108edt

This page is a stub. You can help the Xenharmonic Wiki by expanding it.

← 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

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.

Intervals

Steps	Cents	Approximate ratios
0	0	1/1
1	17.611
2	35.221	47/46
3	52.832	34/33
4	70.443	25/24
5	88.053	20/19, 41/39
6	105.664
7	123.275	29/27, 44/41
8	140.886	38/35
9	158.496	23/21, 34/31
10	176.107	41/37
11	193.718	47/42
12	211.328	26/23
13	228.939	8/7
14	246.55	15/13
15	264.16
16	281.771
17	299.382	19/16, 44/37
18	316.993	6/5
19	334.603
20	352.214
21	369.825	26/21, 47/38
22	387.435	5/4
23	405.046	24/19, 43/34
24	422.657	23/18, 37/29
25	440.267
26	457.878	30/23, 43/33
27	475.489	25/19
28	493.099
29	510.71	39/29, 47/35
30	528.321	19/14
31	545.932	37/27
32	563.542	18/13
33	581.153	7/5
34	598.764	41/29
35	616.374	10/7
36	633.985
37	651.596	35/24
38	669.206	28/19
39	686.817
40	704.428
41	722.038	41/27, 44/29
42	739.649	23/15
43	757.26
44	774.871	25/16, 36/23
45	792.481	30/19
46	810.092
47	827.703	29/18
48	845.313	44/27
49	862.924
50	880.535
51	898.145	37/22, 42/25, 47/28
52	915.756	39/23
53	933.367	12/7
54	950.978	26/15, 45/26
55	968.588	7/4
56	986.199	23/13
57	1003.81	25/14
58	1021.42
59	1039.031	31/17
60	1056.642	35/19, 46/25
61	1074.252
62	1091.863	47/25
63	1109.474	19/10
64	1127.084	23/12
65	1144.695
66	1162.306	43/22, 45/23, 47/24
67	1179.917
68	1197.527
69	1215.138
70	1232.749
71	1250.359
72	1267.97
73	1285.581	21/10
74	1303.191
75	1320.802	15/7
76	1338.413	13/6
77	1356.023	35/16, 46/21
78	1373.634	42/19
79	1391.245	29/13
80	1408.856
81	1426.466	41/18
82	1444.077	23/10
83	1461.688
84	1479.298	47/20
85	1496.909	19/8
86	1514.52	12/5
87	1532.13	46/19
88	1549.741
89	1567.352	47/19
90	1584.963	5/2
91	1602.573
92	1620.184
93	1637.795
94	1655.405	13/5
95	1673.016	21/8
96	1690.627
97	1708.237
98	1725.848
99	1743.459
100	1761.069
101	1778.68
102	1796.291
103	1813.902
104	1831.512
105	1849.123
106	1866.734	47/16
107	1884.344
108	1901.955	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)