User:FloraC/Sandbox: Difference between revisions
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== Septimal meantone == | |||
Period: 1\1 | |||
Optimal ([[POTE]]) generator: ~3/2 = 696.495 | |||
EDO generators: [[12edo|7\12]], [[19edo|11\19]], [[31edo|18\31]], [[43edo|25\43]], [[50edo|29\50]] | |||
Scales: [[Meantone5]], [[Meantone7]], [[Meantone12]] | |||
<div class="toccolours mw-collapsible mw-collapsed" style="width:600px; overflow:auto;"> | |||
<div style="line-height:1.6;">Interval table (12-note MOS, 2.3.5.7 POTE tuning)</div> | |||
<div class="mw-collapsible-content"> | |||
{| class="wikitable right-1 right-2 sortable" | |||
|+ | |||
|- | |||
! #Gens up | |||
! Cents <ref>octave-reduced</ref> | |||
! class="unsortable"| Approximate ratios<ref>2.3.5.7, odd limit ≤ 27</ref> | |||
|- | |||
| 0 | |||
| 0.00 | |||
| 1/1 | |||
|- | |||
| 1 | |||
| 696.5 | |||
| 3/2 | |||
|- | |||
| 2 | |||
| 193.0 | |||
| 9/8, 10/9 | |||
|- | |||
| 3 | |||
| 889.5 | |||
| 5/3 | |||
|- | |||
| 4 | |||
| 386.0 | |||
| 5/4 | |||
|- | |||
| 5 | |||
| 1082.5 | |||
| 15/8, 28/15 | |||
|- | |||
| 6 | |||
| 579.0 | |||
| 7/5 | |||
|- | |||
| 7 | |||
| 75.5 | |||
| 21/20, 25/24, 28/27 | |||
|- | |||
| 8 | |||
| 772.0 | |||
| 14/9, 25/16 | |||
|- | |||
| 9 | |||
| 268.5 | |||
| 7/6 | |||
|- | |||
| 10 | |||
| 965.0 | |||
| 7/4 | |||
|- | |||
| 11 | |||
| 461.4 | |||
| 21/16 | |||
|} | |||
<references/></div></div> | |||
<div class="toccolours mw-collapsible mw-collapsed" style="width:400px; overflow:auto;"> | |||
<div style="line-height:1.6;">Technical data</div> | |||
<div class="mw-collapsible-content"> | |||
[[Mappings|Period-generator mapping]]: [<1 0 -4 -13|, <0 1 4 10|] | |||
[[Comma]]s: 81/80, 126/125 | |||
7 and [[9-odd-limit|9-limit]] minimax | |||
[{{Monzo| 1 0 0 0 }}, {{Monzo| 1 0 1/4 0 }}, {{Monzo| 0 0 1 0 }}, {{Monzo| -3 0 5/2 0 }}] | |||
[[Eigenmonzo]]s: 2, 5 | |||
[[Tuning Ranges of Regular Temperaments|Valid range]]: [694.737, 700.000] (19 to 12) | |||
Nice range: [694.786, 701.955] | |||
Strict range: [694.786, 700.000] | |||
Mapping generator: ~3 | |||
Algebraic generator: Cybozem, the real root of 15''x''<sup>3</sup> - 10''x''<sup>2</sup> - 18, which comes to 503.4257 cents. The recurrence converges quickly. | |||
[[Wedgie]]: <<1 4 10 4 13 12|| | |||
[[Val]]s: 5, 7, 12, 19, 26, 31, 43, 45, 50, 55, 67, 69, 74, 81, 88, 98, 105, 117, 131b, 212bb, 293bb | |||
[[Badness]]: 0.0137 | |||
</div></div> | |||
== Commas == | == Commas == | ||