Zeus

Zeus is a rank-3 temperament generated by an octave, a fifth, and a neutral second which stands in for both undecimal neutral seconds of 11/10 and 12/11 as well as the septimal neutral second of 35/32, tempering out 121/120, 176/175, and 385/384. Notice 121/120 = (176/175)⋅(385/384). That makes 11-limit harmony particularly efficient and deeply entangled with 7-limit harmony. This 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 Biyatismic clan #Zeus for technical data.

Interval lattice

• 
  11-limit zeus
• 
  13-limit zeus

Chords and harmony

Zeus enables essentially tempered chords of biyatismic, valinorsmic, keenanismic, and zeus. In the 13-limit, it enables chords of ratwolfsmic, major minthmic, and catadictmic.

Scales

• Zeus1
• Zeus2
• Zeus3
• Zeus4
• Zeus5
• Zeus6
• Zeus7
• Zeus7tri
• Zeus8tri
• Genus1155zeus

Tunings

Tuning spectrum

This spectrum assumes pure 2 and 7/5.

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

Mundoworld

• Cloudtop Reverie (2021) – in Zeus[7], 99edo tuning