octave	84\133edt (1201.23¢) (→12\19edt)
Consistency limit	10
Distinct consistency limit	10

133 equal divisions of the tritave, perfect twelfth, or 3rd harmonic (abbreviated 133edt or 133ed3), is a nonoctave tuning system that divides the interval of 3/1 into 133 equal parts of about 14.3 ¢ each. Each step represents a frequency ratio of 3^1/133, or the 133rd root of 3.

Intervals

Steps	Cents	Approximate Ratios
0	0	1/1
1	14.3
2	28.601
3	42.901	40/39, 41/40, 42/41
4	57.202	30/29, 31/30
5	71.502	25/24
6	85.802	21/20, 41/39
7	100.103	18/17
8	114.403	31/29, 47/44
9	128.704	14/13
10	143.004	25/23, 51/47
11	157.305	23/21
12	171.605	32/29
13	185.905	39/35
14	200.206	46/41
15	214.506	43/38
16	228.807
17	243.107	23/20, 38/33
18	257.407	29/25, 36/31
19	271.708	48/41
20	286.008	46/39
21	300.309	25/21, 44/37
22	314.609	6/5
23	328.91	29/24
24	343.21	39/32, 50/41
25	357.51
26	371.811	31/25
27	386.111	5/4
28	400.412	29/23, 34/27
29	414.712	47/37
30	429.012	32/25, 41/32, 50/39
31	443.313	31/24
32	457.613	43/33
33	471.914	21/16, 46/35
34	486.214	45/34
35	500.514
36	514.815	35/26
37	529.115
38	543.416
39	557.716	29/21, 40/29
40	572.017	32/23, 39/28
41	586.317
42	600.617	41/29
43	614.918
44	629.218	23/16
45	643.519	29/20, 45/31
46	657.819
47	672.119
48	686.42	52/35
49	700.72	3/2
50	715.021
51	729.321	32/21
52	743.622
53	757.922	31/20, 48/31
54	772.222	25/16
55	786.523
56	800.823	27/17
57	815.124	8/5
58	829.424	21/13
59	843.724	44/27
60	858.025	23/14, 41/25
61	872.325	48/29
62	886.626
63	900.926	37/22
64	915.226	39/23
65	929.527
66	943.827	50/29
67	958.128	40/23, 47/27
68	972.428
69	986.729	23/13
70	1001.029	41/23
71	1015.329
72	1029.63	29/16
73	1043.93	42/23
74	1058.231
75	1072.531	13/7
76	1086.831	15/8
77	1101.132	17/9
78	1115.432	40/21
79	1129.733	48/25
80	1144.033	31/16
81	1158.333	41/21
82	1172.634
83	1186.934
84	1201.235	2/1
85	1215.535
86	1229.836
87	1244.136	41/20
88	1258.436	31/15
89	1272.737	48/23
90	1287.037
91	1301.338
92	1315.638	47/22
93	1329.938	28/13
94	1344.239	50/23
95	1358.539	46/21
96	1372.84
97	1387.14
98	1401.441
99	1415.741	34/15, 43/19
100	1430.041	16/7
101	1444.342
102	1458.642
103	1472.943
104	1487.243
105	1501.543	50/21
106	1515.844	12/5
107	1530.144
108	1544.445
109	1558.745	32/13
110	1573.045
111	1587.346	5/2
112	1601.646
113	1615.947
114	1630.247	41/16
115	1644.548	31/12
116	1658.848
117	1673.148
118	1687.449
119	1701.749
120	1716.05	35/13
121	1730.35
122	1744.65
123	1758.951	47/17
124	1773.251	39/14
125	1787.552
126	1801.852	17/6
127	1816.153	20/7
128	1830.453
129	1844.753	29/10
130	1859.054	41/14
131	1873.354
132	1887.655
133	1901.955	3/1

Harmonics

Approximation of harmonics in 133edt

Harmonic		2	3	4	5	6	7	8	9	10	11	12
Error	Absolute (¢)	+1.23	+0.00	+2.47	+2.27	+1.23	+6.07	+3.70	+0.00	+3.50	-4.20	+2.47
	Relative (%)	+8.6	+0.0	+17.3	+15.9	+8.6	+42.5	+25.9	+0.0	+24.5	-29.4	+17.3
Steps (reduced)		84 (84)	133 (0)	168 (35)	195 (62)	217 (84)	236 (103)	252 (119)	266 (0)	279 (13)	290 (24)	301 (35)

Approximation of harmonics in 133edt

Harmonic		13	14	15	16	17	18	19	20	21	22	23
Error	Absolute (¢)	+6.90	-6.99	+2.27	+4.94	+0.09	+1.23	-6.57	+4.74	+6.07	-2.96	+5.88
	Relative (%)	+48.3	-48.9	+15.9	+34.5	+0.6	+8.6	-45.9	+33.1	+42.5	-20.7	+41.1
Steps (reduced)		311 (45)	319 (53)	328 (62)	336 (70)	343 (77)	350 (84)	356 (90)	363 (97)	369 (103)	374 (108)	380 (114)