Escapade family: Difference between revisions
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= Strong extensions = | |||
{| class="wikitable center-all" | {| class="wikitable center-all" | ||
|+ style="font-size: 105%;" | Map to strong full 7- and 11-limit extensions | |+ style="font-size: 105%;" | Map to strong full 7- and 11-limit extensions | ||
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<nowiki/>* Defined as the range in which the extension specified has a better mapping of 7 compared to its neighboring extensions | <nowiki/>* Defined as the range in which the extension specified has a better mapping of 7 compared to its neighboring extensions | ||
== Escaped == | |||
''[[#Strong extensions|Return to the map]]'' | ''[[#Strong extensions|Return to the map]]'' | ||
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Here, [[245/243]] is tempered out so that [[9/7]] is equated to the square root of 5/3 (at 8 generators) present in the temperament. This works best where 5/3 is slightly flat, therefore on the end of the spectrum approaching [[22edo]]. | Here, [[245/243]] is tempered out so that [[9/7]] is equated to the square root of 5/3 (at 8 generators) present in the temperament. This works best where 5/3 is slightly flat, therefore on the end of the spectrum approaching [[22edo]]. | ||
[[Subgroup]]: 2.3.5.7 | [[Subgroup]]: 2.3.5.7 | ||
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[[Badness]] (Smith): 0.088746 | [[Badness]] (Smith): 0.088746 | ||
=== 11-limit === | |||
Subgroup: 2.3.5.7.11 | Subgroup: 2.3.5.7.11 | ||
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Badness (Smith): 0.031366 | Badness (Smith): 0.031366 | ||
== Alphaquarter == | |||
''[[#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 the [[7-limit]]; the cost is that the harmonic 7 is exceedingly complex, located all the way at 61 generators up. | ||
[[Subgroup]]: 2.3.5.7 | [[Subgroup]]: 2.3.5.7 | ||
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[[Badness]] (Smith): 0.116594 | [[Badness]] (Smith): 0.116594 | ||
=== 11-limit === | |||
Subgroup: 2.3.5.7.11 | Subgroup: 2.3.5.7.11 | ||
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Badness (Smith): 0.025344 | Badness (Smith): 0.025344 | ||
== Escapist == | |||
''[[#Strong extensions|Return to the map]]'' | ''[[#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]]. | 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 | [[Subgroup]]: 2.3.5.7 | ||
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[[Badness]] (Smith): 0.077950 | [[Badness]] (Smith): 0.077950 | ||
=== 11-limit === | |||
Subgroup: 2.3.5.7.11 | Subgroup: 2.3.5.7.11 | ||
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Badness (Smith): 0.035261 | Badness (Smith): 0.035261 | ||
= Weak extensions = | |||
{| class="wikitable center-all" | {| class="wikitable center-all" | ||
|+ style="font-size: 105%;" | Map to weak extensions | |+ style="font-size: 105%;" | Map to weak extensions | ||
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|} | |} | ||
== Septisuperfourth == | |||
''[[#Weak extensions|Return to map]]'' | ''[[#Weak extensions|Return to map]]'' | ||
[[Subgroup]]: 2.3.5.7 | [[Subgroup]]: 2.3.5.7 | ||
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[[Badness]] (Smith): 0.059241 | [[Badness]] (Smith): 0.059241 | ||
=== 11-limit === | |||
Subgroup: 2.3.5.7.11 | Subgroup: 2.3.5.7.11 | ||
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|} | |} | ||
==== 13-limit ==== | |||
Subgroup: 2.3.5.7.11.13 | Subgroup: 2.3.5.7.11.13 | ||
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Badness (Smith): 0.022887 | Badness (Smith): 0.022887 | ||
==== Septisuperquad ==== | |||
This temperament is also known as "biscapade". | This temperament is also known as "biscapade". | ||
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Badness (Smith): 0.033038 | Badness (Smith): 0.033038 | ||
== Arch == | |||
''[[#Weak extensions|Return to map]]'' | ''[[#Weak extensions|Return to map]]'' | ||
[[Subgroup]]: 2.3.5.7 | [[Subgroup]]: 2.3.5.7 | ||
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[[Badness]] (Smith): 0.094345 | [[Badness]] (Smith): 0.094345 | ||
=== 11-limit === | |||
Subgroup: 2.3.5.7.11 | Subgroup: 2.3.5.7.11 | ||