Leapday
- Not to be confused with calendar-based scales such as those in 293edo, 400edo, 353edo or Irvian mode.
Leapday is a regular temperament for the 7-, 11-, 13-, 17-, and 19-limit JI. It has a fifth generator of ~3/2 = 704.2¢, eight of them makes ~13/8, eleven of them makes ~11/8, fifteen of them makes ~7/4, twenty-one of them makes ~5/4 and twenty-four of them makes ~17/16. Equivalently, the fifth of leapday in size is ~2.3 cents sharp of 3/2, 13/8 is represented by an augmented fifth, 11/8 is represented by an augmented third, 7/4 is represented by a double-augmented fifth, 5/4 is represented by a triple-augmented unison, and 17/16 is represented by a negative triple-diminished third.
The temperament was named by Herman Miller in 2004[1][2].
See Hemifamity temperaments #Leapday for more technical data.
Tuning spectrum
Gencom: [2 3/2; 91/90 121/120 133/132 136/135 154/153 169/168]
Gencom mapping: [⟨1 1 -10 -6 -3 -1 -10 6], ⟨0 1 21 15 11 8 24 -3]]
| EDO generator |
eigenmonzo (unchanged-interval) |
generator (¢) |
comments |
|---|---|---|---|
| 19/16 | 700.829 | ||
| 24/19 | 701.110 | ||
| 19/18 | 701.279 | ||
| 4/3 | 701.955 | ||
| 24\41 | 702.439 | ||
| 15/14 | 702.778 | ||
| 7/5 | 702.915 | ||
| 21/20 | 703.107 | ||
| 15/11 | 703.359 | ||
| 15/13 | 703.410 | ||
| 17\29 | 703.448 | ||
| 11/10 | 703.500 | ||
| 13/10 | 703.522 | ||
| 13/11 | 703.597 | ||
| 19/15 | 703.630 | ||
| 20/19 | 703.700 | ||
| 26/21 | 703.782 | ||
| 22/19 | 703.843 | ||
| 21/19 | 703.856 | ||
| 22/21 | 703.893 | ||
| 26/19 | 703.910 | ||
| 19/14 | 703.962 | ||
| 19/17 | 703.979 | 19- and 21-odd-limit minimax | |
| 44\75 | 704.000 | ||
| 16/15 | 704.012 | ||
| 17/14 | 704.014 | ||
| 17/13 | 704.027 | ||
| 14/13 | 704.043 | ||
| 5/4 | 704.110 | 5-odd-limit minimax | |
| 22/17 | 704.126 | ||
| 71\121 | 704.132 | ||
| 6/5 | 704.218 | 7-, 15- and 17-odd-limit minimax | |
| 21/17 | 704.272 | ||
| 10/9 | 704.337 | 9-, 11- and 13-odd-limit minimax | |
| 27\46 | 704.348 | ||
| 17/16 | 704.373 | ||
| 14/11 | 704.377 | ||
| 21/16 | 704.424 | ||
| 24/17 | 704.478 | ||
| 8/7 | 704.588 | ||
| 18/17 | 704.593 | ||
| 11/8 | 704.665 | ||
| 37\63 | 704.762 | ||
| 7/6 | 704.776 | ||
| 12/11 | 704.936 | ||
| 9/7 | 704.994 | ||
| 16/13 | 705.066 | ||
| 11/9 | 705.268 | ||
| 13/12 | 705.510 | ||
| 10\17 | 705.882 | ||
| 18/13 | 706.103 | ||
| 20/17 | 706.214 | ||
| 17/15 | 708.343 |