Halftone: Difference between revisions

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[[File:halftone6.wav|Halftone[6] example in 16edf and 4<nowiki>|</nowiki>1 mode]]

'''Halftone''' is a [[nonoctave]] (fifth-repeating) [[regular temperament]] in the 3/2.5/2.7/2 fractional subgroup that tempers out 9604/9375. It could be used as a harmonic basis for "1/2 prime" (3/2.5/2.7/2.11/2.13/2 etc.) systems with the equivalence as [[3/2]], similar to [[meantone]] for full prime-limit systems with the equivalence as [[2/1]] and [[BPS]] for no-twos systems with the equivalence as [[3/1]]. Halftone temperament can be extended to the 11-limit (3/2.5/2.7/2.11/2) by additionally tempering out 1232/1215, the difference between [[15/14]] and [[88/81]] (the fifth-reduction of 11/2). Small [[EDF]]s that [[support]] halftone with relatively low error include [[11edf]], [[16edf]], [[17edf]] (not in the patent val), and [[23edf]] (not in the patent val). 11edf particularly is an interesting case because it is also an approximation of [[19edo]], which allows for playing both meantone and halftone music.

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== Interval chain ==

== Scales ==

{|class="wikitable"

|-

|}

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+[[File:halftone6.wav|Halftone[6] example in 16edf and 4<nowiki>|</nowiki>1 mode]]
 '''Halftone''' is a [[nonoctave]] (fifth-repeating) [[regular temperament]] in the 3/2.5/2.7/2 fractional subgroup that tempers out 9604/9375. It could be used as a harmonic basis for "1/2 prime" (3/2.5/2.7/2.11/2.13/2 etc.) systems with the equivalence as [[3/2]], similar to [[meantone]] for full prime-limit systems with the equivalence as [[2/1]] and [[BPS]] for no-twos systems with the equivalence as [[3/1]]. Halftone temperament can be extended to the 11-limit (3/2.5/2.7/2.11/2) by additionally tempering out 1232/1215, the difference between [[15/14]] and [[88/81]] (the fifth-reduction of 11/2). Small [[EDF]]s that [[support]] halftone with relatively low error include [[11edf]], [[16edf]], [[17edf]] (not in the patent val), and [[23edf]] (not in the patent val). 11edf particularly is an interesting case because it is also an approximation of [[19edo]], which allows for playing both meantone and halftone music.
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 == Interval chain ==
 == Scales ==
+{|class="wikitable"
+|-
+|}