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	3
Distinct consistency limit	3

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.

Theory

104edt has a terrible 2, 5, and 6; a reasonable 4, 7, and 12; a good 8; and a stellar 10 and 11. This means that chords such as 1:3:10 (a very open major triad) sound very good.

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)

Intervals

Steps	Cents	Hekts	Approximate ratios
0	0	0	1/1
1	18.3	12.5
2	36.6	25
3	54.9	37.5	31/30
4	73.2	50
5	91.4	62.5	19/18, 39/37
6	109.7	75	33/31
7	128	87.5	14/13
8	146.3	100	37/34
9	164.6	112.5	11/10
10	182.9	125	10/9
11	201.2	137.5	46/41
12	219.5	150	42/37
13	237.7	162.5	31/27, 39/34
14	256	175	22/19
15	274.3	187.5	34/29
16	292.6	200
17	310.9	212.5
18	329.2	225	23/19
19	347.5	237.5	11/9
20	365.8	250	21/17
21	384	262.5
22	402.3	275	29/23
23	420.6	287.5	37/29
24	438.9	300
25	457.2	312.5	43/33
26	475.5	325
27	493.8	337.5
28	512.1	350	39/29
29	530.4	362.5	19/14
30	548.6	375
31	566.9	387.5	43/31
32	585.2	400
33	603.5	412.5
34	621.8	425	43/30
35	640.1	437.5	42/29
36	658.4	450	19/13, 41/28
37	676.7	462.5	34/23
38	694.9	475
39	713.2	487.5
40	731.5	500	29/19
41	749.8	512.5
42	768.1	525
43	786.4	537.5	41/26
44	804.7	550	43/27
45	823	562.5	37/23
46	841.2	575
47	859.5	587.5	23/14
48	877.8	600
49	896.1	612.5
50	914.4	625	39/23
51	932.7	637.5
52	951	650
53	969.3	662.5
54	987.6	675	23/13
55	1005.8	687.5	34/19
56	1024.1	700
57	1042.4	712.5	31/17, 42/23
58	1060.7	725
59	1079	737.5	41/22
60	1097.3	750
61	1115.6	762.5
62	1133.9	775
63	1152.1	787.5	37/19
64	1170.4	800
65	1188.7	812.5
66	1207	825
67	1225.3	837.5
68	1243.6	850	39/19, 41/20
69	1261.9	862.5	29/14
70	1280.2	875
71	1298.5	887.5
72	1316.7	900
73	1335	912.5
74	1353.3	925
75	1371.6	937.5	42/19
76	1389.9	950	29/13
77	1408.2	962.5
78	1426.5	975	41/18
79	1444.8	987.5
80	1463	1000
81	1481.3	1012.5
82	1499.6	1025
83	1517.9	1037.5
84	1536.2	1050	17/7
85	1554.5	1062.5	27/11
86	1572.8	1075
87	1591.1	1087.5
88	1609.3	1100
89	1627.6	1112.5
90	1645.9	1125
91	1664.2	1137.5	34/13
92	1682.5	1150	37/14
93	1700.8	1162.5
94	1719.1	1175	27/10
95	1737.4	1187.5	30/11
96	1755.7	1200
97	1773.9	1212.5	39/14
98	1792.2	1225	31/11
99	1810.5	1237.5	37/13
100	1828.8	1250
101	1847.1	1262.5
102	1865.4	1275
103	1883.7	1287.5
104	1902	1300	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)