Schismatic family: Difference between revisions

Improve intro (standard degree terms easily make sense for fifth-generator temperaments)
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The 5-limit parent comma for the '''schismatic 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 just major third and a Pythagorean diminished fourth. Its [[monzo]] is {{monzo| -15 8 1 }}, and flipping that yields &lt;&lt;1 -8 -15|| for the [[wedgie]]. This tells us the generator is a fifth and that we will need eight fourths in succession to reach the pitch class of a major third. In fact, 10 = (4/3)<sup>8</sup> × 32805/32768.
The 5-limit parent comma for the '''schismatic 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 just major third and a 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. In fact, 10 = (4/3)<sup>8</sup> × 32805/32768.


= Schismatic aka Helmholtz =
= Schismatic aka Helmholtz =