POTE tuning: Difference between revisions

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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.

== Weaknesses ==

* POTE tuning inherits problems of TE in being chosen for mathematical simplicity rather than a sound psychoacoustic basis.

* Like [[Kees height]], POTE agrees with TE for arbitrarily small intervals, which means it puts less emphasis on actually audible intervals, particularly those larger than an octave. This tendency is mediated by [[Constrained_tuning#CTWE_tuning|Constrained Tenney–Weil–Euclidean tuning]]

* Something must be lost by not tempering the octaves

== Approximate Kees optimality ==

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 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.
+== Weaknesses ==
+* POTE tuning inherits problems of TE in being chosen for mathematical simplicity rather than a sound psychoacoustic basis.
+* Like [[Kees height]], POTE agrees with TE for arbitrarily small intervals, which means it puts less emphasis on actually audible intervals, particularly those larger than an octave.  This tendency is mediated by [[Constrained_tuning#CTWE_tuning|Constrained Tenney–Weil–Euclidean tuning]]
+* Something must be lost by not tempering the octaves
 == Approximate Kees optimality ==