16/15: Difference between revisions

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 {{Infobox Interval
-| Icon =
+| Name = just diatonic semitone, classic(al) diatonic semitone, ptolemaic diatonic semitone
-| Ratio = 16/15
+| Comma = yes
-| Monzo = 4 -1 -1
-| Cents = 111.73129
-| Name = diatonic semitone, <br>classic minor second
 | Color name = g2, gu 2nd
-| FJS name = m2<sub>5</sub>
 | Sound = jid_16_15_pluck_adu_dr220.mp3
 }}
+{{Wikipedia|Semitone}}
+The [[5-limit]] [[superparticular]] interval '''16/15''' is the '''just diatonic semitone''', '''classic(al) diatonic semitone''' or '''ptolemaic diatonic semitone'''<ref>For reference, see [[5-limit]]. </ref>.
-The [[5-limit]] just '''diatonic semitone''' is the [[superparticular]] interval '''16/15''' – the difference between the major third [[5/4]] and the fourth [[4/3]], and between [[3/2]] and [[8/5]].
+It is the difference between:
+* the major second [[9/8]] and the minor third [[6/5]];
+* the major third [[5/4]] and the fourth [[4/3]];
+* the perfect fifth [[3/2]] and the minor sixth [[8/5]];
+* the major sixth [[5/3]] and the minor seventh [[16/9]];
+* the major seventh [[15/8]] and the perfect octave [[2/1]].
-When this ratio is taken as a comma to be tempered, it produces [[father]] temperament, where 4/3 and 5/4 are equated. In this temperament, major thirds and fifths become [[octave-inverses]] of each other.
+== Approximation ==
+/15 is very accurately approximated by [[43edo]] (4\43).
+== Temperaments ==
+When this ratio is taken as a [[comma]] to be [[tempering out|tempered out]], it produces [[father]] temperament, and lends itself the name '''father comma'''. In this [[exotemperament]], 4/3 and 5/4 are equated, and major thirds and fifths become [[octave complement]]s of each other. It is a [[Mersenne comma]].
+The following [[linear temperament]]s are [[generate]]d by a [[~]]16/15:
+* [[Vavoom]]
+* [[Stockhausenic]]
+In addition, this [[fractional-octave temperaments]] are generated by a ~16/15:
+* [[Quintosec]]
+{{todo|complete list}}
+Some [[11th-octave temperaments]] treat ~16/15 as the period, including [[hendecatonic]].
 == See also ==
 * [[15/8]] – its [[octave complement]]
 * [[45/32]] – its [[fifth complement]]
+* [[5/4]] – its [[fourth complement]]
+* [[256/243]] – the Pythagorean (3-limit) diatonic semitone
 * [[Gallery of just intervals]]
+* [[List of superparticular intervals]]
+== Notes ==
+<references/>
-[[Category:5-limit]]
-[[Category:Interval]]
-[[Category:Just interval]]
-[[Category:Ratio]]
-[[Category:Listen]]
 [[Category:Second]]
 [[Category:Semitone]]
-[[Category:Superparticular]]
+[[Category:Father]]
-[[Category:Subharmonic]]
+[[Category:Commas named after their interval size]]