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	Hekts	Approximate ratios
0	0	0	1/1
1	18.1	12.4
2	36.2	24.8	46/45
3	54.3	37.1
4	72.5	49.5
5	90.6	61.9	20/19, 39/37
6	108.7	74.3	33/31
7	126.8	86.7	14/13, 43/40
8	144.9	99	25/23, 37/34
9	163	111.4	11/10, 45/41
10	181.1	123.8	10/9
11	199.3	136.2	37/33, 46/41
12	217.4	148.6	17/15, 42/37
13	235.5	161	39/34
14	253.6	173.3	22/19
15	271.7	185.7	41/35
16	289.8	198.1	13/11
17	307.9	210.5	37/31, 43/36
18	326	222.9	35/29, 41/34
19	344.2	235.2
20	362.3	247.6	37/30
21	380.4	260
22	398.5	272.4	34/27, 39/31
23	416.6	284.8	14/11
24	434.7	297.1	9/7
25	452.8	309.5	13/10
26	471	321.9	46/35
27	489.1	334.3
28	507.2	346.7
29	525.3	359	23/17, 42/31
30	543.4	371.4	26/19, 37/27
31	561.5	383.8	18/13
32	579.6	396.2
33	597.8	408.6	41/29
34	615.9	421	10/7
35	634	433.3
36	652.1	445.7
37	670.2	458.1	28/19
38	688.3	470.5
39	706.4	482.9
40	724.6	495.2	35/23, 41/27
41	742.7	507.6	43/28
42	760.8	520	31/20, 45/29
43	778.9	532.4
44	797	544.8	19/12, 46/29
45	815.1	557.1
46	833.2	569.5	34/21
47	851.4	581.9	18/11
48	869.5	594.3	43/26
49	887.6	606.7
50	905.7	619
51	923.8	631.4	29/17, 46/27
52	941.9	643.8	31/18
53	960	656.2
54	978.1	668.6
55	996.3	681
56	1014.4	693.3
57	1032.5	705.7
58	1050.6	718.1	11/6
59	1068.7	730.5
60	1086.8	742.9
61	1104.9	755.2	36/19
62	1123.1	767.6
63	1141.2	780	29/15
64	1159.3	792.4	41/21, 43/22
65	1177.4	804.8
66	1195.5	817.1
67	1213.6	829.5
68	1231.7	841.9
69	1249.9	854.3	35/17
70	1268	866.7
71	1286.1	879	21/10
72	1304.2	891.4
73	1322.3	903.8
74	1340.4	916.2	13/6
75	1358.5	928.6	46/21
76	1376.7	941	31/14
77	1394.8	953.3
78	1412.9	965.7	43/19
79	1431	978.1
80	1449.1	990.5	30/13
81	1467.2	1002.9	7/3
82	1485.3	1015.2	33/14
83	1503.5	1027.6	31/13
84	1521.6	1040
85	1539.7	1052.4
86	1557.8	1064.8
87	1575.9	1077.1
88	1594	1089.5
89	1612.1	1101.9	33/13
90	1630.2	1114.3
91	1648.4	1126.7
92	1666.5	1139	34/13
93	1684.6	1151.4	37/14, 45/17
94	1702.7	1163.8
95	1720.8	1176.2	27/10
96	1738.9	1188.6	30/11, 41/15
97	1757	1201
98	1775.2	1213.3	39/14
99	1793.3	1225.7	31/11
100	1811.4	1238.1	37/13
101	1829.5	1250.5
102	1847.6	1262.9
103	1865.7	1275.2
104	1883.8	1287.6
105	1902	1300	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)