118th-octave temperaments
118edo is the 17th zeta peak edo, and it is accurate for harmonics 3 and 5, so various 118th-octave temperaments naturally occur through temperament merging of its supersets.
Parakleischis
118edo and its multiples are members of both parakleismic and schismic, and from this it derives its name.
Subgroup: 2.3.5.7
Comma list: 32805/32768, 1224440064/1220703125
Mapping: [⟨118 187 274 0], ⟨0 0 0 1]]
Mapping generators: ~15625/15552, ~7
Optimal tuning (POTE): ~7/4 = 968.7235
Optimal ET sequence: 118, 236, 354, 472, 2242, 2714b, 3186b, 3658b
Badness: 0.145166
11-limit
Subgroup: 2.3.5.7.11
Comma list: 9801/9800, 32805/32768, 137781/137500
Mapping: [⟨118 187 274 0 77], ⟨0 0 0 1 1]]
Optimal tuning (POTE): ~7/4 = 968.5117
Optimal ET sequence: 118, 354, 472
Badness: 0.049316
Centenniamajor
Named after the fact that 18 is the age of majority in most countries, and 100 (centennial) + 18 (major) = 118.
Subgroup: 2.3.5.7.11
Comma list: 32805/32768, 151263/151250, 1224440064/1220703125
Mapping: [⟨118 187 274 0 -420], ⟨0 0 0 2 5]]
Mapping generators: ~15625/15552, ~405504/153125
Optimal tuning (CTE): ~202752/153125 = 484.4837
Optimal ET sequence: 354, 944e, 1298
Badness: 0.357
13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 1716/1715, 32805/32768, 34398/34375, 384912/384475
Mapping: [⟨118 187 274 0 -420 271], ⟨0 0 0 2 5 1]]
Optimal tuning (CTE): ~8125/6144 = 484.4867
Optimal ET sequence: 354, 944e, 1298
Badness: 0.122
Oganesson
Named after the 118th element. In the 13-limit, the period corresponds to 169/168, and in the 17-limit, it corresponds also to 170/169, meaning that 28561/28560 is tempered out. As opposed to being an extension of parakleischis, this has the generator that splits the third harmonic into three equal parts.
In the 7-limit and 11-limit, the period corresponds to bronzisma.
Subgroup: 2.3.5.7
Comma list: [30 10 -27 6⟩, [77 -20 -5 -12⟩
Mapping: [⟨118 0 274 643], ⟨0 3 0 -5]]
Mapping generators: ~2097152/2083725, ~1953125/1354752
Optimal tuning (CTE): ~1953125/1354752 = 634.0068
Optimal ET sequence: 354, 2360, 2714, 3068, 3442, 3776, 7198cd, 10974bccdd
Badness: 2.66
11-limit
Subgroup: 2.3.5.7.11
Comma list: 9801/9800, [13 -1 4 -16 7⟩, [55 -7 -15 -2 -1⟩
Mapping: [⟨118 0 274 643 1094], ⟨0 3 0 -5 -11]]
Optimal tuning (CTE): ~1953125/1354752 = 634.0085
Optimal ET sequence: 354, 3068e, 3442, 3776, 11682ccdde
Badness: 0.568
13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 4096/4095, 9801/9800, 537403776/537109375, 453874312332/453857421875
Mapping: [⟨118 0 274 643 1094 499], ⟨0 3 0 -5 -11 -1]]
Mapping generators: ~169/168, ~1124864/779625
Optimal tuning (CTE): ~1124864/779625 = 634.0087
Optimal ET sequence: 354, 3068e, 3422, 3776
Badness: 0.172
17-limit
Subgroup: 2.3.5.7.11.13.17
Comma list: 4096/4095, 9801/9800, 34391/34375, 361250/361179, 562432/562275
Mapping: [⟨118 0 274 643 1094 499 607], ⟨0 3 0 -5 -11 -1 2]]
Mapping generators: ~170/169, ~238/165
Optimal tuning (CTE): ~238/165 = 634.0080
Optimal ET sequence: 354, 3068e, 3422, 3776
Badness: 0.105