Ripple family: Difference between revisions
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== Ripple == | == Ripple == | ||
The generator of ripple is a semitone representing 27/25, five of which give 4/3, and eight of which give 8/5. The ploidacot of ripple is omega-pentacot. This means that 27/25 is severely flattened, so that the characteristic damage is a strongly flat-tempered fourth reached at 5 semitones. Interestingly, in optimal tunings, the major third of ~5/4 does not tend to be damaged much sharpwards as one might expect from the equivalence, and is in practice sometimes even flat, so that prime 3 takes on practically the whole damage of the 5-limit equivalence, for which it has the advantage of being the simplest so still having a good chance at psychoacoustic viability. As a result though, the mapping of ~9/8 is often very flat, so that ripple can in practice be thought of as a [[dual-fifth temperament]] unless you use tunings close to [[12edo]]. | The generator of ripple is a semitone representing 27/25, five of which give 4/3, and eight of which give 8/5. The [[ploidacot]] of ripple is omega-pentacot. This means that 27/25 is severely flattened, so that the characteristic damage is a strongly flat-tempered fourth reached at 5 semitones. Interestingly, in optimal tunings, the major third of ~5/4 does not tend to be damaged much sharpwards as one might expect from the equivalence, and is in practice sometimes even flat, so that prime 3 takes on practically the whole damage of the 5-limit equivalence, for which it has the advantage of being the simplest so still having a good chance at psychoacoustic viability. As a result though, the mapping of ~9/8 is often very flat, so that ripple can in practice be thought of as a [[dual-fifth temperament]] unless you use tunings close to [[12edo]]. | ||
Reasonable [[patent val]] tunings not appearing in the optimal ET sequence are [[35edo]] and [[47edo]]. | Reasonable [[patent val]] tunings not appearing in the optimal ET sequence are [[35edo]] and [[47edo]]. | ||
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[[Badness]] (Sintel): 3.26 | [[Badness]] (Sintel): 3.26 | ||
=== Overview to extensions === | |||
The second comma of the comma list defines which 7-limit family member we are looking at: | |||
* Septimal ripple adds [[126/125]]; | |||
* Rip adds [[36/35]]; | |||
Both use the same nominal generator as ripple. | |||
For weak extensions, we have hemiripple and cohemiripple. Hemiripple adds [[49/48]], spliting the semitone generator in two. Cohemiripple adds [[245/243]], spliting the [[octave complement]] of the semitone generator in two. | |||
== Septimal ripple == | == Septimal ripple == | ||
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== Hemiripple == | == Hemiripple == | ||
Hemiripple tempers out 49/48 and splits the semitone generator in two for ~36/35. Its ploidacot is omega-decacot. | |||
[[Subgroup]]: 2.3.5.7 | [[Subgroup]]: 2.3.5.7 | ||
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{{Mapping|legend=1| 1 2 3 3 | 0 -10 -16 -5 }} | {{Mapping|legend=1| 1 2 3 3 | 0 -10 -16 -5 }} | ||
: mapping generators: ~2, ~36/35 | |||
[[Optimal tuning]]s: | [[Optimal tuning]]s: | ||
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Badness (Sintel): 1.93 | Badness (Sintel): 1.93 | ||
[[Category:Ripple family| ]] <!-- main article --> | [[Category:Ripple family| ]] <!-- main article --> | ||
[[Category:Ripple| ]] <!-- key article --> | [[Category:Ripple| ]] <!-- key article --> | ||
[[Category: | [[Category:Temperament families]] | ||
[[Category:Catalogs of rank-2 temperaments]] | |||