Height: Difference between revisions

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Height functions can also be put on the points of [http://planetmath.org/encyclopedia/QuasiProjectiveVariety.html projective varieties]. Since [[abstract regular temperament]]s can be identified with rational points on [http://en.wikipedia.org/wiki/Grassmannian Grassmann varieties], complexity measures of regular temperaments are also height functions.

== History ==

The concept of height was introduced to xenharmonics by [[Gene Ward Smith]] in 2001<ref>https://yahootuninggroupsultimatebackup.github.io/tuning/topicId_31418#31488</ref>; it comes from the mathematical field of number theory (for more information, see [[Wikipedia:Height_function|height function]]). It is not to be confused with the musical notion of [[Wikipedia:Pitch_(music)#Theories_of_pitch_perception|''pitch height'' (as opposed to ''pitch chroma'')]]<ref>Though it has also been used to refer to the size of an interval in cents. On page 23 of https://www.plainsound.org/pdfs/JC&ToH.pdf, Tenney writes: "The one-dimensional continuum of pitch-height (i.e. 'pitch' as ordinarily defined)", and graphs it ''as opposed to'' his concept of "harmonic distance", which was ironically the first measurement named by Gene Ward Smith as a "height": "Tenney height".</ref>.

== See also ==

* [[Commas by taxicab distance]]

== References ==

[[Category:Theory]]

@@ Line 85: / Line 85: @@
 Height functions can also be put on the points of [http://planetmath.org/encyclopedia/QuasiProjectiveVariety.html projective varieties]. Since [[abstract regular temperament]]s can be identified with rational points on [http://en.wikipedia.org/wiki/Grassmannian Grassmann varieties], complexity measures of regular temperaments are also height functions.
+== History ==
+The concept of height was introduced to xenharmonics by [[Gene Ward Smith]] in 2001<ref>https://yahootuninggroupsultimatebackup.github.io/tuning/topicId_31418#31488</ref>; it comes from the mathematical field of number theory (for more information, see [[Wikipedia:Height_function|height function]]). It is not to be confused with the musical notion of [[Wikipedia:Pitch_(music)#Theories_of_pitch_perception|''pitch height'' (as opposed to ''pitch chroma'')]]<ref>Though it has also been used to refer to the size of an interval in cents. On page 23 of https://www.plainsound.org/pdfs/JC&ToH.pdf, Tenney writes: "The one-dimensional continuum of pitch-height (i.e. 'pitch' as ordinarily defined)", and graphs it ''as opposed to'' his concept of "harmonic distance", which was ironically the first measurement named by Gene Ward Smith as a "height": "Tenney height".</ref>.
 == See also ==
 * [[Commas by taxicab distance]]
+== References ==
+<references/>
 [[Category:Theory]]