105edt

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← 104edt

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	18.1
2	36.2	46/45
3	54.3
4	72.5
5	90.6	20/19, 39/37
6	108.7	33/31
7	126.8	14/13, 43/40
8	144.9	25/23, 37/34
9	163	11/10, 45/41
10	181.1	10/9
11	199.3	37/33, 46/41
12	217.4	17/15, 42/37
13	235.5	39/34
14	253.6	22/19
15	271.7	41/35
16	289.8	13/11
17	307.9	37/31, 43/36
18	326	35/29, 41/34
19	344.2
20	362.3	37/30
21	380.4
22	398.5	34/27, 39/31
23	416.6	14/11
24	434.7	9/7
25	452.8	13/10
26	471	46/35
27	489.1
28	507.2
29	525.3	23/17, 42/31
30	543.4	26/19, 37/27
31	561.5	18/13
32	579.6
33	597.8	41/29
34	615.9	10/7
35	634
36	652.1
37	670.2	28/19
38	688.3
39	706.4
40	724.6	35/23, 41/27
41	742.7	43/28
42	760.8	31/20, 45/29
43	778.9
44	797	19/12, 46/29
45	815.1
46	833.2	34/21
47	851.4	18/11
48	869.5	43/26
49	887.6
50	905.7
51	923.8	29/17, 46/27
52	941.9	31/18
53	960
54	978.1
55	996.3
56	1014.4
57	1032.5
58	1050.6	11/6
59	1068.7
60	1086.8
61	1104.9	36/19
62	1123.1
63	1141.2	29/15
64	1159.3	41/21, 43/22
65	1177.4
66	1195.5
67	1213.6
68	1231.7
69	1249.9	35/17
70	1268
71	1286.1	21/10
72	1304.2
73	1322.3
74	1340.4	13/6
75	1358.5	46/21
76	1376.7	31/14
77	1394.8
78	1412.9	43/19
79	1431
80	1449.1	30/13
81	1467.2	7/3
82	1485.3	33/14
83	1503.5	31/13
84	1521.6
85	1539.7
86	1557.8
87	1575.9
88	1594
89	1612.1	33/13
90	1630.2
91	1648.4
92	1666.5	34/13
93	1684.6	37/14, 45/17
94	1702.7
95	1720.8	27/10
96	1738.9	30/11, 41/15
97	1757
98	1775.2	39/14
99	1793.3	31/11
100	1811.4	37/13
101	1829.5
102	1847.6
103	1865.7
104	1883.8
105	1902	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)