Escapade family: Difference between revisions

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m moved escapist down, since escaped should be pseudo-canonical
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=== 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


=== 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 ==