80th-octave temperaments: Difference between revisions
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{{Technical data page}} | |||
{{Infobox fractional-octave|80}} | |||
80edo is extremely accurate for the 17th harmonic, a relationship which is seen in | This page describes 80th-octave temperaments. [[80edo]] is extremely accurate for the [[17/1|17th harmonic]], a relationship which is so far seen in all documented temperaments on this page. In addition, it is the first equal division to be consistent in the [[19-limit]]. | ||
Temperaments discussed elsewhere include | |||
'' | |||
* ''Octogintic'', → [[Parkleiness temperaments#Octogintic|Parkleiness temperaments]] | |||
== Tetraicosic == | == Tetraicosic == | ||
Tetraicosic is described as | Tetraicosic is described as 1600 & 2320, and named after the fact that 4 × 20 = 80. | ||
[[Subgroup]]: 2.3.5.7 | [[Subgroup]]: 2.3.5.7 | ||
| Line 48: | Line 50: | ||
Badness: 0.0741 | Badness: 0.0741 | ||
=== 17-limit === | |||
Subgroup 2.3.5.7.11.13.17 | |||
Comma list: 9801/9800, 14400/14399, 373527/373490, 1812608/1812525, 4685824/4685625 | |||
Mapping: [{{val| 80 1 343 -27 434 13 327}}, {{val| 0 4 -5 8 -5 9 0}}] | |||
Optimal tuning (CTE): ~130/99 = 471.7... | |||
{{Optimal ET sequence|legend=1| 720, 1600, 2320, 3920 }} | |||
=== 19-limit === | |||
Subgroup: 2.3.5.7.11.13.17.19 | |||
Comma list: 9801/9800, 10830/10839, 12636/12635, 23409/23408, 373527/373490, 32133332/32131125 | |||
Mapping: [{{val| 80 1 343 -27 434 13 327 -69}}, {{val| 0 4 -5 8 -5 9 0 13}}] | |||
Optimal tuning (CTE): ~67473/51376 = 471.732 | |||
{{Optimal ET sequence|legend=1| 720, 1600, 2320, 3920 }} | |||
== Mercury == | == Mercury == | ||
Named after the 80th element, defined as the 320 & 2000 temperament. 7 | Named after the 80th element, defined as the 320 & 2000 temperament. | ||
=== 13-limit === | |||
Subgroup: 2.3.5.7.11.13 | |||
Comma list: 9801/9800, 67392/67375, 1399680/1399489, {{monzo|14 -8 -8 5 2 -1}} | |||
{{mapping|legend=1| 80 3 161 -23 252 197 | 0 5 1 10 1 4 }} | |||
: mapping generators: ~9295/9216, ~2304/1859 | |||
Optimal tuning (CTE): ~2304/1859 = 371.385 | |||
{{Optimal ET sequence|legend=1|320, 2000, 4320}} | |||
=== 17-limit === | |||
Subgroup: 2.3.5.7.11.13.17 | |||
Comma list: 9801/9800, 12376/12375, 67392/67375, 4230144/4229225, 494534656/494515125 | |||
{{mapping|legend=1| 80 3 161 -23 252 197 327 | 0 5 1 10 1 4 0 }} | |||
: mapping generators: ~459/455, ~1859/1500 | |||
Optimal tuning (CTE): ~2275/1836 = 371.386 | |||
{{Optimal ET sequence|legend=1|320, 2000, 4320}} | |||
=== 19-limit === | === 19-limit === | ||
Subgroup: 2.3.5.7.11.13.17.19 | Subgroup: 2.3.5.7.11.13.17.19 | ||
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Mapping: [{{val|80 3 161 -23 252 197 327 117}}, {{val|0 5 1 10 1 4 0 9}}] | Mapping: [{{val|80 3 161 -23 252 197 327 117}}, {{val|0 5 1 10 1 4 0 9}}] | ||
: mapping generators: ~459/455, ~2275/1836 | |||
Optimal tuning (CTE): ~2275/1836 = 371.386 | Optimal tuning (CTE): ~2275/1836 = 371.386 | ||
| Line 65: | Line 112: | ||
{{Optimal ET sequence|legend=1|320, 2000, 4320}} | {{Optimal ET sequence|legend=1|320, 2000, 4320}} | ||
[[ | == Octodeca == | ||
[[ | Octodeca can be described as the 80 & 1920 temperament. | ||
[[Category: | |||
Subgroup: 2.3.5.7 | |||
Comma list: {{monzo|21 60 -50}}, 184528125/184473632 | |||
{{mapping|legend=1|80 2 36 -25|0 5 6 10}} | |||
: mapping generators: ~1071875/1062882 = 1\80, ~7476806640625/6025163444928 = 374.386 | |||
Optimal tuning (CTE): ~7476806640625/6025163444928 = 374.386 | |||
[[Support]]ing [[ET]]s: {{EDOs|80, 1920, 2000}} | |||
=== 19-limit === | |||
Subgroup: 2.3.5.7.11.13.17.19 | |||
Comma list: 5832/5831, 9801/9800, 89376/89375, 123201/123200, 392445/392392, 653184/653125 | |||
{{mapping|legend=1|80 2 36 -25 -127 -321 -327 -240|0 5 6 10 6 -1 0 4}} | |||
: mapping generators: ~12000/12103 = 1\80, ~1625/1309 = 374.386 | |||
Optimal tuning (CTE): ~1625/1309 = 374.386 | |||
=== 23-limit === | |||
Subgroup: 2.3.5.7.11.13.17.19.23 | |||
Comma list: 5832/5831, 8625/8624, 9801/9800, 10626/10625, 89376/89375, 95013/95000, 123201/123200 | |||
{{mapping|legend=1|80 2 36 -25 -127 -321 -327 -240 -287|0 5 6 10 6 -1 0 4 3}} | |||
: mapping generators: ~12000/12103 = 1\80, ~920/741 = 374.387 | |||
Optimal tuning (CTE): ~920/741 = 374.387 | |||
{{Navbox fractional-octave}} | |||
[[Category:80edo]]] | |||