Schismatic family: Difference between revisions

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The 5-limit parent comma for the '''schismatic''' (or '''schismic''') '''family''' is the [[schisma]] of 32805/32768, which is the amount by which the [[Pythagorean comma]] exceeds the [[Didymus comma]] (81/80), or alternatively put, the difference between a [[5/4|just major third]] and a [[8192/6561|Pythagorean diminished fourth]]. ~~Its [[monzo]] is {{monzo| -15 8 1 }}, and flipping that yields {{multival| 1 -8 -15 }} for the [[wedgie]]. This tells us the~~ generator is a fifth and 5/4 is represented by a diminished fourth.

The 5-limit parent comma for the '''schismatic''' (or '''schismic''') '''family''' is the [[schisma]] of 32805/32768, which is the amount by which the [[Pythagorean comma]] exceeds the [[Didymus comma]] (81/80), or alternatively put, the difference between a [[5/4|just major third]] and a [[8192/6561|Pythagorean diminished fourth]]. The generator is a fifth and 5/4 is represented by a diminished fourth.

This defies the tradition of tertian harmony, as the just major triad on C is C-Fb-G, for example. One may want to adopt an additional module of accidentals such as arrows to represent the comma step, allowing them to write the chord above as C-vE-G.

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-The 5-limit parent comma for the '''schismatic''' (or '''schismic''') '''family''' is the [[schisma]] of 32805/32768, which is the amount by which the [[Pythagorean comma]] exceeds the [[Didymus comma]] (81/80), or alternatively put, the difference between a [[5/4|just major third]] and a [[8192/6561|Pythagorean diminished fourth]]. Its [[monzo]] is {{monzo| -15 8 1 }}, and flipping that yields {{multival| 1 -8 -15 }} for the [[wedgie]]. This tells us the generator is a fifth and 5/4 is represented by a diminished fourth.
+The 5-limit parent comma for the '''schismatic''' (or '''schismic''') '''family''' is the [[schisma]] of 32805/32768, which is the amount by which the [[Pythagorean comma]] exceeds the [[Didymus comma]] (81/80), or alternatively put, the difference between a [[5/4|just major third]] and a [[8192/6561|Pythagorean diminished fourth]]. The generator is a fifth and 5/4 is represented by a diminished fourth.
 This defies the tradition of tertian harmony, as the just major triad on C is C-Fb-G, for example. One may want to adopt an additional module of accidentals such as arrows to represent the comma step, allowing them to write the chord above as C-vE-G.