Stretched and compressed tuning: Difference between revisions

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

~~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~~]]).

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.

~~== In 12edo ==~~

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

~~Stretched tuning is used even outside of a xenharmonic context. Most acoustic and some electric pianos have [[overtone]]s which do not exactly line up with the~~ [[~~harmonic series]], so stretched [[octave~~]]~~s are usually used to compensate~~.

== ~~In xenharmonic music~~ ==

== Inharmonicity compensation for string instruments ==

~~Within a xenharmonic context~~, stretched or compressed ~~tuning may be used to reduce~~ the [[harmonic ~~entropy~~]] ~~of a scale without sacrificing its melodic shape~~, ~~or to achieve other artistic goals~~.

In general, stretched tunings detune intervals in the same way as compressed tunings do, so for instance a 5{{c}} compressed octave should sound as out-of-tune as a 5{{c}} stretched octave. On mechanoacoustic instruments, in particular string instruments, that is not true, as the overtones of the strings tend slightly sharp from their ideal natural harmonics and do not exactly line up with the [[harmonic series]] (especially on spinet pianos with their rather short strings). Because the octave is the most significant partial on the strings, by stretching the octaves we can better match our tuning systems with the timbre.

~~Examples include (~~but ~~are not limited~~ to):

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, with some going so far to say that octave compression should be avoided no matter what other reasons there may be going for them.

* [[23edo and octave ~~stretching]]~~

* Compressed [[27edo]]

== See also ==

* [[~~Musical cells~~]]

* [[Slendro]]

* [[Pelog]]

* [[The Riemann zeta function and tuning#Optimal octave stretch|~~Optimal~~ octave stretch~~]] (zeta stretch)~~

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

** [[5- to 8-tone scales in zeta stretched 15edo]]

* [[Stretched harmonic series]]

[[Category:Tuning]]

@@ Line 1: / Line 1: @@
 {{Wikipedia|Stretched tuning}}
-In stretched tuning, two notes an [[equivalence]] apart, whose fundamental frequencies theoretically have an exact ratio, are tuned slightly farther apart (a stretched [[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).
-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]]).
+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.
-== In 12edo ==
+Optimal octave stretches measured by [[path-based goodness]] can be found on that page.
-Stretched tuning is used even outside of a xenharmonic context. Most acoustic and some electric pianos have [[overtone]]s which do not exactly line up with the [[harmonic series]], so stretched [[octave]]s are usually used to compensate.
-== In xenharmonic music ==
+== Inharmonicity compensation for string instruments ==
-Within a xenharmonic context, stretched or compressed tuning may be used to reduce the [[harmonic entropy]] of a scale without sacrificing its melodic shape, or to achieve other artistic goals.
+In general, stretched tunings detune intervals in the same way as compressed tunings do, so for instance a 5{{c}} compressed octave should sound as out-of-tune as a 5{{c}} stretched octave. On mechanoacoustic instruments, in particular string instruments, that is not true, as the overtones of the strings tend slightly sharp from their ideal natural harmonics and do not exactly line up with the [[harmonic series]] (especially on spinet pianos with their rather short strings). Because the octave is the most significant partial on the strings, by stretching the octaves we can better match our tuning systems with the timbre.
-Examples include (but are not limited to):
+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, with some going so far to say that octave compression should be avoided no matter what other reasons there may be going for them.
-* [[23edo and octave stretching]]
-* Compressed [[27edo]]
+== See also ==
-* [[Musical cells]]
+* [[Slendro]]
 * [[Pelog]]
-* [[The Riemann zeta function and tuning#Optimal octave stretch|Optimal octave stretch]] (zeta stretch)
+* [[The Riemann zeta function and tuning#Optimal octave stretch|Zeta optimal octave stretch]]
-** [[5- to 8-tone scales in zeta stretched 15edo]]
 * [[Stretched harmonic series]]
 [[Category:Tuning]]