Stretched and compressed tuning: Difference between revisions

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[[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.

[[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 narrowed tuning, two notes an equivalence apart, whose fundamental frequencies theoretically have an exact ratio, are tuned slightly closer together (a compressed or narrowed equivalence).

~~In '''stretched~~ tuning~~'''~~, ~~two notes an~~ [[~~equivalence~~]] ~~apart~~, ~~whose fundamental frequencies theoretically have an exact ratio~~, ~~are tuned slightly farther apart (~~a ~~stretched equivalence).~~

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

~~In '''compressed tuning''', also known~~ as ~~narrowed tuning~~, ~~two notes an equivalence apart~~, ~~whose fundamental frequencies theoretically have an exact ratio~~, ~~are tuned slightly closer together (a compressed or narrowed equivalence)~~.

== Inharmonicity compensation for string instruments ==

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The significance of the match is a point of debate. For some, the match but shifts the problem from the timbre to the tuning systems, so no stretch or less stretch than the timbre will be alright. However, with compressed-octave tunings, the discrepancy between our compressed octave and the timbre octave will be larger. For that reason, compressed-octave tunings tend to sound more out of tune. Some would go so far to say that they should be avoided no matter what other reasons there may be going for them.

~~== Improving the approximation quality to JI ==~~

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

== See also ==

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 {{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.
+[[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 narrowed tuning, two notes an equivalence apart, whose fundamental frequencies theoretically have an exact ratio, are tuned slightly closer together (a compressed or narrowed equivalence).
-In '''stretched tuning''', two notes an [[equivalence]] apart, whose fundamental frequencies theoretically have an exact ratio, are tuned slightly farther apart (a stretched equivalence).
+The most common goal of stretching or compressing the octave is to improve the intonation of some intervals, such as harmonics, without sacrificing the melodic shape or harmonic structure of the tuning system. For example, [[19edo]] benefits from a stretch as it tunes harmonics 3, 5, 7, and 13 all flat. The stretch makes these harmonics less flat. 27edo benefits from a compression as it tunes harmonics 3, 5, 7, and 13 all sharp. The compression makes these harmonics less sharp.
-In '''compressed tuning''', also known as narrowed tuning, two notes an equivalence apart, whose fundamental frequencies theoretically have an exact ratio, are tuned slightly closer together (a compressed or narrowed equivalence).
 == Inharmonicity compensation for string instruments ==
@@ Line 10: / Line 8: @@
 The significance of the match is a point of debate. For some, the match but shifts the problem from the timbre to the tuning systems, so no stretch or less stretch than the timbre will be alright. However, with compressed-octave tunings, the discrepancy between our compressed octave and the timbre octave will be larger. For that reason, compressed-octave tunings tend to sound more out of tune. Some would go so far to say that they should be avoided no matter what other reasons there may be going for them.
-== Improving the approximation quality to JI ==
-The most common goal of stretching or compressing the octave is to improve the intonation of some intervals, such as harmonics, without sacrificing the melodic shape or harmonic structure of the tuning system. For example, [[19edo]] benefits from a stretch as it tunes harmonics 3, 5, 7, and 13 all flat. The stretch makes these harmonics less flat. 27edo benefits from a compression as it tunes harmonics 3, 5, 7, and 13 all sharp. The compression makes these harmonics less sharp.
 == See also ==