108edt

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108 equal divisions of the tritave, perfect twelfth, or 3rd harmonic (abbreviated 108edt or 108ed3), is a nonoctave tuning system that divides the interval of 3/1 into 108 equal parts of about 17.6 ¢ each. Each step represents a frequency ratio of 3^1/108, or the 108th root of 3.

← 107edt

108edt

109edt →

Prime factorization	22 × 33
Step size	17.6107 ¢
Octave	68\108edt (1197.53 ¢) (→ 17\27edt)
Consistency limit	10
Distinct consistency limit	10

Intervals

Steps	Cents	Hekts	Approximate ratios
0	0	0	1/1
1	17.6	12
2	35.2	24.1	47/46
3	52.8	36.1	34/33
4	70.4	48.1	25/24
5	88.1	60.2	20/19, 41/39
6	105.7	72.2
7	123.3	84.3	29/27, 44/41
8	140.9	96.3	38/35
9	158.5	108.3	23/21, 34/31
10	176.1	120.4	41/37
11	193.7	132.4	47/42
12	211.3	144.4	26/23
13	228.9	156.5	8/7
14	246.5	168.5	15/13
15	264.2	180.6
16	281.8	192.6
17	299.4	204.6	19/16, 44/37
18	317	216.7	6/5
19	334.6	228.7
20	352.2	240.7
21	369.8	252.8	26/21, 47/38
22	387.4	264.8	5/4
23	405	276.9	24/19, 43/34
24	422.7	288.9	23/18, 37/29
25	440.3	300.9
26	457.9	313	30/23, 43/33
27	475.5	325	25/19
28	493.1	337
29	510.7	349.1	39/29, 47/35
30	528.3	361.1	19/14
31	545.9	373.1	37/27
32	563.5	385.2	18/13
33	581.2	397.2	7/5
34	598.8	409.3	41/29
35	616.4	421.3	10/7
36	634	433.3
37	651.6	445.4	35/24
38	669.2	457.4	28/19
39	686.8	469.4
40	704.4	481.5
41	722	493.5	41/27, 44/29
42	739.6	505.6	23/15
43	757.3	517.6
44	774.9	529.6	25/16, 36/23
45	792.5	541.7	30/19
46	810.1	553.7
47	827.7	565.7	29/18
48	845.3	577.8	44/27
49	862.9	589.8
50	880.5	601.9
51	898.1	613.9	37/22, 42/25, 47/28
52	915.8	625.9	39/23
53	933.4	638	12/7
54	951	650	26/15, 45/26
55	968.6	662	7/4
56	986.2	674.1	23/13
57	1003.8	686.1	25/14
58	1021.4	698.1
59	1039	710.2	31/17
60	1056.6	722.2	35/19, 46/25
61	1074.3	734.3
62	1091.9	746.3	47/25
63	1109.5	758.3	19/10
64	1127.1	770.4	23/12
65	1144.7	782.4
66	1162.3	794.4	43/22, 45/23, 47/24
67	1179.9	806.5
68	1197.5	818.5
69	1215.1	830.6
70	1232.7	842.6
71	1250.4	854.6
72	1268	866.7
73	1285.6	878.7	21/10
74	1303.2	890.7
75	1320.8	902.8	15/7
76	1338.4	914.8	13/6
77	1356	926.9	35/16, 46/21
78	1373.6	938.9	42/19
79	1391.2	950.9	29/13
80	1408.9	963
81	1426.5	975	41/18
82	1444.1	987	23/10
83	1461.7	999.1
84	1479.3	1011.1	47/20
85	1496.9	1023.1	19/8
86	1514.5	1035.2	12/5
87	1532.1	1047.2	46/19
88	1549.7	1059.3
89	1567.4	1071.3	47/19
90	1585	1083.3	5/2
91	1602.6	1095.4
92	1620.2	1107.4
93	1637.8	1119.4
94	1655.4	1131.5	13/5
95	1673	1143.5	21/8
96	1690.6	1155.6
97	1708.2	1167.6
98	1725.8	1179.6
99	1743.5	1191.7
100	1761.1	1203.7
101	1778.7	1215.7
102	1796.3	1227.8
103	1813.9	1239.8
104	1831.5	1251.9
105	1849.1	1263.9
106	1866.7	1275.9	47/16
107	1884.3	1288
108	1902	1300	3/1

Harmonics

Approximation of harmonics in 108edt

Harmonic		2	3	4	5	6	7	8	9	10	11	12
Error	Absolute (¢)	-2.47	+0.00	-4.95	-3.82	-2.47	-5.18	-7.42	+0.00	-6.30	+4.81	-4.95
	Relative (%)	-14.0	+0.0	-28.1	-21.7	-14.0	-29.4	-42.1	+0.0	-35.8	+27.3	-28.1
Steps (reduced)		68 (68)	108 (0)	136 (28)	158 (50)	176 (68)	191 (83)	204 (96)	216 (0)	226 (10)	236 (20)	244 (28)

Approximation of harmonics in 108edt

Harmonic		13	14	15	16	17	18	19	20	21	22	23
Error	Absolute (¢)	-2.63	-7.66	-3.82	+7.72	+8.43	-2.47	-8.02	-8.77	-5.18	+2.33	-4.18
	Relative (%)	-14.9	-43.5	-21.7	+43.8	+47.9	-14.0	-45.6	-49.8	-29.4	+13.2	-23.7
Steps (reduced)		252 (36)	259 (43)	266 (50)	273 (57)	279 (63)	284 (68)	289 (73)	294 (78)	299 (83)	304 (88)	308 (92)