POTE tuning: Difference between revisions

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POTE has practical advantages for tuning instruments constrained to pure octaves as part of a band targeting TE. You can set the absolute pitch reference for each instrument so that it agrees with the TE background for a target register. Guitars (or other fretted string instruments) can implement this within themselves by having the frets assuming pure octaves and the open strings following the TE stretch.

Psychoacoustics shows ~~(Terhardt's website was a good reference for this{{citation needed}})~~ that many bands are tuned according to stretched octaves even when the instruments are producing harmonic timbres. This might be with each instrument having a stretched scale, or high-pitched instruments having a slightly sharp pitch reference. The magnitude of this stretch often swamps the optimal stretch for TE (which can be in either direction). So, if you are not going to observe the TE stretch, you might as well simplify it out. There are other reasons for putting instruments deliberately out of tune, for example solo instruments can be tuned slightly sharp to make them stand out. This leads to an upward drift of pitch reference in European orchestras: pianos are tuned slightly sharp to make them sound bright, and then the orchestra sharpens up to follow them.

Psychoacoustics shows that many bands are tuned according to stretched octaves even when the instruments are producing harmonic timbres ([https://terhardt.userweb.mwn.de/ter/top/scalestretch.html Terhardt: Stretch of the musical tone scale]). This might be with each instrument having a stretched scale, or high-pitched instruments having a slightly sharp pitch reference. The magnitude of this stretch often swamps the optimal stretch for TE (which can be in either direction). So, if you are not going to observe the TE stretch, you might as well simplify it out. There are other reasons for putting instruments deliberately out of tune, for example solo instruments can be tuned slightly sharp to make them stand out. This leads to an upward drift of pitch reference in European orchestras: pianos are tuned slightly sharp to make them sound bright, and then the orchestra sharpens up to follow them.

== Approximate Kees optimality ==

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 POTE has practical advantages for tuning instruments constrained to pure octaves as part of a band targeting TE. You can set the absolute pitch reference for each instrument so that it agrees with the TE background for a target register. Guitars (or other fretted string instruments) can implement this within themselves by having the frets assuming pure octaves and the open strings following the TE stretch.
-Psychoacoustics shows (Terhardt's website was a good reference for this{{citation needed}}) that many bands are tuned according to stretched octaves even when the instruments are producing harmonic timbres. This might be with each instrument having a stretched scale, or high-pitched instruments having a slightly sharp pitch reference. The magnitude of this stretch often swamps the optimal stretch for TE (which can be in either direction). So, if you are not going to observe the TE stretch, you might as well simplify it out. There are other reasons for putting instruments deliberately out of tune, for example solo instruments can be tuned slightly sharp to make them stand out. This leads to an upward drift of pitch reference in European orchestras: pianos are tuned slightly sharp to make them sound bright, and then the orchestra sharpens up to follow them.
+Psychoacoustics shows that many bands are tuned according to stretched octaves even when the instruments are producing harmonic timbres ([https://terhardt.userweb.mwn.de/ter/top/scalestretch.html Terhardt: Stretch of the musical tone scale]). This might be with each instrument having a stretched scale, or high-pitched instruments having a slightly sharp pitch reference. The magnitude of this stretch often swamps the optimal stretch for TE (which can be in either direction). So, if you are not going to observe the TE stretch, you might as well simplify it out. There are other reasons for putting instruments deliberately out of tune, for example solo instruments can be tuned slightly sharp to make them stand out. This leads to an upward drift of pitch reference in European orchestras: pianos are tuned slightly sharp to make them sound bright, and then the orchestra sharpens up to follow them.
 == Approximate Kees optimality ==