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	18.3
2	36.6
3	54.9	31/30
4	73.2
5	91.4	19/18, 39/37
6	109.7	33/31
7	128	14/13
8	146.3	37/34
9	164.6	11/10
10	182.9	10/9
11	201.2	46/41
12	219.5	42/37
13	237.7	31/27, 39/34
14	256	22/19
15	274.3	34/29
16	292.6
17	310.9
18	329.2	23/19
19	347.5	11/9
20	365.8	21/17
21	384
22	402.3	29/23
23	420.6	37/29
24	438.9
25	457.2	43/33
26	475.5
27	493.8
28	512.1	39/29
29	530.4	19/14
30	548.6
31	566.9	43/31
32	585.2
33	603.5
34	621.8	43/30
35	640.1	42/29
36	658.4	19/13, 41/28
37	676.7	34/23
38	694.9
39	713.2
40	731.5	29/19
41	749.8
42	768.1
43	786.4	41/26
44	804.7	43/27
45	823	37/23
46	841.2
47	859.5	23/14
48	877.8
49	896.1
50	914.4	39/23
51	932.7
52	951
53	969.3
54	987.6	23/13
55	1005.8	34/19
56	1024.1
57	1042.4	31/17, 42/23
58	1060.7
59	1079	41/22
60	1097.3
61	1115.6
62	1133.9
63	1152.1	37/19
64	1170.4
65	1188.7
66	1207
67	1225.3
68	1243.6	39/19, 41/20
69	1261.9	29/14
70	1280.2
71	1298.5
72	1316.7
73	1335
74	1353.3
75	1371.6	42/19
76	1389.9	29/13
77	1408.2
78	1426.5	41/18
79	1444.8
80	1463
81	1481.3
82	1499.6
83	1517.9
84	1536.2	17/7
85	1554.5	27/11
86	1572.8
87	1591.1
88	1609.3
89	1627.6
90	1645.9
91	1664.2	34/13
92	1682.5	37/14
93	1700.8
94	1719.1	27/10
95	1737.4	30/11
96	1755.7
97	1773.9	39/14
98	1792.2	31/11
99	1810.5	37/13
100	1828.8
101	1847.1
102	1865.4
103	1883.7
104	1902	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)