135/112: Difference between revisions

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{{Infobox Interval

| Name = septimal wide minor third, ~~marvelous~~ minor third

| Name = septimal wide minor third, marvel-ptolemaic minor third, hemifamity augmented second

| Color name = ry2, ruyo 2nd

}}

'''135/112''', the '''septimal wide minor third''', or '''marvel-ptolemaic minor third''', is a [[7-limit]] interval that is sharp of the [[32/27|Pythagorean minor third]] by [[3645/3584]], i.e. a [[81/80|syntonic comma]] plus a [[225/224|marvel comma]]. This interval functionally doubles as a type of augmented second, sharp of the [[19683/16384|Pythagorean augmented second]] by [[5120/5103]]. This gives rise to the name '''hemifamity augmented second'''.

~~'''135/112''', the '''septimal wide minor third''', or '''marvelous minor third''', is a [[7-limit]]~~ interval ~~which~~ has the distinction of being almost half of a [[16/11]] ~~minor~~ fifth- in fact, a stack of two 135/112 differs from [[16/11]] by [[200704/200475]], a comma less than two cents in size. ~~As the octave complement of 224/135 this interval functionally doubles as a type of augmented second, nevertheless, because~~ of the relationship between 135/112 and 16/11, one can easily form a triad consisting of 1/~~1-135/112-16~~/11, to which one can then add [[135/77]] as a seventh.

This interval has the distinction of being almost half of a [[16/11]] semidiminished fifth – in fact, a stack of two 135/112's differs from [[16/11]] by [[200704/200475]], a comma less than two cents in size. Because of the relationship between 135/112 and 16/11, one can easily form a triad consisting of 1–135/112–16/11, to which one can then add [[135/77]] as a seventh.

== See also ==

* [[224/135]] – its octave complement

* [[224/135]] -- its octave complement

* [[56/45]] – its fifth complement

* [[56/45]] -- its fifth complement

* [[Gallery of just intervals]]

[[Category:Third]]

[[Category:Minor third]]

[[Category:Second]]

[[Category:Augmented second]]

[[Category:Hemifamity]]

@@ Line 1: / Line 1: @@
 {{Infobox Interval
-| Name = septimal wide minor third, marvelous minor third
+| Name = septimal wide minor third, marvel-ptolemaic minor third, hemifamity augmented second
 | Color name = ry2, ruyo 2nd
 }}
+'''135/112''', the '''septimal wide minor third''', or '''marvel-ptolemaic minor third''', is a [[7-limit]] interval that is sharp of the [[32/27|Pythagorean minor third]] by [[3645/3584]], i.e. a [[81/80|syntonic comma]] plus a [[225/224|marvel comma]]. This interval functionally doubles as a type of augmented second, sharp of the [[19683/16384|Pythagorean augmented second]] by [[5120/5103]]. This gives rise to the name '''hemifamity augmented second'''.
-'''135/112''', the '''septimal wide minor third''', or '''marvelous minor third''', is a [[7-limit]] interval which has the distinction of being almost half of a [[16/11]] minor fifth- in fact, a stack of two 135/112 differs from [[16/11]] by [[200704/200475]], a comma less than two cents in size.  As the octave complement of 224/135 this interval functionally doubles as a type of augmented second, nevertheless, because of the relationship between 135/112 and 16/11, one can easily form a triad consisting of 1/1-135/112-16/11, to which one can then add [[135/77]] as a seventh.
+This interval has the distinction of being almost half of a [[16/11]] semidiminished fifth – in fact, a stack of two 135/112's differs from [[16/11]] by [[200704/200475]], a comma less than two cents in size. Because of the relationship between 135/112 and 16/11, one can easily form a triad consisting of 1–135/112–16/11, to which one can then add [[135/77]] as a seventh.
 == See also ==
+* [[224/135]] – its octave complement
-* [[224/135]] -- its octave complement
+* [[56/45]] – its fifth complement
-* [[56/45]]  -- its fifth complement
 * [[Gallery of just intervals]]
 [[Category:Third]]
 [[Category:Minor third]]
+[[Category:Second]]
+[[Category:Augmented second]]
+[[Category:Hemifamity]]