Escapade family: Difference between revisions
mNo edit summary |
m moved escapist down, since escaped should be pseudo-canonical |
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| 31/16 || 1144.724 || -0.311 | | 31/16 || 1144.724 || -0.311 | ||
|} | |} | ||
=== Escaped === | === Escaped === | ||
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Badness: 0.025344 | Badness: 0.025344 | ||
=== Escapist === | |||
''[[#Strong extensions|Return to the map]]'' | |||
This temperament makes the identification of the 4-generator interval, representing (16/15)<sup>2</sup>, with [[8/7]] by tempering out [[225/224]] (along with [[12288/12005]]); however, this is somewhat inaccurate as the ~16/15 in escapade is slightly flat, while for a good marvel tuning it needs to be tempered sharpward to equate it with [[15/14]]. | |||
Subgroup: 2.3.5.7.11 | |||
Comma list: 99/98, 176/175, 2560/2541 | |||
Mapping: {{mapping| 1 2 2 3 3 | 0 -9 7 -4 10 }} | |||
Optimal tuning (POTE): ~2 = 1\1, ~33/32 = 55.354 | |||
{{Optimal ET sequence|legend=1| 21, 22, 43, 65d }} | |||
Badness: 0.036700 | |||
{| class="wikitable center-1 center-2 center-3 center-4 mw-collapsible mw-collapsed" | |||
|+ style="font-size: 105%;" | Harmonics | |||
|- | |||
! rowspan="2" | Prime harmonic !! colspan="2" | Tunings | |||
|- | |||
! CTE tuning !! Deviation from just | |||
|- | |||
| 3/2 || 701.626 || -0.329 | |||
|- | |||
| 5/4 || 387.624 || +1.310 | |||
|- | |||
| 7/4 || 978.501 || +9.675 | |||
|- | |||
| 11/8 || 553.749 || +2.431 | |||
|} | |||
==== 13-limit ==== | |||
Subgroup: 2.3.5.7.11.13 | |||
Comma list: 78/77, 99/98, 176/175, 507/500 | |||
Mapping: {{mapping| 1 2 2 3 3 3 | 0 -9 7 -4 10 15 }} | |||
Optimal tuning (POTE): ~2 = 1\1, ~26/25 = 55.550 | |||
{{Optimal ET sequence|legend=1| 21, 22, 43 }} | |||
Badness: 0.035261 | |||
== Weak extensions == | == Weak extensions == |