80th-octave temperaments: Difference between revisions

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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]].

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== Mercury ==

: ''Not to be confused with [[mercury meantone]] and [[mercurial comma|mercurial]].''

Named after the 80th element, defined as the 320 & 2000 temperament.

=== 13-limit ===

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~~Mapping~~ generators: ~9295/9216, ~2304/1859

: mapping generators: ~9295/9216, ~2304/1859

Optimal tuning (CTE): ~2304/1859 = 371.385

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~~Mapping~~ generators: ~459/455, ~1859/1500

: mapping generators: ~459/455, ~1859/1500

Optimal tuning (CTE): ~2275/1836 = 371.386

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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

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Optimal tuning (CTE): ~920/741 = 374.387

[[Category:80edo]]

~~[[Category:Temperament collections]]~~

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-{{Fractional-octave navigation|80}}
+{{Technical data page}}
+{{Infobox fractional-octave|80}}
 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]].
@@ Line 73: / Line 74: @@
 == Mercury ==
+: ''Not to be confused with [[mercury meantone]] and [[mercurial comma|mercurial]].''
 Named after the 80th element, defined as the 320 & 2000 temperament.
 === 13-limit ===
@@ Line 81: / Line 84: @@
 {{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 93: / Line 96: @@
 {{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 105: / Line 108: @@
 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 148: / Line 151: @@
 Optimal tuning (CTE): ~920/741 = 374.387
+{{Navbox fractional-octave}}
 [[Category:80edo]]
-[[Category:Temperament collections]]