107edt

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107edt

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Prime factorization	107 (prime)
Step size	17.7753¢
Octave	68\107edt (1208.72¢)
Consistency limit	2
Distinct consistency limit	2

107 equal divisions of the tritave, perfect twelfth, or 3rd harmonic (abbreviated 107edt or 107ed3), is a nonoctave tuning system that divides the interval of 3/1 into 107 equal parts of about 17.8 ¢ each. Each step represents a frequency ratio of 3^1/107, or the 107th root of 3.

Intervals

Steps	Cents	Approximate ratios
0	0	1/1
1	17.8
2	35.6
3	53.3	34/33
4	71.1
5	88.9	39/37
6	106.7
7	124.4	29/27
8	142.2	38/35
9	160	45/41
10	177.8	41/37
11	195.5
12	213.3
13	231.1
14	248.9	15/13
15	266.6	7/6
16	284.4	46/39
17	302.2	25/21
18	320
19	337.7	45/37
20	355.5
21	373.3
22	391.1
23	408.8	19/15
24	426.6
25	444.4
26	462.2	17/13
27	479.9	33/25
28	497.7
29	515.5	31/23, 35/26
30	533.3	34/25
31	551
32	568.8	25/18
33	586.6
34	604.4
35	622.1
36	639.9
37	657.7	19/13
38	675.5
39	693.2
40	711
41	728.8
42	746.6
43	764.3
44	782.1	11/7
45	799.9	27/17, 46/29
46	817.7
47	835.4	34/21
48	853.2	18/11
49	871
50	888.8
51	906.5
52	924.3	29/17, 46/27
53	942.1
54	959.9
55	977.6
56	995.4
57	1013.2
58	1031
59	1048.7	11/6
60	1066.5
61	1084.3	43/23
62	1102.1	17/9
63	1119.8	21/11
64	1137.6
65	1155.4	37/19
66	1173.2
67	1190.9
68	1208.7
69	1226.5
70	1244.3	39/19
71	1262
72	1279.8
73	1297.6
74	1315.4
75	1333.1	41/19
76	1350.9
77	1368.7
78	1386.5
79	1404.2
80	1422	25/11
81	1439.8	39/17
82	1457.6
83	1475.3
84	1493.1	45/19
85	1510.9
86	1528.7	46/19
87	1546.4
88	1564.2	37/15
89	1582
90	1599.8
91	1617.6
92	1635.3	18/7
93	1653.1	13/5
94	1670.9
95	1688.7
96	1706.4
97	1724.2	46/17
98	1742	41/15
99	1759.8
100	1777.5
101	1795.3
102	1813.1	37/13
103	1830.9
104	1848.6
105	1866.4
106	1884.2
107	1902	3/1

Harmonics

Approximation of harmonics in 107edt

Harmonic		2	3	4	5	6	7	8	9	10	11	12
Error	Absolute (¢)	+8.72	+0.00	-0.34	+4.41	+8.72	+8.48	+8.38	+0.00	-4.65	+8.10	-0.34
	Relative (%)	+49.1	+0.0	-1.9	+24.8	+49.1	+47.7	+47.2	+0.0	-26.2	+45.6	-1.9
Steps (reduced)		68 (68)	107 (0)	135 (28)	157 (50)	175 (68)	190 (83)	203 (96)	214 (0)	224 (10)	234 (20)	242 (28)

Approximation of harmonics in 107edt

Harmonic		13	14	15	16	17	18	19	20	21	22	23
Error	Absolute (¢)	+3.29	-0.58	+4.41	-0.67	+1.02	+8.72	+3.99	+4.07	+8.48	-0.96	-6.81
	Relative (%)	+18.5	-3.3	+24.8	-3.8	+5.7	+49.1	+22.5	+22.9	+47.7	-5.4	-38.3
Steps (reduced)		250 (36)	257 (43)	264 (50)	270 (56)	276 (62)	282 (68)	287 (73)	292 (78)	297 (83)	301 (87)	305 (91)