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).

~~In srutal~~, 7/4 is represented by 15 ~~diatonic~~ semitones ~~minus~~ half octave, or five 6/~~5s minus~~ half octave.

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.

~~In diaschismic, 7/4 is represented by one and half octaves minus 8 diatonic semitones, or four 5/4s minus half octave.~~

Both of these can be extended naturally 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.

~~They~~ can be extended naturally to the 11-, 13-, and 17-limit by adding 176/175, 352/351, and 221/220 to the comma list in this order.

== 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).
-In srutal, 7/4 is represented by 15 diatonic semitones minus half octave, or five 6/5s minus half octave.
+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.
-In diaschismic, 7/4 is represented by one and half octaves minus 8 diatonic semitones, or four 5/4s minus half octave.
+Both of these can be extended naturally 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.
-They can be extended naturally to the 11-, 13-, and 17-limit by adding 176/175, 352/351, and 221/220 to the comma list in this order.
 == Intervals ==