79edo
| ← 78edo | 79edo | 80edo → |
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 to the no-7 13-odd-limit, even though it is a zeta valley edo (notably, it is the last one until 5941edo).
Regular temperament properties
79edo supports the bluebirds temperament. It also supports oceanfront and sentinel. Its alternate 79c val supports meantone in the 5-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.
79edo's fifth is very close to 1/7-comma meantone, but 79edo does not support meantone in its patent val. This is because 79edo's fifth is very close to 12edo and stacking 4 fifths upwards results in a sharp approximation of 5/4 which is not the best approximation. The best 5/4 is actually reached by stacking a whopping 16 fifths up (a doubly-augmented second), which corresponds to the python temperament. On the other hand, the 79c val which uses the second-best approximation of 5/4 and thus supports meantone.
Odd harmonics
| 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 | 15.2 | ^D, E♭♭ | |
| 2 | 30.4 | ^^D, ^E♭♭ | |
| 3 | 45.6 | 36/35, 38/37 | ^3D, ^^E♭♭ |
| 4 | 60.8 | 29/28 | vvD♯, v3E♭ |
| 5 | 75.9 | 23/22, 24/23 | vD♯, vvE♭ |
| 6 | 91.1 | D♯, vE♭ | |
| 7 | 106.3 | 17/16, 33/31 | ^D♯, E♭ |
| 8 | 121.5 | ^^D♯, ^E♭ | |
| 9 | 136.7 | 13/12 | ^3D♯, ^^E♭ |
| 10 | 151.9 | 12/11, 35/32 | vvD𝄪, v3E |
| 11 | 167.1 | 11/10 | vD𝄪, vvE |
| 12 | 182.3 | 10/9 | D𝄪, vE |
| 13 | 197.5 | E | |
| 14 | 212.7 | 26/23, 35/31 | ^E, F♭ |
| 15 | 227.8 | ^^E, ^F♭ | |
| 16 | 243 | 23/20 | ^3E, ^^F♭ |
| 17 | 258.2 | 36/31 | vvE♯, v3F |
| 18 | 273.4 | 34/29 | vE♯, vvF |
| 19 | 288.6 | 13/11 | E♯, vF |
| 20 | 303.8 | 31/26 | F |
| 21 | 319 | ^F, G♭♭ | |
| 22 | 334.2 | 17/14 | ^^F, ^G♭♭ |
| 23 | 349.4 | 11/9 | ^3F, ^^G♭♭ |
| 24 | 364.6 | 21/17 | vvF♯, v3G♭ |
| 25 | 379.7 | vF♯, vvG♭ | |
| 26 | 394.9 | 39/31 | F♯, vG♭ |
| 27 | 410.1 | 33/26 | ^F♯, G♭ |
| 28 | 425.3 | 23/18 | ^^F♯, ^G♭ |
| 29 | 440.5 | 31/24 | ^3F♯, ^^G♭ |
| 30 | 455.7 | 13/10 | vvF𝄪, v3G |
| 31 | 470.9 | 21/16, 38/29 | vF𝄪, vvG |
| 32 | 486.1 | F𝄪, vG | |
| 33 | 501.3 | 4/3 | G |
| 34 | 516.5 | 27/20, 31/23, 35/26 | ^G, A♭♭ |
| 35 | 531.6 | 19/14 | ^^G, ^A♭♭ |
| 36 | 546.8 | ^3G, ^^A♭♭ | |
| 37 | 562 | 18/13, 29/21 | vvG♯, v3A♭ |
| 38 | 577.2 | vG♯, vvA♭ | |
| 39 | 592.4 | 31/22 | G♯, vA♭ |
| 40 | 607.6 | ^G♯, A♭ | |
| 41 | 622.8 | 33/23 | ^^G♯, ^A♭ |
| 42 | 638 | 13/9 | ^3G♯, ^^A♭ |
| 43 | 653.2 | 35/24 | vvG𝄪, v3A |
| 44 | 668.4 | 28/19 | vG𝄪, vvA |
| 45 | 683.5 | G𝄪, vA | |
| 46 | 698.7 | 3/2 | A |
| 47 | 713.9 | ^A, B♭♭ | |
| 48 | 729.1 | 29/19, 32/21, 35/23 | ^^A, ^B♭♭ |
| 49 | 744.3 | 20/13 | ^3A, ^^B♭♭ |
| 50 | 759.5 | 31/20 | vvA♯, v3B♭ |
| 51 | 774.7 | 36/23 | vA♯, vvB♭ |
| 52 | 789.9 | A♯, vB♭ | |
| 53 | 805.1 | 35/22 | ^A♯, B♭ |
| 54 | 820.3 | ^^A♯, ^B♭ | |
| 55 | 835.4 | 34/21 | ^3A♯, ^^B♭ |
| 56 | 850.6 | 18/11 | vvA𝄪, v3B |
| 57 | 865.8 | 28/17, 33/20 | vA𝄪, vvB |
| 58 | 881 | A𝄪, vB | |
| 59 | 896.2 | B | |
| 60 | 911.4 | 22/13, 39/23 | ^B, C♭ |
| 61 | 926.6 | 29/17 | ^^B, ^C♭ |
| 62 | 941.8 | 31/18 | ^3B, ^^C♭ |
| 63 | 957 | vvB♯, v3C | |
| 64 | 972.2 | vB♯, vvC | |
| 65 | 987.3 | 23/13 | B♯, vC |
| 66 | 1002.5 | C | |
| 67 | 1017.7 | 9/5 | ^C, D♭♭ |
| 68 | 1032.9 | 20/11 | ^^C, ^D♭♭ |
| 69 | 1048.1 | 11/6 | ^3C, ^^D♭♭ |
| 70 | 1063.3 | 24/13 | vvC♯, v3D♭ |
| 71 | 1078.5 | vC♯, vvD♭ | |
| 72 | 1093.7 | 32/17 | C♯, vD♭ |
| 73 | 1108.9 | ^C♯, D♭ | |
| 74 | 1124.1 | 23/12 | ^^C♯, ^D♭ |
| 75 | 1139.2 | ^3C♯, ^^D♭ | |
| 76 | 1154.4 | 35/18, 37/19, 39/20 | vvC𝄪, v3D |
| 77 | 1169.6 | vC𝄪, vvD | |
| 78 | 1184.8 | C𝄪, vD | |
| 79 | 1200 | 2/1 | D |
Scales
Mos scales
- Bluebirds[6, 7, 13, 20, 33…]
- Meantone[7, 12, 19, 31…]
- Oceanfront[7, 12, 17, 22, 27…]
- Subsets of the above: see oceanfront scales
- Sentinel[5, 8, 11, 14, 17, 31…]
Others
- Meantone Minor Hexatonic: 13 7 13 13 20 13 ((13, 20, 33, 46, 66, 79)\79)
- 180rotator's 9-tone 33\79 scale: 7 13 7 6 7 13 7 6 7 6
Instruments
Lumatone
Skip fretting
Skip fretting system 79 7 19 is a skip fretting system for 79edo. All examples are for 5-string bass.
- Harmonics
1/1: string 2 open
2/1: string 1 fret 14
3/2: string 5 fret 21
5/4: string 5 fret 18
7/4: string 5 fret 2
11/8: string 4 fret 11
13/8: string 5 fret 11
17/16: string 2 fret 1
19/16: string 5 fret 6
Music
Modern renderings
- Rusino
- Looping the Rooms (2025) — microtonal cover in 79edo by Bryan Deister (2026)
21st century
- microtonal improvisation in 79edo (2025)
- 79edo groove (2026)
- Gold (2022)
- Silence and Secrecy (Julian Malerman)