135/112: Difference between revisions

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{{Infobox Interval

~~| Ratio = 135/112~~

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

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

| Color name = ry2, ruyo 2nd

~~| Cents = 323.35281~~

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

| Color name =

~~| FJS name =~~

~~| Sound =~~

}}

'''135/112''', conventionally known as 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 an [[3645/3584|aberdiesis (3645/3584)]], i.e. a [[81/80|syntonic comma (81/80)]] plus a [[225/224|marvel comma (225/224)]]. This interval functionally doubles as a type of augmented second, sharp of the [[19683/16384|Pythagorean augmented second (19683/16384)]] by an [[5120/5103|aberschisma (5120/5103)]]. This gives rise to the more precise name '''aberschismic augmented second'''. In fact it forms the difference between [[9/7]] and [[16/15]].

~~'''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|undecimal semidiminished fifth (16/11)]] – in fact, a stack of two 135/112's differs from [[16/11]] by a [[200704/200475|"reef comma" (200704/200475)]], which is 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:7-limit]]~~

[[Category:Third]]

[[Category:Minor third]]

[[Category:Second]]

~~{{todo|add color name}}~~

[[Category:Augmented second]]

[[Category:Aberschismic]]

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 {{Infobox Interval
-| Ratio = 135/112
+| Name = septimal wide minor third, marvel-ptolemaic minor third, aberschismic augmented second
-| Monzo = -4, 3, 1, -1
+| Color name = ry2, ruyo 2nd
-| Cents = 323.35281
-| Name = septimal wide minor third, <br> marvelous minor third
-| Color name =
-| FJS name =
-| Sound =
 }}
+'''135/112''', conventionally known as 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 an [[3645/3584|aberdiesis (3645/3584)]], i.e. a [[81/80|syntonic comma (81/80)]] plus a [[225/224|marvel comma (225/224)]]. This interval functionally doubles as a type of augmented second, sharp of the [[19683/16384|Pythagorean augmented second (19683/16384)]] by an [[5120/5103|aberschisma (5120/5103)]]. This gives rise to the more precise name '''aberschismic augmented second'''. In fact it forms the difference between [[9/7]] and [[16/15]].
-'''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|undecimal semidiminished fifth (16/11)]] – in fact, a stack of two <u>135/112</u>'s differs from [[16/11]] by a [[200704/200475|"reef comma" (200704/200475)]], which is less than two cents in size. Because of the relationship between <u>135/112</u> 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:7-limit]]
 [[Category:Third]]
 [[Category:Minor third]]
+[[Category:Second]]
-{{todo|add color name}}
+[[Category:Augmented second]]
+[[Category:Aberschismic]]