Diaschismic extensions: Difference between revisions

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The two alternative names for this temperament are assigned to different strong extensions to the [[7-limit]]: srutal (34d&46) and diaschismic (46&58), though there are other mappings that are comparable in complexity and error: [[pajara]] (12&22) and keen (22&34).

Srutal tempers out [[4375/4374]] in addition to the diaschisma, and therefore [[7/4]] is represented by 15 semitones less a half octave, or five [[6/5]]s less a half octave. Diaschismic sacrifices a slight amount of accuracy by tempering out [[126/125]], but slightly reduces complexity: [[8/7]] is represented by 8 semitones less a half-octave, or we can say 7/4 is equated to four [[5/4]]s less a half octave.

=== Srutal ===

Srutal tempers out [[4375/4374]] in addition to the diaschisma, and therefore [[7/4]] is represented by 15 semitones less a half octave, or five [[6/5]]s less a half octave.

For technical data on 7-limit and higher-limit srutal: see [[Diaschismic family #Srutal]].

=== Diaschismic ===

Diaschismic sacrifices a slight amount of accuracy by tempering out [[126/125]], but slightly reduces complexity: [[8/7]] is represented by 8 semitones less a half-octave, or we can say 7/4 is equated to four [[5/4]]s less a half octave.

For technical data on 7-limit and higher-limit diaschismic: see [[Diaschismic family #Septimal diaschismic]].

Both of these can be extended straightforwardly to the [[11-limit|11-]], [[13-limit|13-]], and [[17-limit]] by adding 176/175, 352/351, and 221/220 to the comma list in this order.

For technical data on 7-limit and higher-limit ~~diaschismic:~~ see [[Diaschismic family #~~Septimal diaschismic~~]].

=== Pajara ===

[[Pajara]] combines diaschismic with [[archy]], tempering the fifth to about 709 cents. The interval of two stacked fifths is equated to 16/7, and the harmonic seventh [[7/4]] and the just major third [[5/4]] are separated by a perfect semioctave.

For technical data on 7-limit and higher-limit pajara, see [[Diaschismic family #Pajara]].

~~For technical data on 7-limit and higher-limit srutal: see [[Diaschismic family #Srutal]].~~

=== Keen ===

== Intervals ==

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 The two alternative names for this temperament are assigned to different strong extensions to the [[7-limit]]: srutal (34d&amp;46) and diaschismic (46&amp;58), though there are other mappings that are comparable in complexity and error: [[pajara]] (12&amp;22) and keen (22&amp;34).
-Srutal tempers out [[4375/4374]] in addition to the diaschisma, and therefore [[7/4]] is represented by 15 semitones less a half octave, or five [[6/5]]s less a half octave. Diaschismic sacrifices a slight amount of accuracy by tempering out [[126/125]], but slightly reduces complexity: [[8/7]] is represented by 8 semitones less a half-octave, or we can say 7/4 is equated to four [[5/4]]s less a half octave.
+=== Srutal ===
+Srutal tempers out [[4375/4374]] in addition to the diaschisma, and therefore [[7/4]] is represented by 15 semitones less a half octave, or five [[6/5]]s less a half octave.
+For technical data on 7-limit and higher-limit srutal: see [[Diaschismic family #Srutal]].
+=== Diaschismic ===
+Diaschismic sacrifices a slight amount of accuracy by tempering out [[126/125]], but slightly reduces complexity: [[8/7]] is represented by 8 semitones less a half-octave, or we can say 7/4 is equated to four [[5/4]]s less a half octave.
+For technical data on 7-limit and higher-limit diaschismic: see [[Diaschismic family #Septimal diaschismic]].
 Both of these can be extended straightforwardly to the [[11-limit|11-]], [[13-limit|13-]], and [[17-limit]] by adding 176/175, 352/351, and 221/220 to the comma list in this order.
-For technical data on 7-limit and higher-limit diaschismic: see [[Diaschismic family #Septimal diaschismic]].
+=== Pajara ===
+[[Pajara]] combines diaschismic with [[archy]], tempering the fifth to about 709 cents. The interval of two stacked fifths is equated to 16/7, and the harmonic seventh [[7/4]] and the just major third [[5/4]] are separated by a perfect semioctave.
+For technical data on 7-limit and higher-limit pajara, see [[Diaschismic family #Pajara]].
-For technical data on 7-limit and higher-limit srutal: see [[Diaschismic family #Srutal]].
+=== Keen ===
 == Intervals ==