Archytas family: Difference between revisions
Cmloegcmluin (talk | contribs) "optimal GPV sequence" → "optimal ET sequence", per Talk:Optimal_ET_sequence |
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[[Comma list]]: [[64/63]] | [[Comma list]]: [[64/63]] | ||
{{Mapping|legend=1| 1 0 0 6 | 0 1 0 -2 | 0 0 1 0 }} | |||
: mapping generators: ~2, ~3, ~5 | |||
[[Mapping to lattice]]: [{{val| 0 1 0 -2 }}, {{val| 0 0 1 0 }}] | [[Mapping to lattice]]: [{{val| 0 1 0 -2 }}, {{val| 0 0 1 0 }}] | ||
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: Angle (3/2, 5/4) = 90 degrees | : Angle (3/2, 5/4) = 90 degrees | ||
[[Optimal tuning]] ([[POTE]]): ~3/2 = 709.3213, ~5/4 = 393.3747 | [[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~3/2 = 709.3213, ~5/4 = 393.3747 | ||
[[Minimax tuning]]: | [[Minimax tuning]]: | ||
* [[7-odd-limit]] | * [[7-odd-limit]] | ||
: | : {{monzo list| 1 0 0 0 | 2 1/3 0 -1/3 | 2 -2/3 1 -1/3 | 2 -2/3 0 2/3 }} | ||
: [[Eigenmonzo basis | : [[Eigenmonzo basis|eigenmonzo (unchanged-interval) basis]]: 2.5/3.7/3 | ||
* [[9-odd-limit]] | * [[9-odd-limit]] | ||
: | : {{monzo list| 1 0 0 0 | 3/2 1/2 0 -1/4 | 3/2 -1/2 1 -1/4 | 3 -1 0 1/2 }} | ||
: [[Eigenmonzo basis | : [[Eigenmonzo basis|eigenmonzo (unchanged-interval) basis]]: 2.5/3.9/7 | ||
{{Optimal ET sequence|legend=1| 5, 7, 10, 12, 15, 22, 27, 39d, 49, 88bcd, 110bcdd }} | {{Optimal ET sequence|legend=1| 5, 7, 10, 12, 15, 22, 27, 39d, 49, 88bcd, 110bcdd }} | ||
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; Music | ; Music | ||
* Chris Vaisvil – [http://micro.soonlabel.com/hobbit_scales/daily201031--hobbit-archytas12.mp3 12 archytas hobbits with ale] | * [[Chris Vaisvil]] – [http://micro.soonlabel.com/hobbit_scales/daily201031--hobbit-archytas12.mp3 ''12 archytas hobbits with ale''] | ||
* Joel Taylor – [http://micro.soonlabel.com/gene_ward_smith/Others/Taylor/Archytas12%20sync%20Study%203.mp3 Portrait of a Tragedy (Death of a Son) - Archytas12 sync Study 3] | * [[Joel Taylor]] – [http://micro.soonlabel.com/gene_ward_smith/Others/Taylor/Archytas12%20sync%20Study%203.mp3 ''Portrait of a Tragedy (Death of a Son) - Archytas12 sync Study 3''] | ||
== Ares == | == Ares == | ||
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[[Comma list]]: 64/63, 100/99 | [[Comma list]]: 64/63, 100/99 | ||
{{Mapping|legend=1| 1 0 0 6 2 | 0 1 0 -2 -2 | 0 0 1 0 2 }} | |||
Mapping to lattice: [{{val| 0 1 1 -2 0 }}, {{val| 0 0 -1 0 -2 }}] | Mapping to lattice: [{{val| 0 1 1 -2 0 }}, {{val| 0 0 -1 0 -2 }}] | ||
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: Angle (3/2, 6/5) = 75.0475 degrees | : Angle (3/2, 6/5) = 75.0475 degrees | ||
[[Optimal tuning]] ([[POTE]]): ~3/2 = 709.6869, ~5/4 = 391.4507 | [[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~3/2 = 709.6869, ~5/4 = 391.4507 | ||
[[Minimax tuning]]: | [[Minimax tuning]]: | ||
* [[11-odd-limit]] | * [[11-odd-limit]] | ||
: [{{monzo| 1 0 0 0 0 }}, {{monzo| 3/2 1/2 0 -1/4 0 }}, {{monzo| 2 0 0 -1/2 1/2 }}, {{monzo| 3 -1 0 1/2 0 }}, {{monzo| 3 -1 0 -1/2 1 }}] | : [{{monzo| 1 0 0 0 0 }}, {{monzo| 3/2 1/2 0 -1/4 0 }}, {{monzo| 2 0 0 -1/2 1/2 }}, {{monzo| 3 -1 0 1/2 0 }}, {{monzo| 3 -1 0 -1/2 1 }}] | ||
: [[Eigenmonzo basis | : [[Eigenmonzo basis|eigenmonzo (unchanged-interval) basis]]: 2.11/9.9/7 | ||
{{Optimal ET sequence|legend=1| 12, 15, 22, 27e, 34d, 49, 181bbcddeeee }} | {{Optimal ET sequence|legend=1| 12, 15, 22, 27e, 34d, 49, 181bbcddeeee }} | ||
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[[Comma list]]: 56/55, 64/63 | [[Comma list]]: 56/55, 64/63 | ||
{{Mapping|legend=1| 1 0 0 6 9 | 0 1 0 -2 -2 | 0 0 1 0 -1 }} | |||
[[Optimal tuning]] ([[POTE]]): ~3/2 = 710.9720, ~5/4 = 401.2699 | [[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~3/2 = 710.9720, ~5/4 = 401.2699 | ||
{{Optimal ET sequence|legend=1| 5, 10, 12, 15, 27e }} | {{Optimal ET sequence|legend=1| 5, 10, 12, 15, 27e }} | ||