111edt

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111edt

112edt →

Prime factorization	3 × 37
Step size	17.1347¢
Octave	70\111edt (1199.43¢)
Consistency limit	10
Distinct consistency limit	10

111 equal divisions of the tritave, perfect twelfth, or 3rd harmonic (abbreviated 111edt or 111ed3), is a nonoctave tuning system that divides the interval of 3/1 into 111 equal parts of about 17.1 ¢ each. Each step represents a frequency ratio of 3^1/111, or the 111th root of 3.

Intervals

Steps	Cents	Approximate ratios
0	0	1/1
1	17.135
2	34.269
3	51.404	33/32, 34/33
4	68.539
5	85.674	21/20, 41/39
6	102.808	17/16
7	119.943	15/14
8	137.078	13/12, 40/37
9	154.213	47/43
10	171.347	32/29
11	188.482	29/26
12	205.617	9/8
13	222.751	33/29
14	239.886	23/20, 31/27
15	257.021	36/31
16	274.156	34/29
17	291.29	13/11
18	308.425	37/31, 43/36
19	325.56	29/24, 41/34
20	342.695	28/23, 39/32
21	359.829	16/13
22	376.964	41/33, 46/37
23	394.099
24	411.234	33/26
25	428.368	41/32
26	445.503	22/17
27	462.638	17/13, 47/36
28	479.772	29/22
29	496.907	4/3
30	514.042	39/29
31	531.177
32	548.311
33	565.446	18/13, 43/31
34	582.581	7/5
35	599.716	41/29
36	616.85	10/7
37	633.985
38	651.12
39	668.254
40	685.389	46/31
41	702.524	3/2
42	719.659	44/29, 47/31
43	736.793	26/17
44	753.928	17/11
45	771.063
46	788.198	41/26
47	805.332	43/27
48	822.467	37/23, 45/28
49	839.602	13/8
50	856.736
51	873.871
52	891.006
53	908.141
54	925.275	29/17, 41/24
55	942.41	31/18
56	959.545	40/23, 47/27
57	976.68
58	993.814
59	1010.949	43/24
60	1028.084	29/16
61	1045.219
62	1062.353	24/13
63	1079.488	28/15, 41/22
64	1096.623	32/17
65	1113.757	40/21
66	1130.892
67	1148.027	33/17
68	1165.162	47/24
69	1182.296
70	1199.431	2/1
71	1216.566
72	1233.701
73	1250.835
74	1267.97
75	1285.105	21/10
76	1302.239
77	1319.374	15/7
78	1336.509	13/6
79	1353.644
80	1370.778
81	1387.913	29/13
82	1405.048	9/4
83	1422.183
84	1439.317	39/17
85	1456.452
86	1473.587
87	1490.721	26/11
88	1507.856	43/18
89	1524.991	41/17
90	1542.126	39/16
91	1559.26	32/13
92	1576.395
93	1593.53
94	1610.665	33/13
95	1627.799	41/16
96	1644.934	31/12, 44/17
97	1662.069	47/18
98	1679.204	29/11
99	1696.338	8/3
100	1713.473	43/16
101	1730.608
102	1747.742
103	1764.877	36/13
104	1782.012	14/5
105	1799.147
106	1816.281	20/7
107	1833.416
108	1850.551	32/11
109	1867.686	47/16
110	1884.82
111	1901.955	3/1

Harmonics

Approximation of harmonics in 111edt

Harmonic		2	3	4	5	6	7	8	9	10	11	12
Error	Absolute (¢)	-0.57	+0.00	-1.14	+6.65	-0.57	+6.72	-1.71	+0.00	+6.08	-4.71	-1.14
	Relative (%)	-3.3	+0.0	-6.6	+38.8	-3.3	+39.2	-10.0	+0.0	+35.5	-27.5	-6.6
Steps (reduced)		70 (70)	111 (0)	140 (29)	163 (52)	181 (70)	197 (86)	210 (99)	222 (0)	233 (11)	242 (20)	251 (29)

Approximation of harmonics in 111edt

Harmonic		13	14	15	16	17	18	19	20	21	22	23
Error	Absolute (¢)	-2.63	+6.15	+6.65	-2.28	-4.42	-0.57	-8.50	+5.51	+6.72	-5.28	+3.43
	Relative (%)	-15.4	+35.9	+38.8	-13.3	-25.8	-3.3	-49.6	+32.2	+39.2	-30.8	+20.0
Steps (reduced)		259 (37)	267 (45)	274 (52)	280 (58)	286 (64)	292 (70)	297 (75)	303 (81)	308 (86)	312 (90)	317 (95)