110edt

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110edt

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Prime factorization	2 × 5 × 11
Step size	17.2905¢
Octave	69\110edt (1193.04¢)
Consistency limit	2
Distinct consistency limit	2

110 equal divisions of the tritave, perfect twelfth, or 3rd harmonic (abbreviated 110edt or 110ed3), is a nonoctave tuning system that divides the interval of 3/1 into 110 equal parts of about 17.3 ¢ each. Each step represents a frequency ratio of 3^1/110, or the 110th root of 3.

Intervals

Steps	Cents	Approximate ratios
0	0	1/1
1	17.291
2	34.581
3	51.872	34/33, 35/34
4	69.162	26/25
5	86.453	41/39
6	103.743	35/33
7	121.034	15/14
8	138.324
9	155.615	23/21, 47/43
10	172.905	21/19
11	190.196	29/26
12	207.486
13	224.777	33/29
14	242.067	38/33
15	259.358	43/37
16	276.648	27/23, 34/29
17	293.939	45/38
18	311.229
19	328.52
20	345.81	11/9
21	363.101
22	380.391
23	397.682	34/27, 39/31
24	414.972	47/37
25	432.263
26	449.553	35/27
27	466.844	38/29
28	484.134	41/31, 45/34
29	501.425
30	518.715	31/23
31	536.006	15/11
32	553.296
33	570.587	25/18
34	587.877
35	605.168
36	622.458
37	639.749	42/29
38	657.039	19/13
39	674.33	31/21
40	691.62
41	708.911
42	726.201	35/23, 38/25
43	743.492
44	760.782	45/29
45	778.073
46	795.363
47	812.654
48	829.944	21/13
49	847.235	31/19
50	864.525
51	881.816
52	899.106	42/25
53	916.397	39/23
54	933.687
55	950.978	26/15, 45/26
56	968.268
57	985.559	23/13
58	1002.849	25/14, 41/23
59	1020.14
60	1037.43
61	1054.721	46/25
62	1072.011	13/7
63	1089.302
64	1106.592
65	1123.883
66	1141.173	29/15
67	1158.464	41/21
68	1175.754
69	1193.045
70	1210.335
71	1227.626
72	1244.916	39/19
73	1262.207	29/14
74	1279.497
75	1296.788
76	1314.078
77	1331.369	41/19
78	1348.659
79	1365.95	11/5
80	1383.24
81	1400.531
82	1417.821	34/15
83	1435.112
84	1452.402
85	1469.693
86	1486.983
87	1504.274	31/13
88	1521.564
89	1538.855
90	1556.145	27/11
91	1573.436
92	1590.726
93	1608.017	38/15, 43/17
94	1625.307	23/9
95	1642.598
96	1659.888
97	1677.179	29/11
98	1694.469
99	1711.76
100	1729.05	19/7
101	1746.341
102	1763.631
103	1780.922	14/5
104	1798.212
105	1815.503
106	1832.793
107	1850.084
108	1867.374
109	1884.665
110	1901.955	3/1

Harmonics

Approximation of harmonics in 110edt

Harmonic		2	3	4	5	6	7	8	9	10	11	12
Error	Absolute (¢)	-6.96	+0.00	+3.38	-2.54	-6.96	+2.82	-3.58	+0.00	+7.79	-1.60	+3.38
	Relative (%)	-40.2	+0.0	+19.5	-14.7	-40.2	+16.3	-20.7	+0.0	+45.1	-9.2	+19.5
Steps (reduced)		69 (69)	110 (0)	139 (29)	161 (51)	179 (69)	195 (85)	208 (98)	220 (0)	231 (11)	240 (20)	249 (29)

Approximation of harmonics in 110edt

Harmonic		13	14	15	16	17	18	19	20	21	22	23
Error	Absolute (¢)	+3.13	-4.13	-2.54	+6.76	+5.55	-6.96	+3.18	+0.84	+2.82	-8.55	+0.94
	Relative (%)	+18.1	-23.9	-14.7	+39.1	+32.1	-40.2	+18.4	+4.8	+16.3	-49.5	+5.5
Steps (reduced)		257 (37)	264 (44)	271 (51)	278 (58)	284 (64)	289 (69)	295 (75)	300 (80)	305 (85)	309 (89)	314 (94)