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	14.4
2	28.8
3	43.2	39/38, 42/41
4	57.6
5	72	25/24, 49/47
6	86.5	41/39
7	100.9	35/33
8	115.3	31/29, 46/43
9	129.7	14/13
10	144.1	38/35
11	158.5	23/21
12	172.9	21/19
13	187.3	39/35
14	201.7
15	216.1	17/15
16	230.5
17	244.9	38/33
18	259.4	43/37
19	273.8	41/35
20	288.2	13/11
21	302.6
22	317	6/5
23	331.4	23/19
24	345.8	11/9
25	360.2
26	374.6	41/33
27	389
28	403.4
29	417.9	14/11
30	432.3
31	446.7	22/17
32	461.1
33	475.5
34	489.9
35	504.3
36	518.7
37	533.1	34/25
38	547.5
39	561.9	18/13
40	576.4	46/33
41	590.8	38/27
42	605.2
43	619.6
44	634
45	648.4
46	662.8	22/15
47	677.2
48	691.6
49	706
50	720.4	47/31
51	734.8	26/17
52	749.3
53	763.7	14/9
54	778.1
55	792.5	49/31
56	806.9	43/27
57	821.3	37/23, 45/28
58	835.7	47/29
59	850.1
60	864.5	28/17
61	878.9
62	893.3
63	907.8	49/29
64	922.2	46/27
65	936.6
66	951	26/15, 45/26
67	965.4
68	979.8	37/21, 44/25
69	994.2
70	1008.6
71	1023
72	1037.4	51/28
73	1051.8
74	1066.2
75	1080.7	28/15
76	1095.1
77	1109.5
78	1123.9
79	1138.3	27/14
80	1152.7	35/18, 37/19
81	1167.1	51/26
82	1181.5
83	1195.9
84	1210.3
85	1224.7
86	1239.2	43/21, 45/22
87	1253.6
88	1268	52/25
89	1282.4
90	1296.8
91	1311.2
92	1325.6
93	1340	13/6
94	1354.4
95	1368.8
96	1383.2
97	1397.6
98	1412.1
99	1426.5	41/18
100	1440.9
101	1455.3	51/22
102	1469.7
103	1484.1	33/14
104	1498.5
105	1512.9
106	1527.3
107	1541.7
108	1556.1	27/11
109	1570.6
110	1585	5/2
111	1599.4
112	1613.8	33/13
113	1628.2
114	1642.6
115	1657
116	1671.4
117	1685.8	45/17
118	1700.2
119	1714.6	35/13
120	1729.1	19/7
121	1743.5
122	1757.9
123	1772.3	39/14
124	1786.7
125	1801.1
126	1815.5
127	1829.9
128	1844.3
129	1858.7	38/13, 41/14
130	1873.1
131	1887.5
132	1902	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)