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	17.943
2	35.886
3	53.829	34/33
4	71.772	24/23
5	89.715	20/19, 39/37
6	107.658	33/31
7	125.601	29/27, 43/40
8	143.544	38/35
9	161.487	34/31, 45/41
10	179.43	41/37
11	197.373	37/33
12	215.316	17/15, 43/38
13	233.259	8/7
14	251.202
15	269.145	7/6
16	287.088	13/11
17	305.031	31/26, 37/31
18	322.973	41/34
19	340.916	28/23, 45/37
20	358.859
21	376.802	41/33
22	394.745	44/35
23	412.688	33/26
24	430.631
25	448.574	22/17, 35/27
26	466.517	17/13, 38/29
27	484.46	41/31, 45/34
28	502.403
29	520.346	27/20
30	538.289	15/11
31	556.232	40/29
32	574.175
33	592.118	31/22, 38/27
34	610.061	27/19, 37/26
35	628.004	23/16
36	645.947	45/31
37	663.89	22/15
38	681.833	40/27, 43/29
39	699.776	3/2
40	717.719
41	735.662	26/17
42	753.605	17/11
43	771.548	39/25
44	789.491	30/19, 41/26
45	807.434	43/27
46	825.377	29/18
47	843.32	44/27
48	861.263	23/14
49	879.206
50	897.149
51	915.092
52	933.035	12/7
53	950.978	26/15, 45/26
54	968.92	7/4
55	986.863
56	1004.806
57	1022.749
58	1040.692	31/17, 42/23
59	1058.635	35/19
60	1076.578	41/22
61	1094.521
62	1112.464	19/10
63	1130.407	25/13
64	1148.35	33/17
65	1166.293
66	1184.236
67	1202.179	2/1
68	1220.122
69	1238.065	45/22
70	1256.008	31/15
71	1273.951
72	1291.894	19/9
73	1309.837
74	1327.78
75	1345.723	37/17
76	1363.666	11/5
77	1381.609	20/9
78	1399.552
79	1417.495	34/15
80	1435.438	39/17
81	1453.381	44/19
82	1471.324
83	1489.267	26/11
84	1507.21	43/18
85	1525.153	41/17
86	1543.096
87	1561.039	37/15
88	1578.982
89	1596.924
90	1614.867	33/13
91	1632.81	18/7
92	1650.753
93	1668.696	21/8
94	1686.639	45/17
95	1704.582
96	1722.525
97	1740.468	41/15
98	1758.411
99	1776.354
100	1794.297	31/11
101	1812.24	37/13
102	1830.183	23/8
103	1848.126
104	1866.069
105	1884.012
106	1901.955	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)