152edt

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152edt

153edt →

Prime factorization	23 × 19
Step size	12.5129 ¢
Octave	96\152edt (1201.23 ¢) (→ 12\19edt)
Consistency limit	6
Distinct consistency limit	6

152 equal divisions of the tritave, perfect twelfth, or 3rd harmonic (abbreviated 152edt or 152ed3), is a nonoctave tuning system that divides the interval of 3/1 into 152 equal parts of about 12.5 ¢ each. Each step represents a frequency ratio of 3^1/152, or the 152nd root of 3.

Intervals

Steps	Cents	Hekts	Approximate ratios
0	0	0	1/1
1	12.5	8.6
2	25	17.1
3	37.5	25.7	45/44, 46/45, 47/46, 48/47
4	50.1	34.2	35/34, 36/35
5	62.6	42.8	28/27
6	75.1	51.3	24/23, 47/45
7	87.6	59.9	41/39
8	100.1	68.4	18/17
9	112.6	77	16/15
10	125.1	85.5	29/27
11	137.6	94.1	13/12
12	150.2	102.6	12/11
13	162.7	111.2	45/41, 56/51
14	175.2	119.7	31/28, 52/47
15	187.7	128.3	29/26, 39/35
16	200.2	136.8	46/41
17	212.7	145.4	26/23, 43/38
18	225.2	153.9	41/36, 49/43
19	237.7	162.5	31/27, 39/34, 47/41
20	250.3	171.1	37/32, 52/45
21	262.8	179.6	57/49
22	275.3	188.2	34/29, 41/35
23	287.8	196.7	13/11
24	300.3	205.3	44/37
25	312.8	213.8
26	325.3	222.4	35/29, 41/34
27	337.8	230.9	45/37
28	350.4	239.5
29	362.9	248	37/30, 58/47
30	375.4	256.6	36/29, 41/33
31	387.9	265.1
32	400.4	273.7	29/23, 34/27
33	412.9	282.2	33/26, 47/37, 52/41
34	425.4	290.8	23/18
35	438	299.3	58/45
36	450.5	307.9	35/27, 48/37
37	463	316.4	17/13, 47/36
38	475.5	325	54/41
39	488	333.6	57/43
40	500.5	342.1
41	513	350.7	39/29
42	525.5	359.2	42/31
43	538.1	367.8	15/11
44	550.6	376.3	11/8
45	563.1	384.9	18/13
46	575.6	393.4	46/33
47	588.1	402	52/37
48	600.6	410.5	41/29, 58/41
49	613.1	419.1	47/33
50	625.6	427.6	33/23, 56/39
51	638.2	436.2
52	650.7	444.7	51/35
53	663.2	453.3	22/15
54	675.7	461.8	31/21, 34/23
55	688.2	470.4	58/39
56	700.7	478.9	3/2
57	713.2	487.5
58	725.7	496.1	35/23
59	738.3	504.6
60	750.8	513.2	37/24, 54/35
61	763.3	521.7
62	775.8	530.3	36/23, 47/30
63	788.3	538.8	41/26, 52/33
64	800.8	547.4	27/17
65	813.3	555.9	8/5
66	825.8	564.5	29/18
67	838.4	573
68	850.9	581.6
69	863.4	590.1	28/17, 51/31
70	875.9	598.7	58/35
71	888.4	607.2
72	900.9	615.8	37/22
73	913.4	624.3	39/23
74	926	632.9	29/17, 41/24
75	938.5	641.4	55/32
76	951	650	26/15, 45/26
77	963.5	658.6
78	976	667.1	51/29, 58/33
79	988.5	675.7	23/13
80	1001	684.2	41/23
81	1013.5	692.8
82	1026.1	701.3	38/21, 47/26
83	1038.6	709.9	31/17, 51/28
84	1051.1	718.4
85	1063.6	727	37/20
86	1076.1	735.5	54/29
87	1088.6	744.1	15/8
88	1101.1	752.6	17/9
89	1113.6	761.2
90	1126.2	769.7	23/12
91	1138.7	778.3	56/29
92	1151.2	786.8	35/18
93	1163.7	795.4	47/24
94	1176.2	803.9
95	1188.7	812.5
96	1201.2	821.1	2/1
97	1213.7	829.6
98	1226.3	838.2
99	1238.8	846.7	45/22
100	1251.3	855.3	35/17
101	1263.8	863.8	56/27
102	1276.3	872.4	23/11
103	1288.8	880.9
104	1301.3	889.5
105	1313.9	898	47/22
106	1326.4	906.6
107	1338.9	915.1	13/6
108	1351.4	923.7	24/11
109	1363.9	932.2	11/5
110	1376.4	940.8	31/14
111	1388.9	949.3	29/13
112	1401.4	957.9
113	1414	966.4	43/19
114	1426.5	975	41/18
115	1439	983.6	39/17
116	1451.5	992.1	37/16
117	1464	1000.7
118	1476.5	1009.2	54/23
119	1489	1017.8	26/11
120	1501.5	1026.3
121	1514.1	1034.9
122	1526.6	1043.4	29/12
123	1539.1	1052	56/23
124	1551.6	1060.5
125	1564.1	1069.1	37/15
126	1576.6	1077.6
127	1589.1	1086.2
128	1601.6	1094.7	58/23
129	1614.2	1103.3	33/13
130	1626.7	1111.8
131	1639.2	1120.4	49/19
132	1651.7	1128.9
133	1664.2	1137.5	34/13
134	1676.7	1146.1
135	1689.2	1154.6
136	1701.7	1163.2
137	1714.3	1171.7	35/13
138	1726.8	1180.3
139	1739.3	1188.8	41/15
140	1751.8	1197.4	11/4
141	1764.3	1205.9	36/13
142	1776.8	1214.5
143	1789.3	1223	45/16
144	1801.9	1231.6	17/6
145	1814.4	1240.1
146	1826.9	1248.7	23/8
147	1839.4	1257.2
148	1851.9	1265.8	35/12
149	1864.4	1274.3	44/15, 47/16
150	1876.9	1282.9
151	1889.4	1291.4
152	1902	1300	3/1

Harmonics

Approximation of harmonics in 152edt

Harmonic		2	3	4	5	6	7	8	9	10	11	12
Error	Absolute (¢)	+1.23	+0.00	+2.47	+4.05	+1.23	-2.87	+3.70	+0.00	+5.29	+2.95	+2.47
	Relative (%)	+9.9	+0.0	+19.7	+32.4	+9.9	-22.9	+29.6	+0.0	+42.3	+23.6	+19.7
Steps (reduced)		96 (96)	152 (0)	192 (40)	223 (71)	248 (96)	269 (117)	288 (136)	304 (0)	319 (15)	332 (28)	344 (40)

Approximation of harmonics in 152edt

Harmonic		13	14	15	16	17	18	19	20	21	22	23
Error	Absolute (¢)	+1.54	-1.63	+4.05	+4.94	+0.09	+1.23	-4.78	-5.99	-2.87	+4.19	+2.31
	Relative (%)	+12.3	-13.0	+32.4	+39.5	+0.7	+9.9	-38.2	-47.9	-22.9	+33.5	+18.4
Steps (reduced)		355 (51)	365 (61)	375 (71)	384 (80)	392 (88)	400 (96)	407 (103)	414 (110)	421 (117)	428 (124)	434 (130)