Father–3 equivalence continuum: Difference between revisions

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~~{{See also| Father–3 equivalence continuum/Godtone's approach }}~~

The '''father–3 equivalence continuum''' is a [[equivalence continuum|continuum]] of [[5-limit]] [[regular temperament|temperaments]] which equate a number of [[16/15|classical diatonic semitones (16/15)]] with the [[32/27|Pythagorean minor third (32/27)]].

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Godtone has conceptualized this continuum as ''augmented–chromatic equivalence continuum'', where ''chromatic'' refers to the classical version of the semitone. See [[{{PAGENAME}}/Godtone's approach]].

Others prefer conceptualizing this continuum in terms of {{nowrap|''k'' {{=}} {{sfrac|1|''n'' − 2}}}} such that temperaments satisfy {{nowrap|(25/24)<sup>''k''</sup> {{=}} 16/15}}. This gives rise to the name ''chromatic–diatonic equivalence continuum'', where both ''chromatic'' and ''diatonic'' refer to the classical versions of semitones. The just value of ''k'' is approximately 1.58097…

Others prefer conceptualizing this continuum in terms of {{nowrap| ''k'' {{=}} {{sfrac|1|''n'' − 2}} }} such that temperaments satisfy {{nowrap|(25/24)<sup>''k''</sup> {{=}} 16/15}}. This gives rise to the name ''chromatic–diatonic equivalence continuum'', where both ''chromatic'' and ''diatonic'' refer to the classical versions of semitones. The just value of ''k'' is approximately 1.58097…

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-{{See also| Father–3 equivalence continuum/Godtone's approach }}
 The '''father–3 equivalence continuum''' is a [[equivalence continuum|continuum]] of [[5-limit]] [[regular temperament|temperaments]] which equate a number of [[16/15|classical diatonic semitones (16/15)]] with the [[32/27|Pythagorean minor third (32/27)]].
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 Godtone has conceptualized this continuum as ''augmented–chromatic equivalence continuum'', where ''chromatic'' refers to the classical version of the semitone. See [[{{PAGENAME}}/Godtone's approach]].
-Others prefer conceptualizing this continuum in terms of {{nowrap|''k'' {{=}} {{sfrac|1|''n'' − 2}}}} such that temperaments satisfy {{nowrap|(25/24)<sup>''k''</sup> {{=}} 16/15}}. This gives rise to the name ''chromatic–diatonic equivalence continuum'', where both ''chromatic'' and ''diatonic'' refer to the classical versions of semitones. The just value of ''k'' is approximately 1.58097…
+Others prefer conceptualizing this continuum in terms of {{nowrap| ''k'' {{=}} {{sfrac|1|''n'' − 2}} }} such that temperaments satisfy {{nowrap|(25/24)<sup>''k''</sup> {{=}} 16/15}}. This gives rise to the name ''chromatic–diatonic equivalence continuum'', where both ''chromatic'' and ''diatonic'' refer to the classical versions of semitones. The just value of ''k'' is approximately 1.58097…
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