Diaschismic extensions: Difference between revisions

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~~{{Infobox Regtemp~~

~~| Title = Srutal; srutal archagall~~

~~| Subgroups = 2.3.5, 2.3.5.17~~

~~| Comma basis = [[2048/2025]] (2.3.5); <br /> [[136/135]], [[256/255]] (2.3.5.17)~~

~~| Edo join 1 = 12 | Edo join 2 = 22~~

~~| Generator = 16/15 | Generator tuning = 104.898 | Optimization method = POTE~~

~~| MOS scales = [[2L 8s]], [[10L 2s]], [[12L 10s]]~~

~~| Mapping = 2; 1 -2 1~~

~~| Pergen = (P8/2, P5)~~

~~| Color name = Saguguti~~

~~| Odd limit 1 = 5 | Mistuning 1 = 3.259 | Complexity 1 = 12~~

~~| Odd limit 2 = (2.3.5.17) 25 | Mistuning 2 = ??? | Complexity 2 = 22~~

}}

'''Srutal''', known interchangeably as '''diaschismic''' in the [[5-limit]], is a [[regular temperament]] defined by [[tempering out]] the comma [[2048/2025]] = [11 -4 -2⟩, 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]].

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 {{URWTC}}
-{{Infobox Regtemp
-| Title = Srutal; srutal archagall
-| Subgroups = 2.3.5, 2.3.5.17
-| Comma basis = [[2048/2025]] (2.3.5); <br /> [[136/135]], [[256/255]] (2.3.5.17)
-| Edo join 1 = 12 | Edo join 2 = 22
-| Generator = 16/15 | Generator tuning = 104.898 | Optimization method = POTE
-| MOS scales = [[2L 8s]], [[10L 2s]], [[12L 10s]]
-| Mapping = 2; 1 -2 1
-| Pergen = (P8/2, P5)
-| Color name = Saguguti
-| Odd limit 1 = 5 | Mistuning 1 = 3.259 | Complexity 1 = 12
-| Odd limit 2 = (2.3.5.17) 25 | Mistuning 2 = ??? | Complexity 2 = 22
-}}
 '''Srutal''', known interchangeably as '''diaschismic''' in the [[5-limit]], is a [[regular temperament]] defined by [[tempering out]] the comma [[2048/2025]] = [11 -4 -2⟩, 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]].