104edt

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← 103edt

104edt

105edt →

Prime factorization	23 × 13
Step size	18.288¢
Octave	66\104edt (1207.01¢) (→33\52edt)
Consistency limit	2
Distinct consistency limit	2

104 equal divisions of the tritave, perfect twelfth, or 3rd harmonic (abbreviated 104edt or 104ed3), is a nonoctave tuning system that divides the interval of 3/1 into 104 equal parts of about 18.3 ¢ each. Each step represents a frequency ratio of 3^1/104, or the 104th root of 3.

Intervals

Steps	Cents	Approximate Ratios
0	0	1/1
1	18.288
2	36.576
3	54.864	31/30
4	73.152
5	91.44	19/18, 39/37
6	109.728	33/31
7	128.016	14/13
8	146.304	37/34
9	164.592	11/10
10	182.88	10/9
11	201.168	46/41
12	219.456	42/37
13	237.744	31/27, 39/34
14	256.032	22/19
15	274.32	34/29
16	292.608
17	310.896
18	329.185	23/19
19	347.473	11/9
20	365.761	21/17
21	384.049
22	402.337	29/23
23	420.625	37/29
24	438.913
25	457.201	43/33
26	475.489
27	493.777
28	512.065	39/29
29	530.353	19/14
30	548.641
31	566.929	43/31
32	585.217
33	603.505
34	621.793	43/30
35	640.081	42/29
36	658.369	19/13, 41/28
37	676.657	34/23
38	694.945
39	713.233
40	731.521	29/19
41	749.809
42	768.097
43	786.385	41/26
44	804.673	43/27
45	822.961	37/23
46	841.249
47	859.537	23/14
48	877.825
49	896.113
50	914.401	39/23
51	932.689
52	950.978
53	969.266
54	987.554	23/13
55	1005.842	34/19
56	1024.13
57	1042.418	31/17, 42/23
58	1060.706
59	1078.994	41/22
60	1097.282
61	1115.57
62	1133.858
63	1152.146	37/19
64	1170.434
65	1188.722
66	1207.01
67	1225.298
68	1243.586	39/19, 41/20
69	1261.874	29/14
70	1280.162
71	1298.45
72	1316.738
73	1335.026
74	1353.314
75	1371.602	42/19
76	1389.89	29/13
77	1408.178
78	1426.466	41/18
79	1444.754
80	1463.042
81	1481.33
82	1499.618
83	1517.906
84	1536.194	17/7
85	1554.482	27/11
86	1572.77
87	1591.059
88	1609.347
89	1627.635
90	1645.923
91	1664.211	34/13
92	1682.499	37/14
93	1700.787
94	1719.075	27/10
95	1737.363	30/11
96	1755.651
97	1773.939	39/14
98	1792.227	31/11
99	1810.515	37/13
100	1828.803
101	1847.091
102	1865.379
103	1883.667
104	1901.955	3/1

Harmonics

Approximation of harmonics in 104edt

Harmonic		2	3	4	5	6	7	8	9	10	11	12
Error	Absolute (¢)	+7.01	+0.00	-4.27	-6.53	+7.01	-3.83	+2.74	+0.00	+0.48	+0.06	-4.27
	Relative (%)	+38.3	+0.0	-23.3	-35.7	+38.3	-20.9	+15.0	+0.0	+2.6	+0.4	-23.3
Steps (reduced)		66 (66)	104 (0)	131 (27)	152 (48)	170 (66)	184 (80)	197 (93)	208 (0)	218 (10)	227 (19)	235 (27)

Approximation of harmonics in 104edt

Harmonic		13	14	15	16	17	18	19	20	21	22	23
Error	Absolute (¢)	+3.46	+3.18	-6.53	-8.54	-3.76	+7.01	+4.85	+7.49	-3.83	+7.07	+3.27
	Relative (%)	+18.9	+17.4	-35.7	-46.7	-20.6	+38.3	+26.5	+40.9	-20.9	+38.7	+17.9
Steps (reduced)		243 (35)	250 (42)	256 (48)	262 (54)	268 (60)	274 (66)	279 (71)	284 (76)	288 (80)	293 (85)	297 (89)