106edt

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106edt

107edt →

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. The 39th step of this tuning is just 0.2241 cents off from 12edo, or 1.25% of 1\106edt away.

Intervals

Steps	Cents	Hekts	Approximate ratios
0	0	0	1/1
1	17.9	12.3
2	35.9	24.5
3	53.8	36.8	34/33
4	71.8	49.1	24/23
5	89.7	61.3	20/19, 39/37
6	107.7	73.6	33/31
7	125.6	85.8	29/27, 43/40
8	143.5	98.1	38/35
9	161.5	110.4	34/31, 45/41
10	179.4	122.6	41/37
11	197.4	134.9	37/33
12	215.3	147.2	17/15, 43/38
13	233.3	159.4	8/7
14	251.2	171.7
15	269.1	184	7/6
16	287.1	196.2	13/11
17	305	208.5	31/26, 37/31
18	323	220.8	41/34
19	340.9	233	28/23, 45/37
20	358.9	245.3
21	376.8	257.5	41/33
22	394.7	269.8	44/35
23	412.7	282.1	33/26
24	430.6	294.3
25	448.6	306.6	22/17, 35/27
26	466.5	318.9	17/13, 38/29
27	484.5	331.1	41/31, 45/34
28	502.4	343.4
29	520.3	355.7	27/20
30	538.3	367.9	15/11
31	556.2	380.2	40/29
32	574.2	392.5
33	592.1	404.7	31/22, 38/27
34	610.1	417	27/19, 37/26
35	628	429.2	23/16
36	645.9	441.5	45/31
37	663.9	453.8	22/15
38	681.8	466	40/27, 43/29
39	699.8	478.3	3/2
40	717.7	490.6
41	735.7	502.8	26/17
42	753.6	515.1	17/11
43	771.5	527.4	39/25
44	789.5	539.6	30/19, 41/26
45	807.4	551.9	43/27
46	825.4	564.2	29/18
47	843.3	576.4	44/27
48	861.3	588.7	23/14
49	879.2	600.9
50	897.1	613.2
51	915.1	625.5
52	933	637.7	12/7
53	951	650	26/15, 45/26
54	968.9	662.3	7/4
55	986.9	674.5
56	1004.8	686.8
57	1022.7	699.1
58	1040.7	711.3	31/17, 42/23
59	1058.6	723.6	35/19
60	1076.6	735.8	41/22
61	1094.5	748.1
62	1112.5	760.4	19/10
63	1130.4	772.6	25/13
64	1148.4	784.9	33/17
65	1166.3	797.2
66	1184.2	809.4
67	1202.2	821.7	2/1
68	1220.1	834
69	1238.1	846.2	45/22
70	1256	858.5	31/15
71	1274	870.8
72	1291.9	883	19/9
73	1309.8	895.3
74	1327.8	907.5
75	1345.7	919.8	37/17
76	1363.7	932.1	11/5
77	1381.6	944.3	20/9
78	1399.6	956.6
79	1417.5	968.9	34/15
80	1435.4	981.1	39/17
81	1453.4	993.4	44/19
82	1471.3	1005.7
83	1489.3	1017.9	26/11
84	1507.2	1030.2	43/18
85	1525.2	1042.5	41/17
86	1543.1	1054.7
87	1561	1067	37/15
88	1579	1079.2
89	1596.9	1091.5
90	1614.9	1103.8	33/13
91	1632.8	1116	18/7
92	1650.8	1128.3
93	1668.7	1140.6	21/8
94	1686.6	1152.8	45/17
95	1704.6	1165.1
96	1722.5	1177.4
97	1740.5	1189.6	41/15
98	1758.4	1201.9
99	1776.4	1214.2
100	1794.3	1226.4	31/11
101	1812.2	1238.7	37/13
102	1830.2	1250.9	23/8
103	1848.1	1263.2
104	1866.1	1275.5
105	1884	1287.7
106	1902	1300	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)