133ed4

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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.

← 131ed4

133ed4

135ed4 →

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

Intervals

Steps	Cents	Approximate ratios
0	0	1/1
1	18
2	36.1
3	54.1
4	72.2
5	90.2	39/37
6	108.3	33/31, 49/46, 50/47
7	126.3
8	144.4
9	162.4
10	180.5
11	198.5	37/33
12	216.5
13	234.6
14	252.6
15	270.7
16	288.7	13/11
17	306.8	37/31, 43/36
18	324.8	35/29
19	342.9	50/41
20	360.9
21	378.9	51/41
22	397	39/31
23	415	47/37
24	433.1
25	451.1
26	469.2	38/29
27	487.2
28	505.3
29	523.3	23/17
30	541.4	41/30
31	559.4	29/21
32	577.4
33	595.5
34	613.5	47/33
35	631.6	49/34
36	649.6
37	667.7
38	685.7
39	703.8
40	721.8	47/31
41	739.8
42	757.9
43	775.9	36/23, 47/30
44	794
45	812
46	830.1	21/13
47	848.1	31/19
48	866.2
49	884.2	5/3
50	902.3
51	920.3	17/10
52	938.3
53	956.4	33/19
54	974.4
55	992.5
56	1010.5
57	1028.6
58	1046.6
59	1064.7
60	1082.7	43/23
61	1100.8
62	1118.8	21/11
63	1136.8
64	1154.9	37/19
65	1172.9
66	1191
67	1209
68	1227.1
69	1245.1	39/19
70	1263.2
71	1281.2
72	1299.2	36/17
73	1317.3
74	1335.3
75	1353.4
76	1371.4
77	1389.5	29/13
78	1407.5
79	1425.6	41/18
80	1443.6	23/10
81	1461.7
82	1479.7
83	1497.7
84	1515.8
85	1533.8
86	1551.9	49/20
87	1569.9
88	1588
89	1606	43/17
90	1624.1
91	1642.1
92	1660.2	47/18
93	1678.2	29/11
94	1696.2
95	1714.3	35/13
96	1732.3
97	1750.4
98	1768.4	25/9
99	1786.5
100	1804.5	17/6
101	1822.6
102	1840.6
103	1858.6	38/13
104	1876.7
105	1894.7
106	1912.8
107	1930.8
108	1948.9
109	1966.9
110	1985
111	2003	35/11
112	2021.1
113	2039.1
114	2057.1
115	2075.2
116	2093.2
117	2111.3
118	2129.3
119	2147.4	38/11
120	2165.4
121	2183.5
122	2201.5
123	2219.5
124	2237.6
125	2255.6
126	2273.7
127	2291.7
128	2309.8	19/5
129	2327.8	23/6
130	2345.9
131	2363.9
132	2382
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)