110edt

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110edt

111edt →

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	Hekts	Approximate ratios
0	0	0	1/1
1	17.3	11.8
2	34.6	23.6
3	51.9	35.5	34/33, 35/34
4	69.2	47.3	26/25
5	86.5	59.1	41/39
6	103.7	70.9	35/33
7	121	82.7	15/14
8	138.3	94.5
9	155.6	106.4	23/21, 47/43
10	172.9	118.2	21/19
11	190.2	130	29/26
12	207.5	141.8
13	224.8	153.6	33/29
14	242.1	165.5	38/33
15	259.4	177.3	43/37
16	276.6	189.1	27/23, 34/29
17	293.9	200.9	45/38
18	311.2	212.7
19	328.5	224.5
20	345.8	236.4	11/9
21	363.1	248.2
22	380.4	260
23	397.7	271.8	34/27, 39/31
24	415	283.6	47/37
25	432.3	295.5
26	449.6	307.3	35/27
27	466.8	319.1	38/29
28	484.1	330.9	41/31, 45/34
29	501.4	342.7
30	518.7	354.5	31/23
31	536	366.4	15/11
32	553.3	378.2
33	570.6	390	25/18
34	587.9	401.8
35	605.2	413.6
36	622.5	425.5
37	639.7	437.3	42/29
38	657	449.1	19/13
39	674.3	460.9	31/21
40	691.6	472.7
41	708.9	484.5
42	726.2	496.4	35/23, 38/25
43	743.5	508.2
44	760.8	520	45/29
45	778.1	531.8
46	795.4	543.6
47	812.7	555.5
48	829.9	567.3	21/13
49	847.2	579.1	31/19
50	864.5	590.9
51	881.8	602.7
52	899.1	614.5	42/25
53	916.4	626.4	39/23
54	933.7	638.2
55	951	650	26/15, 45/26
56	968.3	661.8
57	985.6	673.6	23/13
58	1002.8	685.5	25/14, 41/23
59	1020.1	697.3
60	1037.4	709.1
61	1054.7	720.9	46/25
62	1072	732.7	13/7
63	1089.3	744.5
64	1106.6	756.4
65	1123.9	768.2
66	1141.2	780	29/15
67	1158.5	791.8	41/21
68	1175.8	803.6
69	1193	815.5
70	1210.3	827.3
71	1227.6	839.1
72	1244.9	850.9	39/19
73	1262.2	862.7	29/14
74	1279.5	874.5
75	1296.8	886.4
76	1314.1	898.2
77	1331.4	910	41/19
78	1348.7	921.8
79	1365.9	933.6	11/5
80	1383.2	945.5
81	1400.5	957.3
82	1417.8	969.1	34/15
83	1435.1	980.9
84	1452.4	992.7
85	1469.7	1004.5
86	1487	1016.4
87	1504.3	1028.2	31/13
88	1521.6	1040
89	1538.9	1051.8
90	1556.1	1063.6	27/11
91	1573.4	1075.5
92	1590.7	1087.3
93	1608	1099.1	38/15, 43/17
94	1625.3	1110.9	23/9
95	1642.6	1122.7
96	1659.9	1134.5
97	1677.2	1146.4	29/11
98	1694.5	1158.2
99	1711.8	1170
100	1729.1	1181.8	19/7
101	1746.3	1193.6
102	1763.6	1205.5
103	1780.9	1217.3	14/5
104	1798.2	1229.1
105	1815.5	1240.9
106	1832.8	1252.7
107	1850.1	1264.5
108	1867.4	1276.4
109	1884.7	1288.2
110	1902	1300	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)