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Schismic–Pythagorean equivalence continuum: Difference between revisions

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VisualWikitext
The inverted continuum
This m-continuum covers most temps of fractional n.
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We may invert the continuum by setting ''m'' such that 1/''m'' + 1/''n'' = 1. The just value of ''m'' is 1.0908441588…
We may invert the continuum by setting ''m'' such that 1/''m'' + 1/''n'' = 1. This may be called the ''syntonic-Pythagorean equivalence continuum'', which is essentially the same thing. The just value of ''m'' is 1.0908441588…


{| class="wikitable center-1 center-2"
{| class="wikitable center-1 center-2"
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! Ratio
! Ratio
! Monzo
! Monzo
|-
| -1
| [[Python]]
| [[43046721/41943040]]
| {{monzo| -23 16 -1 }}
|-
|-
| 0
| 0
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Examples of temperaments with fractional values of ''n'':
{| class="wikitable"
* Python (''n'' = 1/2 = 0.5)
|+ Temperaments with fractional ''n'' and ''m''
* [[Ripple family|Ripple]] (''n'' = 5/4 = 1.25)
|-
* [[Dimipent family|Diminished]] (''n'' = 4/3 = 1.{{overline|3}})
! Temperament !! ''n'' !! ''m''
* [[Augmented family|Augmented]] (''n'' = 3/2 = 1.5)
|-
* [[Passion family|Passion]] (''n'' = 5/3 = 1.{{overline|6}})
| [[Passion]] || 5/3 = 1.{{overline|6}} || 5/2 = 2.5
* [[Quintaleap family|Quintaleap]] (''n'' = 5/2 = 2.5)
|-
| [[Quintaleap]] || 5/2 = 2.5 || 5/3 = 1.{{overline|6}}
|}


== Compton (12&72) ==
== Compton (12&72) ==
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