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	Hekts	Approximate ratios
0	0	0	1/1
1	17.8	12.1
2	35.6	24.3
3	53.3	36.4	34/33
4	71.1	48.6
5	88.9	60.7	39/37
6	106.7	72.9
7	124.4	85	29/27
8	142.2	97.2	38/35
9	160	109.3	45/41
10	177.8	121.5	41/37
11	195.5	133.6
12	213.3	145.8
13	231.1	157.9
14	248.9	170.1	15/13
15	266.6	182.2	7/6
16	284.4	194.4	46/39
17	302.2	206.5	25/21
18	320	218.7
19	337.7	230.8	45/37
20	355.5	243
21	373.3	255.1
22	391.1	267.3
23	408.8	279.4	19/15
24	426.6	291.6
25	444.4	303.7
26	462.2	315.9	17/13
27	479.9	328	33/25
28	497.7	340.2
29	515.5	352.3	31/23, 35/26
30	533.3	364.5	34/25
31	551	376.6
32	568.8	388.8	25/18
33	586.6	400.9
34	604.4	413.1
35	622.1	425.2
36	639.9	437.4
37	657.7	449.5	19/13
38	675.5	461.7
39	693.2	473.8
40	711	486
41	728.8	498.1
42	746.6	510.3
43	764.3	522.4
44	782.1	534.6	11/7
45	799.9	546.7	27/17, 46/29
46	817.7	558.9
47	835.4	571	34/21
48	853.2	583.2	18/11
49	871	595.3
50	888.8	607.5
51	906.5	619.6
52	924.3	631.8	29/17, 46/27
53	942.1	643.9
54	959.9	656.1
55	977.6	668.2
56	995.4	680.4
57	1013.2	692.5
58	1031	704.7
59	1048.7	716.8	11/6
60	1066.5	729
61	1084.3	741.1	43/23
62	1102.1	753.3	17/9
63	1119.8	765.4	21/11
64	1137.6	777.6
65	1155.4	789.7	37/19
66	1173.2	801.9
67	1190.9	814
68	1208.7	826.2
69	1226.5	838.3
70	1244.3	850.5	39/19
71	1262	862.6
72	1279.8	874.8
73	1297.6	886.9
74	1315.4	899.1
75	1333.1	911.2	41/19
76	1350.9	923.4
77	1368.7	935.5
78	1386.5	947.7
79	1404.2	959.8
80	1422	972	25/11
81	1439.8	984.1	39/17
82	1457.6	996.3
83	1475.3	1008.4
84	1493.1	1020.6	45/19
85	1510.9	1032.7
86	1528.7	1044.9	46/19
87	1546.4	1057
88	1564.2	1069.2	37/15
89	1582	1081.3
90	1599.8	1093.5
91	1617.6	1105.6
92	1635.3	1117.8	18/7
93	1653.1	1129.9	13/5
94	1670.9	1142.1
95	1688.7	1154.2
96	1706.4	1166.4
97	1724.2	1178.5	46/17
98	1742	1190.7	41/15
99	1759.8	1202.8
100	1777.5	1215
101	1795.3	1227.1
102	1813.1	1239.3	37/13
103	1830.9	1251.4
104	1848.6	1263.6
105	1866.4	1275.7
106	1884.2	1287.9
107	1902	1300	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)