80th-octave temperaments: Difference between revisions

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-{{Fractional-octave navigation|80}}
+{{Technical data page}}
+{{Infobox fractional-octave|80}}
-This page describes 80th-octave temperaments.
+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]].
-edo is extremely accurate for the 17th harmonic, a relationship which is seen in some of these temperaments.
+Temperaments discussed elsewhere include
-== Octogintic ==
+* ''Octogintic'', → [[Parkleiness temperaments#Octogintic|Parkleiness temperaments]]
-''Main article: [[Parkleiness temperaments#Octogintic]]''
 == Tetraicosic ==
-Tetraicosic is described as 720 & 1600, and named after the fact that 4 × 20 = 80.
+Tetraicosic is described as 1600 & 2320, and named after the fact that 4 × 20 = 80.
 [[Subgroup]]: 2.3.5.7
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 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 ==
-Named after the 80th element, defined as the 320 & 2000 temperament. 7 periods are mapped to ~[[17/16]], 11 periods are mapped to ~[[11/10]].
+Named after the 80th element, defined as the 320 & 2000 temperament.
 === 13-limit ===
 Subgroup: 2.3.5.7.11.13
@@ Line 60: / Line 82: @@
 {{mapping|legend=1| 80 3 161 -23 252 197 | 0 5 1 10 1 4 }}
-Mapping generators: ~9295/9216, ~2304/1859
+: mapping generators: ~9295/9216, ~2304/1859
 Optimal tuning (CTE): ~2304/1859 = 371.385
@@ Line 72: / Line 94: @@
 {{mapping|legend=1| 80 3 161 -23 252 197 327 | 0 5 1 10 1 4 0 }}
-Mapping generators: ~459/455, ~1859/1500
+: mapping generators: ~459/455, ~1859/1500
 Optimal tuning (CTE): ~2275/1836 = 371.386
@@ Line 84: / Line 106: @@
 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
+: mapping generators: ~459/455, ~2275/1836
 Optimal tuning (CTE): ~2275/1836 = 371.386
@@ Line 90: / Line 112: @@
 {{Optimal ET sequence|legend=1|320, 2000, 4320}}
-[[Category:80edo]]
+== Octodeca ==
-[[Category:Temperament collections]]
+Octodeca can be described as the 80 & 1920 temperament.
-[[Category:Rank 2]]
+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]]]