78edt

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78edt

79edt →

Prime factorization	2 × 3 × 13
Step size	24.384¢
Octave	49\78edt (1194.82¢)
Consistency limit	7
Distinct consistency limit	7

78EDT is the equal division of the third harmonic into 78 parts of 24.3840 cents each, corresponding to 49.2125 edo. It has a distinct flat tendency, in the sense that if 3 is pure, 2 (octave), 5, 7, 11, 13, 17, and 19 are all flat. It is consistent to the no-twos 19-limit, tempering out 245/243 and 3125/3087 in the 7-limit; 1331/1323, 6655/6561, and 9375/9317 in the 11-limit; 275/273, 847/845, 1575/1573, and 2197/2187 in the 13-limit; 875/867 and 2025/2023 in the 17-limit; 325/323, 363/361, 665/663, 935/931, and 1547/1539 in the 19-limit (no-twos subgroup).

78EDT is related to 49 edo, but with octave compression of 5.1821 cents. Patent vals match through the 11-limit, tempering out 64/63, 100/99, 245/243, and 1331/1323. 78EDT tempers out 144/143, 196/195, 275/273, 325/324, 364/363, and 572/567 in the 13-limit; 120/119, 136/135, 154/153, 170/169, and 224/221 in the 17-limit; 96/95, 190/189, and 210/209 in the 19-limit (full integer limit).

Intervals

Steps	Cents	Approximate ratios
0	0	1/1
1	24.4
2	48.8	34/33, 35/34, 36/35, 37/36, 38/37
3	73.2	25/24
4	97.5	18/17, 37/35
5	121.9	15/14, 29/27
6	146.3	37/34
7	170.7	21/19
8	195.1	19/17, 28/25, 37/33
9	219.5	17/15, 25/22
10	243.8	38/33
11	268.2	7/6
12	292.6
13	317	6/5
14	341.4
15	365.8	21/17, 37/30
16	390.1
17	414.5	14/11, 33/26
18	438.9
19	463.3	17/13
20	487.7
21	512.1	35/26, 39/29
22	536.4	15/11
23	560.8	18/13, 29/21
24	585.2	7/5
25	609.6	27/19, 37/26
26	634	13/9, 36/25
27	658.4	19/13
28	682.8
29	707.1
30	731.5	29/19
31	755.9	17/11
32	780.3	11/7
33	804.7	35/22
34	829.1	21/13
35	853.4	18/11
36	877.8
37	902.2	37/22
38	926.6	29/17
39	951	26/15
40	975.4
41	999.7
42	1024.1	38/21
43	1048.5	11/6
44	1072.9	13/7
45	1097.3
46	1121.7	21/11
47	1146	33/17
48	1170.4
49	1194.8
50	1219.2
51	1243.6	39/19
52	1268	25/12, 27/13
53	1292.4	19/9
54	1316.7	15/7
55	1341.1	13/6
56	1365.5	11/5
57	1389.9	29/13, 38/17
58	1414.3	34/15
59	1438.7	39/17
60	1463
61	1487.4	26/11, 33/14
62	1511.8
63	1536.2	17/7
64	1560.6	37/15
65	1585	5/2
66	1609.3	38/15
67	1633.7	18/7
68	1658.1
69	1682.5	37/14
70	1706.9
71	1731.3	19/7
72	1755.7
73	1780	14/5
74	1804.4	17/6
75	1828.8
76	1853.2	35/12
77	1877.6
78	1902	3/1

Harmonics

Approximation of prime harmonics in 78edt

Harmonic		2	3	5	7	11	13	17	19	23	29	31
Error	Absolute (¢)	-5.2	+0.0	-6.5	-3.8	-6.0	-2.6	-3.8	-1.2	+9.4	-1.8	+4.7
	Relative (%)	-21.3	+0.0	-26.8	-15.7	-24.7	-10.8	-15.4	-5.1	+38.4	-7.3	+19.2
Steps (reduced)		49 (49)	78 (0)	114 (36)	138 (60)	170 (14)	182 (26)	201 (45)	209 (53)	223 (67)	239 (5)	244 (10)

Approximation of prime harmonics in 78edt

Harmonic		37	41	43	47	53	59	61	67	71	73	79
Error	Absolute (¢)	-9.0	+8.3	-1.0	-8.7	+2.8	-12.2	+3.3	+11.5	+8.7	+9.3	-5.5
	Relative (%)	-37.0	+34.1	-4.0	-35.5	+11.5	-50.0	+13.3	+47.2	+35.5	+38.3	-22.5
Steps (reduced)		256 (22)	264 (30)	267 (33)	273 (39)	282 (48)	289 (55)	292 (58)	299 (65)	303 (69)	305 (71)	310 (76)