Stretched and compressed tuning: Difference between revisions

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{{Interwiki

| en = Stretched and compressed tuning

| de = Gestreckte/gestauchte_Stimmung

}}

[[Tuning]]s do not necessarily need [[equave]]s to be tuned to their exact [[ratio]]s, and in some cases, equaves (most often [[octave]]s) 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). In '''compressed tuning''', also known as '''~~shrinked~~ tuning''' or '''shrunk tuning''', two notes an equivalence apart, whose fundamental frequencies theoretically have an exact ratio, are tuned slightly closer together (a compressed ~~or shrinked~~ equivalence).

[[Tuning]]s do not necessarily need [[equave]]s to be tuned to their exact [[ratio]]s, and in some cases, equaves (most often [[octave]]s) 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). In '''compressed tuning''', also known as '''squashed tuning''' or '''shrunk tuning''', two notes an equivalence apart, whose fundamental frequencies theoretically have an exact ratio, are tuned slightly closer together (a compressed equivalence).

The most common goal of stretching or compressing the octave is to improve the intonation of some intervals, such as [[harmonic]]s, without sacrificing the melodic shape or harmonic structure of a [[temperament|tempered]] tuning system. For example, [[19edo]] approximates ratios of 3, 5, 7, and 13 well, but tunes all of these harmonics flat, so it benefits from octave stretching. [[27edo]] approximates ratios of 3, 5, 7, and 13 well, but tunes these harmonics sharp, so it benefits from octave compression.

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* [[Slendro]]

* [[Pelog]]

* [[~~The~~ Riemann zeta function ~~and tuning~~#Optimal octave stretch|Zeta optimal octave stretch]]

* [[Riemann zeta function#Optimal octave stretch|Zeta optimal octave stretch]]

* [[Stretched harmonic series]]

[[Category:Tuning]]

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+{{Interwiki
+| en = Stretched and compressed tuning
+| de = Gestreckte/gestauchte_Stimmung
+}}
 {{Wikipedia|Stretched tuning}}
-[[Tuning]]s do not necessarily need [[equave]]s to be tuned to their exact [[ratio]]s, and in some cases, equaves (most often [[octave]]s) 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). In '''compressed tuning''', also known as '''shrinked tuning''' or '''shrunk tuning''', two notes an equivalence apart, whose fundamental frequencies theoretically have an exact ratio, are tuned slightly closer together (a compressed or shrinked equivalence).
+[[Tuning]]s do not necessarily need [[equave]]s to be tuned to their exact [[ratio]]s, and in some cases, equaves (most often [[octave]]s) 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). In '''compressed tuning''', also known as '''squashed tuning''' or '''shrunk tuning''', two notes an equivalence apart, whose fundamental frequencies theoretically have an exact ratio, are tuned slightly closer together (a compressed equivalence).
 The most common goal of stretching or compressing the octave is to improve the intonation of some intervals, such as [[harmonic]]s, without sacrificing the melodic shape or harmonic structure of a [[temperament|tempered]] tuning system. For example, [[19edo]] approximates ratios of 3, 5, 7, and 13 well, but tunes all of these harmonics flat, so it benefits from octave stretching. [[27edo]] approximates ratios of 3, 5, 7, and 13 well, but tunes these harmonics sharp, so it benefits from octave compression.
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 * [[Slendro]]
 * [[Pelog]]
-* [[The Riemann zeta function and tuning#Optimal octave stretch|Zeta optimal octave stretch]]
+* [[Riemann zeta function#Optimal octave stretch|Zeta optimal octave stretch]]
 * [[Stretched harmonic series]]
 [[Category:Tuning]]