60th-octave temperaments

60edo is a highly composite EDO, and some its multiples are notable for their consistency limits, such as 2460edo, which is a zeta edo.

Minutes

Defined as the 2460 & 4320 temperament, starting with the 13-limit. Named "minutes" for period-60, since there's 60 minutes in an hour. In light of 12 being a divisor of 60, minutes tempers out the Kirnberger's atom, and in the limits below 13, it's a contorted atomic temperament.

Subgroup: 2.3.5.7.11.13

Comma list: 9801/9800, 250047/250000, 371293/371250, 184549376/184528125

Mapping: [⟨60 60 385 730 1085 573], ⟨0 1 7 -16 -25 -10]]

Mapping generators: ~2704/2673, ~3/2

Optimal tuning (CTE): ~3/2 = 701.948

Vals: 600e, 1860, 2460, 3060de, 3720de, 4320, 4920, 6180de, 6780, 7380e,

17-limit

Subgroup: 2.3.5.7.11.13.17

Comma list: 9801/9800, 12376/12375, 28561/28560, 250047/250000, 253755392/253746675

Mapping: [⟨60 60 385 730 1085 573 877], ⟨0 1 7 -16 -25 -10 -18]]

Mapping generators: ~3520/3213, ~3/2

Optimal tuning (CTE): ~3/2 = 701.948

19-limit

Subgroup: 2.3.5.7.11.13.17.19

Comma list: 9801/9800, 12376/12375, 27456/27455, 250047/250000, 401408/401375, 1549184/1549125

Mapping: [⟨60 60 385 730 1085 573 877 -61], ⟨0 1 7 -16 -25 -10 -18 9]]

Mapping generators: ~3520/3213, ~3/2

Optimal tuning (CTE): ~3/2 = 701.948

Neodymium

Starts with the 17-limit since it is contorted in 13-limit and below, can be expressed as as 1920 & 4380 or 1920 & 2460.

Subgroup: 2.3.5.7.11.13.17

Comma list: 9801/9800, 123201/123200, 250047/250000, 31213/31212, 1990656/1990625

Mapping: [⟨60 4 30 132 244 386 391], ⟨0 5 6 2 -2 -9 -8]

Mapping generators: ~612/605, ~216/175

Optimal tuning (CTE): ~216/175 = 364.387

Vals: 540, 1380, 1920, 2460, 3000, 3840, 4380, 4920, 6300, 6840e

Neodymium magnet

Defined just as neodymium in 1920 & 4380, except adds a mapping for 29 and 43 via the fact that 87/86 is very close to 1/60th of the octave. Comma which closes a stack of 60 87/86's at the octave, is named magnetisma by Eliora, and thus the extension is called "neodymium magnet". Defined starting with 2.3.5.29.43 all the way into the 2.3.5.7.11.13.17.19.23.29.43 subgroup, and unlike plain neodymium, addition of .29.43 harmonics saves it from contorsion.

Subgroup: 2.3.5.29.43

Comma list: 46235367/46225000, [-3 13 -5 1 -2⟩, [29 20 -35 2 2⟩

Sval mapping: ⟨60 4 30 -164 -221], ⟨0 5 6 25 30]

Sval mapping generators: ~87/86, ~7533637632/6103515625

Optimal tuning (CTE): ~7533637632/6103515625 = 364.385

Vals: 540jn, 1380jn, 1920, 2460, 3000jjnn, 3840jn, 4920jn 4380, 6300, 6840

2.3.5.7.29.43 subgroup

Subgroup: 2.3.5.7.29.43

Comma list: 250047/250000, 6890625/6889472, 634230/634207, 104487018125/104485552128

Sval mapping: ⟨60 4 30 132 -164 -221], ⟨0 5 6 2 25 30]

Sval mapping generators: ~87/86, ~216/175

Optimal tuning (CTE): ~216/175 = 364.385

2.3.5.7.11.29.43 subgroup

Subgroup: 2.3.5.7.11.29.43

Comma list: 7425/7424, 9801/9800, 250047/250000, 2278125/2277968, 10320758525/10319560704

Sval mapping: ⟨60 4 30 132 244 -164 -221], ⟨0 5 6 2 -2 25 30]

Sval mapping generators: ~87/86, ~216/175

Optimal tuning (CTE): ~216/175 = 364.385