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

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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. 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).

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]] 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.

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.

Optimal octave stretches measured by [[path-based goodness]] can be found on that page.

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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. 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''', two notes an equivalence apart, whose fundamental frequencies theoretically have an exact ratio, are tuned slightly closer together (a compressed or shrinked equivalence).
+{{interwiki
+| de = Gestreckte/gestauchte_Stimmung
+| en = Stretched_and_compressed_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).
-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]] 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.
+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.
 Optimal octave stretches measured by [[path-based goodness]] can be found on that page.