133ed4

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133ed4

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Prime factorization	7 × 19
Step size	18.0451¢
Octave	67\133ed4 (1209.02¢)
Twelfth	105\133ed4 (1894.74¢) (→15\19ed4)
Consistency limit	1
Distinct consistency limit	1

133 equal divisions of the 4th harmonic (abbreviated 133ed4) is a nonoctave tuning system that divides the interval of 4/1 into 133 equal parts of about 18 ¢ each. Each step represents a frequency ratio of 4^1/133, or the 133rd root of 4.

Intervals

Steps	Cents	Approximate Ratios
0	0	1/1
1	18.045
2	36.09
3	54.135
4	72.18
5	90.226	39/37
6	108.271	33/31, 49/46, 50/47
7	126.316
8	144.361
9	162.406
10	180.451
11	198.496	37/33
12	216.541
13	234.586
14	252.632
15	270.677
16	288.722	13/11
17	306.767	37/31, 43/36
18	324.812	35/29
19	342.857	50/41
20	360.902
21	378.947	51/41
22	396.992	39/31
23	415.038	47/37
24	433.083
25	451.128
26	469.173	38/29
27	487.218
28	505.263
29	523.308	23/17
30	541.353	41/30
31	559.398	29/21
32	577.444
33	595.489
34	613.534	47/33
35	631.579	49/34
36	649.624
37	667.669
38	685.714
39	703.759
40	721.805	47/31
41	739.85
42	757.895
43	775.94	36/23, 47/30
44	793.985
45	812.03
46	830.075	21/13
47	848.12	31/19
48	866.165
49	884.211	5/3
50	902.256
51	920.301	17/10
52	938.346
53	956.391	33/19
54	974.436
55	992.481
56	1010.526
57	1028.571
58	1046.617
59	1064.662
60	1082.707	43/23
61	1100.752
62	1118.797	21/11
63	1136.842
64	1154.887	37/19
65	1172.932
66	1190.977
67	1209.023
68	1227.068
69	1245.113	39/19
70	1263.158
71	1281.203
72	1299.248	36/17
73	1317.293
74	1335.338
75	1353.383
76	1371.429
77	1389.474	29/13
78	1407.519
79	1425.564	41/18
80	1443.609	23/10
81	1461.654
82	1479.699
83	1497.744
84	1515.789
85	1533.835
86	1551.88	49/20
87	1569.925
88	1587.97
89	1606.015	43/17
90	1624.06
91	1642.105
92	1660.15	47/18
93	1678.195	29/11
94	1696.241
95	1714.286	35/13
96	1732.331
97	1750.376
98	1768.421	25/9
99	1786.466
100	1804.511	17/6
101	1822.556
102	1840.602
103	1858.647	38/13
104	1876.692
105	1894.737
106	1912.782
107	1930.827
108	1948.872
109	1966.917
110	1984.962
111	2003.008	35/11
112	2021.053
113	2039.098
114	2057.143
115	2075.188
116	2093.233
117	2111.278
118	2129.323
119	2147.368	38/11
120	2165.414
121	2183.459
122	2201.504
123	2219.549
124	2237.594
125	2255.639
126	2273.684
127	2291.729
128	2309.774	19/5
129	2327.82	23/6
130	2345.865
131	2363.91
132	2381.955
133	2400

Harmonics

Approximation of harmonics in 133ed4

Harmonic		2	3	4	5	6	7	8	9	10	11	12
Error	Absolute (¢)	+9.02	-7.22	+0.00	-7.37	+1.80	+5.61	+9.02	+3.61	+1.66	-0.94	-7.22
	Relative (%)	+50.0	-40.0	+0.0	-40.8	+10.0	+31.1	+50.0	+20.0	+9.2	-5.2	-40.0
Steps (reduced)		67 (67)	105 (105)	133 (0)	154 (21)	172 (39)	187 (54)	200 (67)	211 (78)	221 (88)	230 (97)	238 (105)

Approximation of harmonics in 133ed4

Harmonic		13	14	15	16	17	18	19	20	21	22	23
Error	Absolute (¢)	-1.43	-3.41	+3.46	+0.00	+3.32	-5.41	-8.79	-7.37	-1.61	+8.08	+3.30
	Relative (%)	-7.9	-18.9	+19.2	+0.0	+18.4	-30.0	-48.7	-40.8	-8.9	+44.8	+18.3
Steps (reduced)		246 (113)	253 (120)	260 (127)	266 (0)	272 (6)	277 (11)	282 (16)	287 (21)	292 (26)	297 (31)	301 (35)