112edt

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112edt

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Prime factorization	24 × 7
Step size	16.9817¢
Octave	71\112edt (1205.7¢)
Consistency limit	2
Distinct consistency limit	2

112 equal divisions of the tritave, perfect twelfth, or 3rd harmonic (abbreviated 112edt or 112ed3), is a nonoctave tuning system that divides the interval of 3/1 into 112 equal parts of about 17 ¢ each. Each step represents a frequency ratio of 3^1/112, or the 112th root of 3.

Intervals

Steps	Cents	Approximate ratios
0	0	1/1
1	16.982
2	33.963
3	50.945
4	67.927	26/25
5	84.909
6	101.89	35/33
7	118.872	15/14
8	135.854
9	152.836
10	169.817	43/39
11	186.799	39/35
12	203.781
13	220.763	25/22, 42/37
14	237.744	31/27, 47/41
15	254.726	22/19
16	271.708
17	288.69	13/11
18	305.671	31/26, 37/31
19	322.653	41/34
20	339.635	28/23, 45/37
21	356.617	27/22, 43/35
22	373.598	31/25
23	390.58
24	407.562	19/15
25	424.544	23/18
26	441.525
27	458.507	30/23, 43/33
28	475.489	25/19
29	492.47
30	509.452
31	526.434	42/31
32	543.416	26/19, 37/27
33	560.397	29/21, 47/34
34	577.379
35	594.361	31/22
36	611.343	37/26
37	628.324
38	645.306	45/31
39	662.288	22/15, 41/28
40	679.27	37/25
41	696.251
42	713.233
43	730.215	29/19
44	747.197
45	764.178	14/9
46	781.16	11/7
47	798.142
48	815.124
49	832.105	21/13
50	849.087	31/19
51	866.069
52	883.051	5/3
53	900.032	37/22, 42/25
54	917.014	17/10
55	933.996
56	950.978	26/15, 45/26
57	967.959
58	984.941	30/17
59	1001.923	25/14, 41/23
60	1018.904	9/5
61	1035.886
62	1052.868
63	1069.85	13/7
64	1086.831
65	1103.813
66	1120.795	21/11
67	1137.777	27/14
68	1154.758	37/19
69	1171.74
70	1188.722
71	1205.704
72	1222.685
73	1239.667	43/21, 45/22
74	1256.649	31/15
75	1273.631
76	1290.612
77	1307.594
78	1324.576
79	1341.558
80	1358.539
81	1375.521	31/14
82	1392.503	38/17
83	1409.485
84	1426.466	41/18
85	1443.448	23/10
86	1460.43
87	1477.411	47/20
88	1494.393	45/19
89	1511.375
90	1528.357
91	1545.338	22/9
92	1562.32	37/15
93	1579.302
94	1596.284
95	1613.265	33/13
96	1630.247
97	1647.229	44/17
98	1664.211
99	1681.192	37/14
100	1698.174
101	1715.156	35/13
102	1732.138
103	1749.119
104	1766.101
105	1783.083	14/5
106	1800.065
107	1817.046
108	1834.028
109	1851.01
110	1867.992
111	1884.973
112	1901.955	3/1

Harmonics

Approximation of harmonics in 112edt

Harmonic		2	3	4	5	6	7	8	9	10	11	12
Error	Absolute (¢)	+5.70	+0.00	-5.57	-1.31	+5.70	-6.44	+0.13	+0.00	+4.40	-7.77	-5.57
	Relative (%)	+33.6	+0.0	-32.8	-7.7	+33.6	-37.9	+0.8	+0.0	+25.9	-45.8	-32.8
Steps (reduced)		71 (71)	112 (0)	141 (29)	164 (52)	183 (71)	198 (86)	212 (100)	224 (0)	235 (11)	244 (20)	253 (29)

Approximation of harmonics in 112edt

Harmonic		13	14	15	16	17	18	19	20	21	22	23
Error	Absolute (¢)	-8.29	-0.74	-1.31	+5.83	+2.77	+5.70	-2.99	-6.88	-6.44	-2.07	+5.88
	Relative (%)	-48.8	-4.3	-7.7	+34.3	+16.3	+33.6	-17.6	-40.5	-37.9	-12.2	+34.6
Steps (reduced)		261 (37)	269 (45)	276 (52)	283 (59)	289 (65)	295 (71)	300 (76)	305 (81)	310 (86)	315 (91)	320 (96)