135/112: Difference between revisions

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{{Infobox Interval

~~| JI glyph =~~

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

~~| Ratio = 135/112~~

| Color name = ry2, ruyo 2nd

~~| Monzo = -4, 3, 1, -1~~

~~| Cents = 323.35281~~

| Name = septimal wide minor third, ~~<br> marvelous~~ minor third

| Color name =

~~| FJS name =~~

~~| Sound =~~

}}

'''135/112''', the '''septimal wide minor third''', or '''marvel-ptolemaic minor third''', is a [[7-limit]] interval that forms the difference between [[9/7]] and [[16/15]]. It 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 is functionally~~ a ~~type of augmented second~~.

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

* [[56/45]] – its fifth complement

* [[Gallery of just intervals]]

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

[[Category:Third]]

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

[[Category:Minor third]]

* [[~~Gallery of just intervals~~]]

[[Category:Second]]

[[Category:Augmented second]]

[[Category:Aberschismic]]

@@ Line 1: / Line 1: @@
 {{Infobox Interval
-| JI glyph =
+| Name = septimal wide minor third, marvel-ptolemaic minor third, hemifamity augmented second
-| Ratio = 135/112
+| Color name = ry2, ruyo 2nd
-| Monzo = -4, 3, 1, -1
-| Cents = 323.35281
-| Name = septimal wide minor third, <br> marvelous minor third
-| Color name =
-| FJS name =
-| Sound =
 }}
+'''135/112''', the '''septimal wide minor third''', or '''marvel-ptolemaic minor third''', is a [[7-limit]] interval that forms the difference between [[9/7]] and [[16/15]]. It 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 is functionally a type of augmented second.
+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
+* [[56/45]] – its fifth complement
+* [[Gallery of just intervals]]
-* [[224/135]] -- its octave complement
+[[Category:Third]]
-* [[56/45]]  -- its fifth complement
+[[Category:Minor third]]
-* [[Gallery of just intervals]]
+[[Category:Second]]
+[[Category:Augmented second]]
+[[Category:Aberschismic]]