106edt

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106edt

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Prime factorization	2 × 53
Step size	17.943¢
Octave	67\106edt (1202.18¢)
Consistency limit	4
Distinct consistency limit	4

106 equal divisions of the tritave, perfect twelfth, or 3rd harmonic (abbreviated 106edt or 106ed3), is a nonoctave tuning system that divides the interval of 3/1 into 106 equal parts of about 17.9⁠ ⁠¢ each. Each step represents a frequency ratio of 3^1/106, or the 106th root of 3.

Intervals

Steps	Cents	Approximate ratios
0	0	1/1
1	17.9
2	35.9
3	53.8	34/33
4	71.8	24/23
5	89.7	20/19, 39/37
6	107.7	33/31
7	125.6	29/27, 43/40
8	143.5	38/35
9	161.5	34/31, 45/41
10	179.4	41/37
11	197.4	37/33
12	215.3	17/15, 43/38
13	233.3	8/7
14	251.2
15	269.1	7/6
16	287.1	13/11
17	305	31/26, 37/31
18	323	41/34
19	340.9	28/23, 45/37
20	358.9
21	376.8	41/33
22	394.7	44/35
23	412.7	33/26
24	430.6
25	448.6	22/17, 35/27
26	466.5	17/13, 38/29
27	484.5	41/31, 45/34
28	502.4
29	520.3	27/20
30	538.3	15/11
31	556.2	40/29
32	574.2
33	592.1	31/22, 38/27
34	610.1	27/19, 37/26
35	628	23/16
36	645.9	45/31
37	663.9	22/15
38	681.8	40/27, 43/29
39	699.8	3/2
40	717.7
41	735.7	26/17
42	753.6	17/11
43	771.5	39/25
44	789.5	30/19, 41/26
45	807.4	43/27
46	825.4	29/18
47	843.3	44/27
48	861.3	23/14
49	879.2
50	897.1
51	915.1
52	933	12/7
53	951	26/15, 45/26
54	968.9	7/4
55	986.9
56	1004.8
57	1022.7
58	1040.7	31/17, 42/23
59	1058.6	35/19
60	1076.6	41/22
61	1094.5
62	1112.5	19/10
63	1130.4	25/13
64	1148.4	33/17
65	1166.3
66	1184.2
67	1202.2	2/1
68	1220.1
69	1238.1	45/22
70	1256	31/15
71	1274
72	1291.9	19/9
73	1309.8
74	1327.8
75	1345.7	37/17
76	1363.7	11/5
77	1381.6	20/9
78	1399.6
79	1417.5	34/15
80	1435.4	39/17
81	1453.4	44/19
82	1471.3
83	1489.3	26/11
84	1507.2	43/18
85	1525.2	41/17
86	1543.1
87	1561	37/15
88	1579
89	1596.9
90	1614.9	33/13
91	1632.8	18/7
92	1650.8
93	1668.7	21/8
94	1686.6	45/17
95	1704.6
96	1722.5
97	1740.5	41/15
98	1758.4
99	1776.4
100	1794.3	31/11
101	1812.2	37/13
102	1830.2	23/8
103	1848.1
104	1866.1
105	1884
106	1902	3/1

Harmonics

Approximation of harmonics in 106edt

Harmonic		2	3	4	5	6	7	8	9	10	11	12
Error	Absolute (¢)	+2.18	+0.00	+4.36	-5.15	+2.18	+4.45	+6.54	+0.00	-2.97	-6.49	+4.36
	Relative (%)	+12.1	+0.0	+24.3	-28.7	+12.1	+24.8	+36.4	+0.0	-16.6	-36.2	+24.3
Steps (reduced)		67 (67)	106 (0)	134 (28)	155 (49)	173 (67)	188 (82)	201 (95)	212 (0)	222 (10)	231 (19)	240 (28)

Approximation of harmonics in 106edt

Harmonic		13	14	15	16	17	18	19	20	21	22	23
Error	Absolute (¢)	-8.61	+6.63	-5.15	+8.72	-6.52	+2.18	-1.71	-0.79	+4.45	-4.31	+8.45
	Relative (%)	-48.0	+37.0	-28.7	+48.6	-36.4	+12.1	-9.5	-4.4	+24.8	-24.0	+47.1
Steps (reduced)		247 (35)	255 (43)	261 (49)	268 (56)	273 (61)	279 (67)	284 (72)	289 (77)	294 (82)	298 (86)	303 (91)