Stretched and compressed tuning: Difference between revisions

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 {{Wikipedia|Stretched tuning}}
-[[Equal divisions of the octave]] tunings do not necessarily need octaves to be exactly 2:1, and in some cases where
+Tunings do not necessarily need equaves to be tuned to their exact ratios, and in some cases, octaves are best stretched or compressed.
 In stretched tuning, two notes an [[equivalence]] apart, whose fundamental frequencies theoretically have an exact ratio, are tuned slightly farther apart (a stretched [[equivalence]]).
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 == In 12edo ==
-Stretched tuning is used even outside of a xenharmonic context. Most acoustic pianos have [[overtone]]s which do not exactly line up with the [[harmonic series]], so stretched [[octave]]s are usually used to compensate.
+Stretched tuning is used even outside of a xenharmonic context. Perhaps the most notable instance of this is in the case of acoustic pianos. Since a piano's [[overtone]]s tend slightly sharp from their ideal natural harmonics and do not exactly line up with the [[harmonic series]], stretched [[octave]]s are usually used to compensate.
 == In xenharmonic music ==