135/112: Difference between revisions

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{{Infobox Interval

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

| Name = septimal wide minor third, marvel-ptolemaic minor third, aberschismic 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 ~~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''', 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]].

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.

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 ==

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[[Category:Second]]

[[Category:Augmented second]]

[[Category:~~Hemifamity~~]]

[[Category:Aberschismic]]

@@ Line 1: / Line 1: @@
 {{Infobox Interval
-| Name = septimal wide minor third, marvel-ptolemaic minor third, hemifamity augmented second
+| Name = septimal wide minor third, marvel-ptolemaic minor third, aberschismic 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 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''', 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]].
-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.
+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 ==
@@ Line 16: / Line 16: @@
 [[Category:Second]]
 [[Category:Augmented second]]
-[[Category:Hemifamity]]
+[[Category:Aberschismic]]