Misty: Difference between revisions

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Misty entails a mildly sharp perfect fifth such that six of them octave reduced (i.e. an augmented fourth) is close in size to [[10/7]], which gives rise to the [[7-limit]] [[extension]] where it tempers out [[5120/5103]]. This implies the [[5/4]] is split into two equal parts each for [[28/25]], tempering out [[3136/3125]], and that [[63/50]] is mapped to the 1/3-octave period, tempering out [[250047/250000]].

It is easy to extend misty to the no-11 no-13 [[19-limit]], where it merges [[16/15]] with [[17/16]], [[18/17]] with [[19/18]], and [[20/19]] with [[21/20]], tempering out [[256/255]] ({{S|16}}), [[324/323]] {{S|18}}, and [[400/399]] ({{S|20}}). This lowers the overall accuracy, but supplies more harmonic resources. Tunings for misty include [[87edo]], [[99edo]] and [[111edo]].

It is easy to extend misty to the no-11 no-13 [[19-limit]], where it merges [[16/15]] with [[17/16]], [[18/17]] with [[19/18]], and [[20/19]] with [[21/20]], tempering out [[256/255]] ({{S|16}}), [[324/323]] ({{S|18}}), and [[400/399]] ({{S|20}}). This lowers the overall accuracy, but supplies more harmonic resources. Tunings for misty include [[87edo]], [[99edo]] and [[111edo]].

See [[Misty family #Misty]] and [[Misty family #Septimal misty|#Septimal misty]] for technical data. See [[Misty extensions]] for a discussion on 11- and 13-limit extensions.

See [[Misty family #Misty]] and [[Misty family #Septimal misty|#Septimal misty]] for technical data. See [[Misty extensions]] for a discussion on [[11-limit|11-]] and [[13-limit]] extensions.

== Interval chain ==

@@ Line 15: / Line 15: @@
 Misty entails a mildly sharp perfect fifth such that six of them octave reduced (i.e. an augmented fourth) is close in size to [[10/7]], which gives rise to the [[7-limit]] [[extension]] where it tempers out [[5120/5103]]. This implies the [[5/4]] is split into two equal parts each for [[28/25]], tempering out [[3136/3125]], and that [[63/50]] is mapped to the 1/3-octave period, tempering out [[250047/250000]].
-It is easy to extend misty to the no-11 no-13 [[19-limit]], where it merges [[16/15]] with [[17/16]], [[18/17]] with [[19/18]], and [[20/19]] with [[21/20]], tempering out [[256/255]] ({{S|16}}), [[324/323]] {{S|18}}, and [[400/399]] ({{S|20}}). This lowers the overall accuracy, but supplies more harmonic resources. Tunings for misty include [[87edo]], [[99edo]] and [[111edo]].
+It is easy to extend misty to the no-11 no-13 [[19-limit]], where it merges [[16/15]] with [[17/16]], [[18/17]] with [[19/18]], and [[20/19]] with [[21/20]], tempering out [[256/255]] ({{S|16}}), [[324/323]] ({{S|18}}), and [[400/399]] ({{S|20}}). This lowers the overall accuracy, but supplies more harmonic resources. Tunings for misty include [[87edo]], [[99edo]] and [[111edo]].
-See [[Misty family #Misty]] and [[Misty family #Septimal misty|#Septimal misty]] for technical data. See [[Misty extensions]] for a discussion on 11- and 13-limit extensions.
+See [[Misty family #Misty]] and [[Misty family #Septimal misty|#Septimal misty]] for technical data. See [[Misty extensions]] for a discussion on [[11-limit|11-]] and [[13-limit]] extensions.
 == Interval chain ==