Diaschismic extensions: Difference between revisions

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'''Srutal''', known interchangeably as '''diaschismic''' in the [[5-limit]], is a [[regular temperament]] defined by [[tempering out]] the comma [[2048/2025]], the diaschisma. The octave is split into two periods, each representing [[~]][[45/32]]~[[64/45]]; and the [[generator]] can be considered to be a perfect fifth (~[[3/2]]), or a perfect fifth less a period, which is a diatonic semitone of ~[[16/15]]. Tempering out the diaschisma implies that two of these semitones are equated to [[9/8]], and therefore as [[9/8]] = ([[18/17]])([[17/16]]), ~[[16/15]] can very naturally be equated to 17/16 and 18/17 as well, producing a 2.3.5.17 [[subgroup]] extension known as '''srutal archagall''', whose commas are [[136/135]] and [[256/255]].

~~For the 5-limit and 2.3.5.17 temperaments:~~ {{Tdlink|Diaschismic family #Srutal aka diaschismic}}

== 7-limit extensions ==

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 '''Srutal''', known interchangeably as '''diaschismic''' in the [[5-limit]], is a [[regular temperament]] defined by [[tempering out]] the comma [[2048/2025]], the diaschisma. The octave is split into two periods, each representing [[~]][[45/32]]~[[64/45]]; and the [[generator]] can be considered to be a perfect fifth (~[[3/2]]), or a perfect fifth less a period, which is a diatonic semitone of ~[[16/15]]. Tempering out the diaschisma implies that two of these semitones are equated to [[9/8]], and therefore as [[9/8]] = ([[18/17]])([[17/16]]), ~[[16/15]] can very naturally be equated to 17/16 and 18/17 as well, producing a 2.3.5.17 [[subgroup]] extension known as '''srutal archagall''', whose commas are [[136/135]] and [[256/255]].
-For the 5-limit and 2.3.5.17 temperaments: {{Tdlink|Diaschismic family #Srutal aka diaschismic}}
+{{Tdlink|Diaschismic family #Srutal aka diaschismic}}
 == 7-limit extensions ==