Luna and hemithirds: Difference between revisions
m 56edo is rather obscure and less accurate than 31; 87edo is better |
Cleanup on infobox |
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{{Infobox | {{Infobox regtemp | ||
| Title = Hemithirds | | Title = Hemithirds | ||
| Subgroups = 2.3.5.7 | | Subgroups = 2.3.5.7 | ||
| Comma basis = [[1029/1024]], [[3136/3125]] (2.3.5.7) | | Comma basis = [[1029/1024]], [[3136/3125]] (2.3.5.7) | ||
| Edo join 1 = 31 | Edo join 2 = 87 | | Edo join 1 = 31 | Edo join 2 = 87 | ||
| | | Mapping = 1; -15 2 5 | ||
| Generators = 28/25 | Generators tuning = 193.2 | Optimization method = CWE | |||
| MOS scales = [[1L 5s]], [[6L 1s]], [[6L 7s]], [[6L 13s]], [[6L 19s]], [[25L 6s]] | | MOS scales = [[1L 5s]], [[6L 1s]], [[6L 7s]], [[6L 13s]], [[6L 19s]], [[25L 6s]] | ||
| Pergen = (P8, ccP4/15) | | Pergen = (P8, ccP4/15) | ||
| Color name = Latrizo & Zozoquinguti | | Color name = Latrizo & Zozoquinguti | ||
| Odd limit 1 = 7 | Mistuning 1 = 2.5 | Complexity 1 = 56 | | Odd limit 1 = 7 | Mistuning 1 = 2.5 | Complexity 1 = 56 | ||
| Odd limit 2 = | | Odd limit 2 = 7-limit 25 | Mistuning 2 = 3.6 | Complexity 2 = 87 | ||
}} | }} | ||
The [[7-limit]] '''hemithirds''' temperament functions as a strong extension of [[didacus]], the 2.5.7 subgroup temperament, which is defined by tempering out [[3136/3125]] such that two of its generators (hemithird, [[~]][[28/25]], around 193.2 [[cent]]s) reach ~[[5/4]], three reach ~[[7/5]], and therefore five reach ~[[7/4]]. Hemithirds extends didacus in the range between [[25edo]] and [[31edo]] tuning, by tempering out [[1029/1024]], such that three intervals of ~[[8/7]] reach ~[[3/2]], therefore finding ~[[4/3]] after fifteen generators in total. The canonical extension to the [[13-limit]] tempers out [[385/384]] and [[441/440]] to reach ~[[55/32]] at four ~8/7s and therefore ~[[11/8]] at 22 generators down, and then [[196/195]] (along with [[352/351]], [[625/624]], and [[1001/1000]]) to interpret the generator as ~[[143/128]] and find ~[[13/8]] at 23 generators up. | The [[7-limit]] '''hemithirds''' temperament functions as a strong extension of [[didacus]], the 2.5.7 subgroup temperament, which is defined by tempering out [[3136/3125]] such that two of its generators (hemithird, [[~]][[28/25]], around 193.2 [[cent]]s) reach ~[[5/4]], three reach ~[[7/5]], and therefore five reach ~[[7/4]]. Hemithirds extends didacus in the range between [[25edo]] and [[31edo]] tuning, by tempering out [[1029/1024]], such that three intervals of ~[[8/7]] reach ~[[3/2]], therefore finding ~[[4/3]] after fifteen generators in total. The canonical extension to the [[13-limit]] tempers out [[385/384]] and [[441/440]] to reach ~[[55/32]] at four ~8/7s and therefore ~[[11/8]] at 22 generators down, and then [[196/195]] (along with [[352/351]], [[625/624]], and [[1001/1000]]) to interpret the generator as ~[[143/128]] and find ~[[13/8]] at 23 generators up. | ||