User:Eufalesio/Enumeration: Difference between revisions

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Enumerations may be used to write approximations of JI chords, such as those appearing in [[Temperament|temperaments]], for example, the [[meantone]] major chord from [[31edo]] can be described as ~4:5:6 even if it is not exact, as it is the most plausible approximation, compared to the more exact but wildly disproportionate 840408126667725:1050985425614545:1256845381902341.

Just as enumerations can be used to model segments of the [[harmonic series]], the reciprocal of enumerations can be used to model segments of the [[subharmonic series]]. For example, the subharmonic chord with the intervals 8/7, 4/3, 8/5 is the octave inversion of [[4:5:6:7]], and while it ''can'' be written as [[60:70:84:105]], it is more intuitive to write it as 1/(7:6:5:4) [numbers in reverse order so that the reciprocals are ordered correctly, since higher subharmonics are lower in pitch], or as a shorthand, as /7:6:5:4. The reciprocal enumeration is spoken "over a, b c d..."

Just as enumerations can be used to model segments of the [[harmonic series]], the reciprocal of enumerations can be used to model segments of the [[subharmonic series]]. For example, the subharmonic chord with the intervals 8/7, 4/3, 8/5 is the octave inversion of [[4:5:6:7]], and while it ''can'' be written as [[60:70:84:105]], it is more intuitive to write it as 1/(7:6:5:4) [numbers in reverse order so that the reciprocals are ordered correctly, since higher subharmonics are lower in pitch], or as a shorthand, as /7:6:5:4. The reciprocal enumeration may be spoken "over a, b c d..."

== Examples ==

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 Enumerations may be used to write approximations of JI chords, such as those appearing in [[Temperament|temperaments]], for example, the [[meantone]] major chord from [[31edo]] can be described as ~4:5:6 even if it is not exact, as it is the most plausible approximation, compared to the more exact but wildly disproportionate 840408126667725:1050985425614545:1256845381902341.
-Just as enumerations can be used to model segments of the [[harmonic series]], the reciprocal of enumerations can be used to model segments of the [[subharmonic series]]. For example, the subharmonic chord with the intervals 8/7, 4/3, 8/5 is the octave inversion of [[4:5:6:7]], and while it ''can'' be written as [[60:70:84:105]], it is more intuitive to write it as 1/(7:6:5:4) [numbers in reverse order so that the reciprocals are ordered correctly, since higher subharmonics are lower in pitch], or as a shorthand, as /7:6:5:4. The reciprocal enumeration is spoken "over a, b c d..."
+Just as enumerations can be used to model segments of the [[harmonic series]], the reciprocal of enumerations can be used to model segments of the [[subharmonic series]]. For example, the subharmonic chord with the intervals 8/7, 4/3, 8/5 is the octave inversion of [[4:5:6:7]], and while it ''can'' be written as [[60:70:84:105]], it is more intuitive to write it as 1/(7:6:5:4) [numbers in reverse order so that the reciprocals are ordered correctly, since higher subharmonics are lower in pitch], or as a shorthand, as /7:6:5:4. The reciprocal enumeration may be spoken "over a, b c d..."
 == Examples ==