Zeus
Zeus is the rank-3 temperament tempering out 121/120, 176/175, and 385/384. Notice 121/120 = (176/175)(385/384), it thus equates the septimal neutral second of 35/32 with both 11/10 and 12/11. That makes 11-limit harmony particularly efficient and deeply entangled with 7-limit harmony. The temperament is, in fact, one of the best ways to further temper on top of tempering out 121/120. That said, 121/120 is such a comma that, on tempering out, will neutralize the distinction between many otonal- and utonal-11 chords, so it might not fit those who wish to explore the subtlety of tones in the 11-limit.
It also has an obvious extension to the 13-limit tempering out 351/350 and 352/351.
See Porwell family #Zeus or Biyatismic clan #Zeus for technical data.
Interval lattice
11-limit zeus
13-limit zeus
Chords
Zeus enables essentially tempered chords of biyatismic, valinorsmic, and keenanismic.
Scales
Tuning spectrum
This spectrum assumes pure 2 and 7/5.
Gencom: [2 3 11/10; 121/120 176/175 351/350]
Gencom mapping: [⟨1 0 1 4 2 7], ⟨0 1 1 -1 1 -2], ⟨0 0 -2 3 -1 -1]]
| Eigenmonzo (Unchanged-interval) |
Fifth (¢) |
Major Third (¢) |
Comments |
|---|---|---|---|
| 12/11 | 685.337 | 384.062 | |
| 15/11 | 689.089 | 384.813 | |
| 5/4 | 696.593 | 386.314 | |
| 11/9 | 697.207 | 386.436 | |
| 14/13 | 700.880 | 387.171 | |
| 16/15 | 701.061 | 387.207 | |
| 15/13 | 701.179 | 387.231 | |
| 16/13 | 701.237 | 387.243 | |
| 13/12 | 701.449 | 387.285 | |
| 18/13 | 701.564 | 387.308 | |
| 4/3 | 701.955 | 387.386 | 7-, 9- and 15-odd-limit minimax |
| 10/9 | 702.551 | 387.505 | 11- and 13-odd-limit minimax |
| 6/5 | 703.296 | 387.654 | |
| 13/11 | 703.597 | 387.714 | |
| 11/8 | 713.034 | 389.602 | |
| 11/10 | 721.254 | 391.246 |
Music
- Cloudtop Reverie (2021) – zeus[7] in 99edo tuning