132edt

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132edt

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Prime factorization	22 × 3 × 11
Step size	14.4088¢
Octave	83\132edt (1195.93¢)
Consistency limit	2
Distinct consistency limit	2

132 equal divisions of the tritave, perfect twelfth, or 3rd harmonic (abbreviated 132edt or 132ed3), is a nonoctave tuning system that divides the interval of 3/1 into 132 equal parts of about 14.4 ¢ each. Each step represents a frequency ratio of 3^1/132, or the 132nd root of 3.

Intervals

Steps	Cents	Approximate Ratios
0	0	1/1
1	14.409
2	28.818
3	43.226	39/38, 42/41
4	57.635
5	72.044	25/24, 49/47
6	86.453	41/39
7	100.861	35/33
8	115.27	31/29, 46/43
9	129.679	14/13
10	144.088	38/35
11	158.496	23/21
12	172.905	21/19
13	187.314	39/35
14	201.723
15	216.131	17/15
16	230.54
17	244.949	38/33
18	259.358	43/37
19	273.766	41/35
20	288.175	13/11
21	302.584
22	316.993	6/5
23	331.401	23/19
24	345.81	11/9
25	360.219
26	374.628	41/33
27	389.036
28	403.445
29	417.854	14/11
30	432.263
31	446.671	22/17
32	461.08
33	475.489
34	489.898
35	504.306
36	518.715
37	533.124	34/25
38	547.533
39	561.941	18/13
40	576.35	46/33
41	590.759	38/27
42	605.168
43	619.576
44	633.985
45	648.394
46	662.803	22/15
47	677.211
48	691.62
49	706.029
50	720.438	47/31
51	734.846	26/17
52	749.255
53	763.664	14/9
54	778.073
55	792.481	49/31
56	806.89	43/27
57	821.299	37/23, 45/28
58	835.708	47/29
59	850.116
60	864.525	28/17
61	878.934
62	893.343
63	907.751	49/29
64	922.16	46/27
65	936.569
66	950.978	26/15, 45/26
67	965.386
68	979.795	37/21, 44/25
69	994.204
70	1008.613
71	1023.021
72	1037.43	51/28
73	1051.839
74	1066.248
75	1080.656	28/15
76	1095.065
77	1109.474
78	1123.883
79	1138.291	27/14
80	1152.7	35/18, 37/19
81	1167.109	51/26
82	1181.518
83	1195.926
84	1210.335
85	1224.744
86	1239.153	43/21, 45/22
87	1253.561
88	1267.97	52/25
89	1282.379
90	1296.788
91	1311.196
92	1325.605
93	1340.014	13/6
94	1354.423
95	1368.831
96	1383.24
97	1397.649
98	1412.058
99	1426.466	41/18
100	1440.875
101	1455.284	51/22
102	1469.693
103	1484.101	33/14
104	1498.51
105	1512.919
106	1527.328
107	1541.736
108	1556.145	27/11
109	1570.554
110	1584.963	5/2
111	1599.371
112	1613.78	33/13
113	1628.189
114	1642.598
115	1657.006
116	1671.415
117	1685.824	45/17
118	1700.233
119	1714.641	35/13
120	1729.05	19/7
121	1743.459
122	1757.868
123	1772.276	39/14
124	1786.685
125	1801.094
126	1815.503
127	1829.911
128	1844.32
129	1858.729	38/13, 41/14
130	1873.138
131	1887.546
132	1901.955	3/1

Harmonics

Approximation of harmonics in 132edt

Harmonic		2	3	4	5	6	7	8	9	10	11	12
Error	Absolute (¢)	-4.07	+0.00	+6.26	-5.42	-4.07	+2.82	+2.19	+0.00	+4.91	-1.60	+6.26
	Relative (%)	-28.3	+0.0	+43.5	-37.7	-28.3	+19.6	+15.2	+0.0	+34.1	-11.1	+43.5
Steps (reduced)		83 (83)	132 (0)	167 (35)	193 (61)	215 (83)	234 (102)	250 (118)	264 (0)	277 (13)	288 (24)	299 (35)

Approximation of harmonics in 132edt

Harmonic		13	14	15	16	17	18	19	20	21	22	23
Error	Absolute (¢)	-2.63	-1.25	-5.42	-1.89	-5.98	-4.07	+3.18	+0.84	+2.82	-5.67	+3.82
	Relative (%)	-18.3	-8.7	-37.7	-13.1	-41.5	-28.3	+22.1	+5.8	+19.6	-39.4	+26.5
Steps (reduced)		308 (44)	317 (53)	325 (61)	333 (69)	340 (76)	347 (83)	354 (90)	360 (96)	366 (102)	371 (107)	377 (113)