105edt

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105edt

106edt →

Prime factorization	3 × 5 × 7
Step size	18.1139¢
Octave	66\105edt (1195.51¢) (→22\35edt)
Consistency limit	4
Distinct consistency limit	4

105 equal divisions of the tritave, perfect twelfth, or 3rd harmonic (abbreviated 105edt or 105ed3), is a nonoctave tuning system that divides the interval of 3/1 into 105 equal parts of about 18.1 ¢ each. Each step represents a frequency ratio of 3^1/105, or the 105th root of 3.

Intervals

Steps	Cents	Approximate Ratios
0	0	1/1
1	18.114
2	36.228	46/45
3	54.342
4	72.455
5	90.569	20/19, 39/37
6	108.683	33/31
7	126.797	14/13, 43/40
8	144.911	25/23, 37/34
9	163.025	11/10, 45/41
10	181.139	10/9
11	199.252	37/33, 46/41
12	217.366	17/15, 42/37
13	235.48	39/34
14	253.594	22/19
15	271.708	41/35
16	289.822	13/11
17	307.936	37/31, 43/36
18	326.049	35/29, 41/34
19	344.163
20	362.277	37/30
21	380.391
22	398.505	34/27, 39/31
23	416.619	14/11
24	434.733	9/7
25	452.846	13/10
26	470.96	46/35
27	489.074
28	507.188
29	525.302	23/17, 42/31
30	543.416	26/19, 37/27
31	561.53	18/13
32	579.643
33	597.757	41/29
34	615.871	10/7
35	633.985
36	652.099
37	670.213	28/19
38	688.327
39	706.44
40	724.554	35/23, 41/27
41	742.668	43/28
42	760.782	31/20, 45/29
43	778.896
44	797.01	19/12, 46/29
45	815.124
46	833.237	34/21
47	851.351	18/11
48	869.465	43/26
49	887.579
50	905.693
51	923.807	29/17, 46/27
52	941.921	31/18
53	960.034
54	978.148
55	996.262
56	1014.376
57	1032.49
58	1050.604	11/6
59	1068.718
60	1086.831
61	1104.945	36/19
62	1123.059
63	1141.173	29/15
64	1159.287	41/21, 43/22
65	1177.401
66	1195.515
67	1213.628
68	1231.742
69	1249.856	35/17
70	1267.97
71	1286.084	21/10
72	1304.198
73	1322.312
74	1340.425	13/6
75	1358.539	46/21
76	1376.653	31/14
77	1394.767
78	1412.881	43/19
79	1430.995
80	1449.109	30/13
81	1467.222	7/3
82	1485.336	33/14
83	1503.45	31/13
84	1521.564
85	1539.678
86	1557.792
87	1575.906
88	1594.019
89	1612.133	33/13
90	1630.247
91	1648.361
92	1666.475	34/13
93	1684.589	37/14, 45/17
94	1702.703
95	1720.816	27/10
96	1738.93	30/11, 41/15
97	1757.044
98	1775.158	39/14
99	1793.272	31/11
100	1811.386	37/13
101	1829.5
102	1847.613
103	1865.727
104	1883.841
105	1901.955	3/1

Harmonics

Approximation of harmonics in 105edt

Harmonic		2	3	4	5	6	7	8	9	10	11	12
Error	Absolute (¢)	-4.49	+0.00	-8.97	+3.22	-4.49	+0.35	+4.66	+0.00	-1.27	-3.24	-8.97
	Relative (%)	-24.8	+0.0	-49.5	+17.8	-24.8	+1.9	+25.7	+0.0	-7.0	-17.9	-49.5
Steps (reduced)		66 (66)	105 (0)	132 (27)	154 (49)	171 (66)	186 (81)	199 (94)	210 (0)	220 (10)	229 (19)	237 (27)

Approximation of harmonics in 105edt

Harmonic		13	14	15	16	17	18	19	20	21	22	23
Error	Absolute (¢)	-2.63	-4.13	+3.22	+0.17	+3.90	-4.49	-7.52	-5.75	+0.35	-7.73	+5.88
	Relative (%)	-14.5	-22.8	+17.8	+1.0	+21.5	-24.8	-41.5	-31.7	+1.9	-42.7	+32.5
Steps (reduced)		245 (35)	252 (42)	259 (49)	265 (55)	271 (61)	276 (66)	281 (71)	286 (76)	291 (81)	295 (85)	300 (90)