Escapade family: Difference between revisions

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{{Mapping|legend=1| 1 2 2 4 | 0 -9 7 -26 }}
{{Mapping|legend=1| 1 2 2 4 | 0 -9 7 -26 }}
{{Multival|legend=1| 9 -7 26 -32 16 80 }}


[[Optimal tuning]] ([[POTE]]): ~2 = 1200.000, ~28/27 = 55.122
[[Optimal tuning]] ([[POTE]]): ~2 = 1200.000, ~28/27 = 55.122
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''[[#Strong extensions|Return to the map]]''
''[[#Strong extensions|Return to the map]]''


Given the slightly sharp ~[[3/2]] in ideal tunings of escapade (between [[65edo]] and [[87edo]]), it does very little damage to temper out [[5120/5103]] to extend it to the [[7-limit]]; the cost is that the harmonic 7 is exceedingly complex, located all the way at 61 generators up.
Given the slightly sharp ~[[3/2]] in ideal tunings of escapade (between [[65edo]] and [[87edo]]), it does very little damage to temper out [[5120/5103]] to extend it to prime 7; the cost is that the harmonic 7 is exceedingly complex, located all the way at 61 generators up.


=== 7-limit ===
=== 7-limit ===
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{{Mapping|legend=1| 1 2 2 0 | 0 -9 7 61 }}
{{Mapping|legend=1| 1 2 2 0 | 0 -9 7 61 }}
{{Multival|legend=1| 9 -7 -61 -32 -122 -122 }}


[[Optimal tuning]] ([[POTE]]): ~2 = 1200.000, ~16128/15625 = 55.243
[[Optimal tuning]] ([[POTE]]): ~2 = 1200.000, ~16128/15625 = 55.243
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{{Mapping|legend=1| 1 2 2 3 | 0 -9 7 -4 }}
{{Mapping|legend=1| 1 2 2 3 | 0 -9 7 -4 }}
{{Multival|legend=1| 9 -7 4 -32 -19 29 }}


[[Optimal tuning]] ([[POTE]]): ~2 = 1200.000, ~49/48 = 55.327
[[Optimal tuning]] ([[POTE]]): ~2 = 1200.000, ~49/48 = 55.327
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: mapping generators: ~343/243, ~16875/16384
: mapping generators: ~343/243, ~16875/16384
{{Multival|legend=1| 18 -14 30 -64 -3 109 }}


[[Optimal tuning]] ([[POTE]]): ~343/243 = 1\2, ~16875/16384 = 55.320
[[Optimal tuning]] ([[POTE]]): ~343/243 = 1\2, ~16875/16384 = 55.320
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: mapping generators: ~2, ~64/63
: mapping generators: ~2, ~64/63
{{Multival|legend=1| 18 -14 -35 -64 -106 -42 }}


[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~64/63 = 27.668
[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~64/63 = 27.668
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[[Category:Temperament families]]
[[Category:Temperament families]]
[[Category:Pages with mostly numerical content]]
[[Category:Escapade family| ]] <!-- main article -->
[[Category:Escapade family| ]] <!-- main article -->
[[Category:Rank 2]]
[[Category:Rank 2]]