112edt

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112edt

113edt →

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	Hekts	Approximate ratios
0	0	0	1/1
1	17	11.6
2	34	23.2
3	50.9	34.8
4	67.9	46.4	26/25
5	84.9	58
6	101.9	69.6	35/33
7	118.9	81.3	15/14
8	135.9	92.9
9	152.8	104.5
10	169.8	116.1	43/39
11	186.8	127.7	39/35
12	203.8	139.3
13	220.8	150.9	25/22, 42/37
14	237.7	162.5	31/27, 47/41
15	254.7	174.1	22/19
16	271.7	185.7
17	288.7	197.3	13/11
18	305.7	208.9	31/26, 37/31
19	322.7	220.5	41/34
20	339.6	232.1	28/23, 45/37
21	356.6	243.8	27/22, 43/35
22	373.6	255.4	31/25
23	390.6	267
24	407.6	278.6	19/15
25	424.5	290.2	23/18
26	441.5	301.8
27	458.5	313.4	30/23, 43/33
28	475.5	325	25/19
29	492.5	336.6
30	509.5	348.2
31	526.4	359.8	42/31
32	543.4	371.4	26/19, 37/27
33	560.4	383	29/21, 47/34
34	577.4	394.6
35	594.4	406.3	31/22
36	611.3	417.9	37/26
37	628.3	429.5
38	645.3	441.1	45/31
39	662.3	452.7	22/15, 41/28
40	679.3	464.3	37/25
41	696.3	475.9
42	713.2	487.5
43	730.2	499.1	29/19
44	747.2	510.7
45	764.2	522.3	14/9
46	781.2	533.9	11/7
47	798.1	545.5
48	815.1	557.1
49	832.1	568.8	21/13
50	849.1	580.4	31/19
51	866.1	592
52	883.1	603.6	5/3
53	900	615.2	37/22, 42/25
54	917	626.8	17/10
55	934	638.4
56	951	650	26/15, 45/26
57	968	661.6
58	984.9	673.2	30/17
59	1001.9	684.8	25/14, 41/23
60	1018.9	696.4	9/5
61	1035.9	708
62	1052.9	719.6
63	1069.8	731.3	13/7
64	1086.8	742.9
65	1103.8	754.5
66	1120.8	766.1	21/11
67	1137.8	777.7	27/14
68	1154.8	789.3	37/19
69	1171.7	800.9
70	1188.7	812.5
71	1205.7	824.1
72	1222.7	835.7
73	1239.7	847.3	43/21, 45/22
74	1256.6	858.9	31/15
75	1273.6	870.5
76	1290.6	882.1
77	1307.6	893.8
78	1324.6	905.4
79	1341.6	917
80	1358.5	928.6
81	1375.5	940.2	31/14
82	1392.5	951.8	38/17
83	1409.5	963.4
84	1426.5	975	41/18
85	1443.4	986.6	23/10
86	1460.4	998.2
87	1477.4	1009.8	47/20
88	1494.4	1021.4	45/19
89	1511.4	1033
90	1528.4	1044.6
91	1545.3	1056.3	22/9
92	1562.3	1067.9	37/15
93	1579.3	1079.5
94	1596.3	1091.1
95	1613.3	1102.7	33/13
96	1630.2	1114.3
97	1647.2	1125.9	44/17
98	1664.2	1137.5
99	1681.2	1149.1	37/14
100	1698.2	1160.7
101	1715.2	1172.3	35/13
102	1732.1	1183.9
103	1749.1	1195.5
104	1766.1	1207.1
105	1783.1	1218.8	14/5
106	1800.1	1230.4
107	1817	1242
108	1834	1253.6
109	1851	1265.2
110	1868	1276.8
111	1885	1288.4
112	1902	1300	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)