Supermatertismic temperaments

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Supermatertismic rank-two temperaments temper out the supermatertismic comma, 52734375/52706752 = [-6 3 9 -7 (lasepru-atritriyo), the amount by which a stack of one 5/4, three 16/15s and seven 7/5s falls short of four octaves.

Temperaments dicussed elsewhere include:

Vydubychi

Subgroup: 2.3.5.7

Comma list: 52734375/52706752, 2199023255552/2197176384375

Mapping: [1 28 -53 -57], 0 -53 111 120]]

Optimal tuning (CTE): ~2 = 1\1, ~10125/7168 = 598.0747

Optimal ET sequence311, 624, 935, 4986d, 5921d, 6856d, 7791bd, 8726bdd, 9661bdd

Badness: 0.156974

11-limit

Subgroup: 2.3.5.7.11

Comma list: 131072/130977, 151263/151250, 161280/161051

Mapping: [1 28 -53 -57 -9], 0 -53 111 120 25]]

Optimal tuning (CTE): ~2 = 1\1, ~847/600 = 598.0745

Optimal ET sequence: 311, 624, 935, 2181e, 3116ee

Badness: 0.066481

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 2080/2079, 4096/4095, 91125/91091, 151263/151250

Mapping: [1 28 -53 -57 -9 66], 0 -53 111 120 25 -125]]

Optimal tuning (CTE): ~2 = 1\1, ~572/405 = 598.0747

Optimal ET sequence: 311, 624, 935

Badness: 0.033925

17-limit

Subgroup: 2.3.5.7.11.13.17

Comma list: 2058/2057, 2080/2079, 2500/2499, 4096/4095, 11016/11011

Mapping: [1 28 -53 -57 -9 66 -124], 0 -53 111 120 25 -125 257]]

Optimal tuning (CTE): ~2 = 1\1, ~544/385 = 598.0744

Optimal ET sequence: 311, 624, 935, 2181e

Badness: 0.023780

19-limit

Subgroup: 2.3.5.7.11.13.17.19

Comma list: 2058/2057, 2080/2079, 2432/2431, 2500/2499, 3136/3135, 11016/11011

Mapping: [1 28 -53 -57 -9 66 -124 -74], 0 -53 111 120 25 -125 257 157]]

Optimal tuning (CTE): ~2 = 1\1, ~171/121 = 598.0742

Optimal ET sequence: 311, 624, 935, 1246e, 2181e

Badness: 0.015527

23-limit

Subgroup: 2.3.5.7.11.13.17.19.23

Comma list: 2025/2024, 2058/2057, 2080/2079, 2432/2431, 2500/2499, 3060/3059, 3520/3519

Mapping: [1 28 -53 -57 -9 66 -124 -74 12], 0 -53 111 120 25 -125 257 157 -15]]

Optimal tuning (CTE): ~2 = 1\1, ~171/121 = 598.0743

Optimal ET sequence: 311, 624, 935, 1246ei, 2181eii

Badness: 0.012821