79edt

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← 78edt 79edt 80edt →
Prime factorization 79 (prime)
Step size 24.0754¢ 
Octave 50\79edt (1203.77¢)
Consistency limit 10
Distinct consistency limit 8

Division of the third harmonic into 79 equal parts (79EDT) is related to 50 edo, but with the 3/1 rather than the 2/1 being just. The octave is about 3.7690 cents stretched and the step size is about 24.0754 cents. It is consistent to the 10-integer-limit.

Additionally, it is an 18-strong consistent circle of the interval 17/15.

Lookalikes: 50edo, 116ed5, 129ed6, 140ed7, 29edf

Intervals

Steps Cents Hekts Approximate ratios
0 0 0 1/1
1 24.1 16.5
2 48.2 32.9 35/34, 36/35, 37/36, 38/37
3 72.2 49.4 25/24
4 96.3 65.8 18/17, 19/18, 37/35
5 120.4 82.3 15/14
6 144.5 98.7 37/34, 38/35
7 168.5 115.2
8 192.6 131.6 19/17
9 216.7 148.1 17/15
10 240.8 164.6 31/27
11 264.8 181 7/6
12 288.9 197.5 13/11
13 313 213.9 6/5
14 337.1 230.4 17/14
15 361.1 246.8 37/30
16 385.2 263.3 5/4
17 409.3 279.7 19/15
18 433.4 296.2 9/7
19 457.4 312.7
20 481.5 329.1 29/22, 37/28
21 505.6 345.6
22 529.7 362 19/14, 34/25
23 553.7 378.5
24 577.8 394.9
25 601.9 411.4 17/12
26 626 427.8 33/23
27 650 444.3 35/24
28 674.1 460.8 28/19, 31/21
29 698.2 477.2
30 722.3 493.7 38/25
31 746.3 510.1 37/24
32 770.4 526.6 25/16
33 794.5 543 19/12
34 818.6 559.5
35 842.6 575.9
36 866.7 592.4 28/17
37 890.8 608.9
38 914.9 625.3 39/23
39 938.9 641.8 31/18
40 963 658.2
41 987.1 674.7 23/13
42 1011.2 691.1
43 1035.2 707.6
44 1059.3 724.1 35/19
45 1083.4 740.5 28/15
46 1107.5 757 36/19
47 1131.5 773.4
48 1155.6 789.9 37/19
49 1179.7 806.3
50 1203.8 822.8
51 1227.8 839.2
52 1251.9 855.7 35/17
53 1276 872.2 23/11
54 1300.1 888.6 36/17
55 1324.1 905.1
56 1348.2 921.5 37/17
57 1372.3 938
58 1396.4 954.4
59 1420.4 970.9
60 1444.5 987.3
61 1468.6 1003.8 7/3
62 1492.7 1020.3
63 1516.7 1036.7 12/5
64 1540.8 1053.2
65 1564.9 1069.6 37/15
66 1589 1086.1 5/2
67 1613.1 1102.5 33/13
68 1637.1 1119 18/7
69 1661.2 1135.4
70 1685.3 1151.9 37/14
71 1709.4 1168.4
72 1733.4 1184.8
73 1757.5 1201.3
74 1781.6 1217.7 14/5
75 1805.7 1234.2 17/6
76 1829.7 1250.6
77 1853.8 1267.1 35/12
78 1877.9 1283.5
79 1902 1300 3/1

Harmonics

79edt's representation of most primes is rather mediocre, however it has the property that many prime harmonics lie close to a quarter of the way or halfway between its steps, which is important in that 316edt, which quadruples it, is one of the strongest systems less than 1000 notes in the no-twos 19-limit, and among them has the best representation of primes beyond 19.

Approximation of prime harmonics in 79edt
Harmonic 2 3 5 7 11 13 17 19 23
Error Absolute (¢) +3.8 +0.0 +6.4 +1.7 -10.4 -10.7 +6.4 +6.5 -11.3
Relative (%) +15.7 +0.0 +26.7 +7.2 -43.0 -44.3 +26.7 +26.9 -47.0
Steps
(reduced)
50
(50)
79
(0)
116
(37)
140
(61)
172
(14)
184
(26)
204
(46)
212
(54)
225
(67)
Approximation of odd harmonics in 79edt
Harmonic 25 27 29 31 33 35 37 39 41 43 45
Error Absolute (¢) -11.2 +0.0 -3.3 +1.6 -10.4 +8.2 +8.3 -10.7 -0.9 -11.2 +6.4
Relative (%) -46.6 +0.0 -13.9 +6.6 -43.0 +33.9 +34.3 -44.3 -3.9 -46.4 +26.7
Steps
(reduced)
231
(73)
237
(0)
242
(5)
247
(10)
251
(14)
256
(19)
260
(23)
263
(26)
267
(30)
270
(33)
274
(37)