79edo

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← 78edo79edo80edo →
Prime factorization 79 (prime)
Step size 15.1899¢ 
Fifth 46\79 (698.734¢)
Semitones (A1:m2) 6:7 (91.14¢ : 106.3¢)
Consistency limit 5
Distinct consistency limit 5

79 equal divisions of the octave (abbreviated 79edo or 79ed2), also called 79-tone equal temperament (79tet) or 79 equal temperament (79et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 79 equal parts of about 15.2 ¢ each. Each step represents a frequency ratio of 21/79, or the 79th root of 2.

Theory

79edo works well as a no-7 13- or 17-limit tuning. It is in fact consistent in the no-7 13-odd-limit.

Using the patent val, it tempers out 3125/3072 in the 5-limit, 1728/1715, 4000/3969 and 4375/4374 in the 7-limit, 99/98, 243/242, 385/384, 1331/1323, and 4000/3993 in the 11-limit, and 169/168, 275/273, 325/324, 351/350, 640/637, 1188/1183, 1575/1573, 2080/2079, and 2200/2197 in the 13-limit. It provides the optimal patent val for the sentinel temperament.

The 79c val supports meantone with a tuning very close to 1/7-comma.

Odd harmonics

Approximation of odd harmonics in 79edo
Harmonic 3 5 7 9 11 13 15 17 19 21 23
Error Absolute (¢) -3.22 -6.57 +3.33 -6.44 -4.48 -5.08 +5.40 +1.37 +6.28 +0.11 -5.49
Relative (%) -21.2 -43.2 +21.9 -42.4 -29.5 -33.5 +35.6 +9.0 +41.4 +0.7 -36.1
Steps
(reduced)
125
(46)
183
(25)
222
(64)
250
(13)
273
(36)
292
(55)
309
(72)
323
(7)
336
(20)
347
(31)
357
(41)

Subsets and supersets

79edo is the 22nd prime edo, past 73edo and before 83edo.

Miscellany

79edo adequately represents the Decaononic way of playing, as 79edo misses 9/8 while having a near-perfect representation of 10/9 as 12\79. A maximal evenness variant of such a scale can be generated by naively stacking six 12edo diatonic majors and one Lydian tetrachord[clarification needed]. Since the final tetrachord does not have a 2nd degree, this results in 6 II's stretched over 6 + 7/12 octaves, which is just enough to make the log2 of the number to be equal to 10/9 [clarification needed]. From a regular temperament theory perspective, these scales are a part of the bluebirds temperament.

Intervals

Steps Cents Approximate Ratios Ups and Downs Notation
0 0 1/1 D
1 15.19 ^D, E♭♭
2 30.38 ^^D, v5E♭
3 45.57 36/35, 38/37 ^3D, v4E♭
4 60.759 29/28 ^4D, v3E♭
5 75.949 23/22, 24/23 ^5D, vvE♭
6 91.139 D♯, vE♭
7 106.329 17/16, 33/31 ^D♯, E♭
8 121.519 ^^D♯, v5E
9 136.709 13/12 ^3D♯, v4E
10 151.899 12/11, 35/32 ^4D♯, v3E
11 167.089 11/10 ^5D♯, vvE
12 182.278 10/9 D𝄪, vE
13 197.468 E
14 212.658 26/23, 35/31 ^E, F♭
15 227.848 ^^E, v5F
16 243.038 23/20 ^3E, v4F
17 258.228 36/31 ^4E, v3F
18 273.418 34/29 ^5E, vvF
19 288.608 13/11 E♯, vF
20 303.797 31/26 F
21 318.987 ^F, G♭♭
22 334.177 17/14 ^^F, v5G♭
23 349.367 11/9 ^3F, v4G♭
24 364.557 21/17 ^4F, v3G♭
25 379.747 ^5F, vvG♭
26 394.937 39/31 F♯, vG♭
27 410.127 33/26 ^F♯, G♭
28 425.316 23/18 ^^F♯, v5G
29 440.506 31/24 ^3F♯, v4G
30 455.696 13/10 ^4F♯, v3G
31 470.886 21/16, 38/29 ^5F♯, vvG
32 486.076 F𝄪, vG
33 501.266 4/3 G
34 516.456 27/20, 31/23, 35/26 ^G, A♭♭
35 531.646 19/14 ^^G, v5A♭
36 546.835 ^3G, v4A♭
37 562.025 18/13, 29/21 ^4G, v3A♭
38 577.215 ^5G, vvA♭
39 592.405 31/22 G♯, vA♭
40 607.595 ^G♯, A♭
41 622.785 33/23 ^^G♯, v5A
42 637.975 13/9 ^3G♯, v4A
43 653.165 35/24 ^4G♯, v3A
44 668.354 28/19 ^5G♯, vvA
45 683.544 G𝄪, vA
46 698.734 3/2 A
47 713.924 ^A, B♭♭
48 729.114 29/19, 32/21, 35/23 ^^A, v5B♭
49 744.304 20/13 ^3A, v4B♭
50 759.494 31/20 ^4A, v3B♭
51 774.684 36/23 ^5A, vvB♭
52 789.873 A♯, vB♭
53 805.063 35/22 ^A♯, B♭
54 820.253 ^^A♯, v5B
55 835.443 34/21 ^3A♯, v4B
56 850.633 18/11 ^4A♯, v3B
57 865.823 28/17, 33/20 ^5A♯, vvB
58 881.013 A𝄪, vB
59 896.203 B
60 911.392 22/13, 39/23 ^B, C♭
61 926.582 29/17 ^^B, v5C
62 941.772 31/18 ^3B, v4C
63 956.962 ^4B, v3C
64 972.152 ^5B, vvC
65 987.342 23/13 B♯, vC
66 1002.532 C
67 1017.722 9/5 ^C, D♭♭
68 1032.911 20/11 ^^C, v5D♭
69 1048.101 11/6 ^3C, v4D♭
70 1063.291 24/13 ^4C, v3D♭
71 1078.481 ^5C, vvD♭
72 1093.671 32/17 C♯, vD♭
73 1108.861 ^C♯, D♭
74 1124.051 23/12 ^^C♯, v5D
75 1139.241 ^3C♯, v4D
76 1154.43 35/18, 37/19, 39/20 ^4C♯, v3D
77 1169.62 ^5C♯, vvD
78 1184.81 C𝄪, vD
79 1200 2/1 D

Regular temperament properties

79edo supports the bluebirds temperament. It also supports oceanfront, meantone and sentinel.

Scales

Mos scales

  • Bluebirds[6, 7, 13, 20, 33…]
  • Meantone[7, 12, 19, 31…]
  • Oceanfront[7, 12, 17, 22, 27…]
  • Sentinel[5, 8, 11, 14, 17, 31…]

Others

  • Meantone Minor Hexatonic: 13 7 13 13 20 13 ((13, 20, 33, 46, 66, 79)\79)

Music

Francium
Silence and Secrecy (Julian Malerman)