76edo
| ← 75edo | 76edo | 77edo → |
Theory
| Harmonic | 3 | 5 | 7 | 9 | 11 | 13 | 15 | 17 | 19 | 21 | 23 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -7.22 | -7.37 | -5.67 | +1.35 | +1.31 | -3.69 | +1.20 | +5.57 | +2.49 | +2.90 | +3.30 |
| Relative (%) | -45.7 | -46.7 | -35.9 | +8.6 | +8.3 | -23.3 | +7.6 | +35.3 | +15.8 | +18.4 | +20.9 | |
| Steps (reduced) |
120 (44) |
176 (24) |
213 (61) |
241 (13) |
263 (35) |
281 (53) |
297 (69) |
311 (7) |
323 (19) |
334 (30) |
344 (40) | |
This tuning's 5-limit patent val is contorted in the 5-limit, reflecting the fact that 76 = 4 * 19. In the 7-limit it tempers out 2401/2400 as well as 81/80, and so supports squares temperament. In the 11-limit, it tempers out 245/242 and 385/384, and supports the 24&26 temperament. In the 13-limit, it tempers out 105/104, 144/143, 351/350 and 364/363. While the 44\76 = 11\19 fifth is already flat, the 43\76 fifth, even flatter, is an almost perfect approximation to the hornbostel temperament POTE fifth, whereas its sharp fifth, 45\76, makes for an excellent superpyth fifth. Hence you can do hornbostel/mavila, squares/meantone, and superpyth all with the same equal division.
Using non-patent vals, 76edo provides an excellent tuning for teff temperament, a low complexity, medium accuracy, and high limit (17 or 19) temperament.
Intervals
| # | Cents | Diatonic interval category |
|---|---|---|
| 0 | 0.0 | perfect unison |
| 1 | 15.8 | superunison |
| 2 | 31.6 | superunison |
| 3 | 47.4 | subminor second |
| 4 | 63.2 | subminor second |
| 5 | 78.9 | subminor second |
| 6 | 94.7 | minor second |
| 7 | 110.5 | minor second |
| 8 | 126.3 | supraminor second |
| 9 | 142.1 | neutral second |
| 10 | 157.9 | neutral second |
| 11 | 173.7 | submajor second |
| 12 | 189.5 | major second |
| 13 | 205.3 | major second |
| 14 | 221.1 | supermajor second |
| 15 | 236.8 | supermajor second |
| 16 | 252.6 | ultramajor second |
| 17 | 268.4 | subminor third |
| 18 | 284.2 | minor third |
| 19 | 300.0 | minor third |
| 20 | 315.8 | minor third |
| 21 | 331.6 | supraminor third |
| 22 | 347.4 | neutral third |
| 23 | 363.2 | submajor third |
| 24 | 378.9 | submajor third |
| 25 | 394.7 | major third |
| 26 | 410.5 | major third |
| 27 | 426.3 | supermajor third |
| 28 | 442.1 | ultramajor third |
| 29 | 457.9 | ultramajor third |
| 30 | 473.7 | subfourth |
| 31 | 489.5 | perfect fourth |
| 32 | 505.3 | perfect fourth |
| 33 | 521.1 | superfourth |
| 34 | 536.8 | superfourth |
| 35 | 552.6 | superfourth |
| 36 | 568.4 | low tritone |
| 37 | 584.2 | low tritone |
| 38 | 600.0 | high tritone |
| 39 | 615.8 | high tritone |
| 40 | 631.6 | high tritone |
| 41 | 647.4 | subfifth |
| 42 | 663.2 | subfifth |
| 43 | 678.9 | subfifth |
| 44 | 694.7 | perfect fifth |
| 45 | 710.5 | perfect fifth |
| 46 | 726.3 | superfifth |
| 47 | 742.1 | ultrafifth |
| 48 | 757.9 | ultrafifth |
| 49 | 773.7 | subminor sixth |
| 50 | 789.5 | minor sixth |
| 51 | 805.3 | minor sixth |
| 52 | 821.1 | supraminor sixth |
| 53 | 836.8 | supraminor sixth |
| 54 | 852.6 | neutral sixth |
| 55 | 868.4 | submajor sixth |
| 56 | 884.2 | major sixth |
| 57 | 900.0 | major sixth |
| 58 | 915.8 | major sixth |
| 59 | 931.6 | supermajor sixth |
| 60 | 947.4 | ultramajor sixth |
| 61 | 963.2 | subminor seventh |
| 62 | 978.9 | subminor seventh |
| 63 | 994.7 | minor seventh |
| 64 | 1010.5 | minor seventh |
| 65 | 1026.3 | supraminor seventh |
| 66 | 1042.1 | neutral seventh |
| 67 | 1057.9 | neutral seventh |
| 68 | 1073.7 | submajor seventh |
| 69 | 1089.5 | major seventh |
| 70 | 1105.3 | major seventh |
| 71 | 1121.1 | supermajor seventh |
| 72 | 1136.8 | supermajor seventh |
| 73 | 1152.6 | ultramajor seventh |
| 74 | 1168.4 | suboctave |
| 75 | 1184.2 | suboctave |
| 76 | 1200.0 | perfect octave |