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	Hekts	Approximate ratios
0	0	0	1/1
1	24.4	16.7
2	48.8	33.3	34/33, 35/34, 36/35, 37/36, 38/37
3	73.2	50	25/24
4	97.5	66.7	18/17, 37/35
5	121.9	83.3	15/14, 29/27
6	146.3	100	37/34
7	170.7	116.7	21/19
8	195.1	133.3	19/17, 28/25, 37/33
9	219.5	150	17/15, 25/22
10	243.8	166.7	38/33
11	268.2	183.3	7/6
12	292.6	200
13	317	216.7	6/5
14	341.4	233.3
15	365.8	250	21/17, 37/30
16	390.1	266.7
17	414.5	283.3	14/11, 33/26
18	438.9	300
19	463.3	316.7	17/13
20	487.7	333.3
21	512.1	350	35/26, 39/29
22	536.4	366.7	15/11
23	560.8	383.3	18/13, 29/21
24	585.2	400	7/5
25	609.6	416.7	27/19, 37/26
26	634	433.3	13/9, 36/25
27	658.4	450	19/13
28	682.8	466.7
29	707.1	483.3
30	731.5	500	29/19
31	755.9	516.7	17/11
32	780.3	533.3	11/7
33	804.7	550	35/22
34	829.1	566.7	21/13
35	853.4	583.3	18/11
36	877.8	600
37	902.2	616.7	37/22
38	926.6	633.3	29/17
39	951	650	26/15
40	975.4	666.7
41	999.7	683.3
42	1024.1	700	38/21
43	1048.5	716.7	11/6
44	1072.9	733.3	13/7
45	1097.3	750
46	1121.7	766.7	21/11
47	1146	783.3	33/17
48	1170.4	800
49	1194.8	816.7
50	1219.2	833.3
51	1243.6	850	39/19
52	1268	866.7	25/12, 27/13
53	1292.4	883.3	19/9
54	1316.7	900	15/7
55	1341.1	916.7	13/6
56	1365.5	933.3	11/5
57	1389.9	950	29/13, 38/17
58	1414.3	966.7	34/15
59	1438.7	983.3	39/17
60	1463	1000
61	1487.4	1016.7	26/11, 33/14
62	1511.8	1033.3
63	1536.2	1050	17/7
64	1560.6	1066.7	37/15
65	1585	1083.3	5/2
66	1609.3	1100	38/15
67	1633.7	1116.7	18/7
68	1658.1	1133.3
69	1682.5	1150	37/14
70	1706.9	1166.7
71	1731.3	1183.3	19/7
72	1755.7	1200
73	1780	1216.7	14/5
74	1804.4	1233.3	17/6
75	1828.8	1250
76	1853.2	1266.7	35/12
77	1877.6	1283.3
78	1902	1300	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)