Stretched and compressed tuning: Difference between revisions
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We need to alert the readers that stretch and compression aren't symmetric and that it's a concern in all tunings, not limited to 12edo. Expand the other section too |
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{{Wikipedia|Stretched tuning}} | {{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 '''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 '''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 == | ||
In general, stretched tunings detune intervals in the same way as compressed tunings do, so for instance a 5-cent compressed octave should sound as out-of-tune as a 5-cent stretched octave. On mechanoacoustic instruments, in particular string instruments, that is not true, as the overtones of the strings tend slighly 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. | |||
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 == | |||
* [[23edo and octave stretching]] | * [[23edo and octave stretching]] | ||
* [[Musical cells]] | * [[Musical cells]] | ||
* [[Slendro]] | * [[Slendro]] | ||
Revision as of 16:42, 15 January 2025
Tunings do not necessarily need equaves to be tuned to their exact ratios, and in some cases, equaves (most often 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).
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
In general, stretched tunings detune intervals in the same way as compressed tunings do, so for instance a 5-cent compressed octave should sound as out-of-tune as a 5-cent stretched octave. On mechanoacoustic instruments, in particular string instruments, that is not true, as the overtones of the strings tend slighly 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.
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.