Escapade family: Difference between revisions
moved weak extensions to underneath 2.3.5.11 |
added strong/weak distinction |
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</div> | </div> | ||
For intervals along the chain of generators in the 2.3.5.11.31 subgroup temperament, out to 22 generators up, see the third column of [[16ed5/3#Intervals]]. | For intervals along the chain of generators in the 2.3.5.11.31 subgroup temperament, out to 22 generators up, see the third column of [[16ed5/3#Intervals]]. | ||
= | = Escapade (5-limit) = | ||
[[Subgroup]]: 2.3.5 | [[Subgroup]]: 2.3.5 | ||
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[[Badness]]: 0.083778 | [[Badness]]: 0.083778 | ||
= | = Escapade (2.3.5.11 subgroup) = | ||
Since (an ideally slightly flat) 4/3 is split in three by the interval of 3 generators, it makes sense to equate that interval to [[11/10]] by tempering out [[4000/3993]], and therefore the generator to (11/10)/(16/15) = [[33/32]]; this does minimal damage to the temperament. This structure in 2.3.5.11 occurs in all extensions of escapade to include prime 7, and therefore will be considered the fount of all further extensions. | Since (an ideally slightly flat) 4/3 is split in three by the interval of 3 generators, it makes sense to equate that interval to [[11/10]] by tempering out [[4000/3993]], and therefore the generator to (11/10)/(16/15) = [[33/32]]; this does minimal damage to the temperament. This structure in 2.3.5.11 occurs in all extensions of escapade to include prime 7, and therefore will be considered the fount of all further extensions. | ||
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Badness: 0.0107 | Badness: 0.0107 | ||
== Strong extensions == | |||
=== 2.3.5.11.31 subgroup === | === 2.3.5.11.31 subgroup === | ||
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Badness: 0.031366 | Badness: 0.031366 | ||
== Weak extensions == | |||
=== Alphaquarter === | === Alphaquarter === | ||