Diarithmedia: Difference between revisions

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| Ratio = 25921/25920

| Name = diarithmedia

| Color name = 23oozzg3 bitwethozo-agu 3rd

| Comma = yes

}}

'''25921/25920''', the '''diarithmedia''', is a [[23-limit]] and 2.3.5.7.23-[[subgroup]] [[square superparticular]] ~~square-particular ratio~~ of about 0.067 [[cent]]s. It is the difference between [[161/160]] and [[162/161]], and between [[49/45]] and [[24/23]]2, and therefore tempering this comma out splits the syntonic comma, [[81/80]] into exact halves alongside 49/45. As a further consequence, it equates [[161/144]], the "arithmetic meantone" (being the arithmetic mean of [[9/8]] and [[10/9]]) with [[180/161]] and splits [[5/4]] in half, providing a way to use hemithirds without equating 9/8 and 10/9 together.

'''25921/25920''', the '''diarithmedia''', is a [[23-limit]] and 2.3.5.7.23-[[subgroup]] [[square superparticular]] comma of about 0.067 [[cent]]s. It is the difference between [[161/160]] and [[162/161]], and between [[49/45]] and ([[24/23]])2, and therefore tempering this comma out splits the syntonic comma, [[81/80]] into exact halves alongside 49/45. As a further consequence, it equates [[161/144]], the "arithmetic meantone" (being the arithmetic mean of [[9/8]] and [[10/9]]) with [[180/161]] and splits [[5/4]] in half, providing a way to use hemithirds without equating 9/8 and 10/9 together.

== Etymology ==

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* [[161/144]]

* [[Meantone]]

[[Category:Commas named for the intervals they stack]]

@@ Line 2: / Line 2: @@
 | Ratio = 25921/25920
 | Name = diarithmedia
+| Color name = 23oozzg3 <br> bitwethozo-agu 3rd
 | Comma = yes
 }}
-'''25921/25920''', the '''diarithmedia''', is a [[23-limit]] and 2.3.5.7.23-[[subgroup]] [[square superparticular]] square-particular ratio of about 0.067 [[cent]]s. It is the difference between [[161/160]] and [[162/161]], and between [[49/45]] and [[24/23]]<sup>2</sup>, and therefore tempering this comma out splits the syntonic comma, [[81/80]] into exact halves alongside 49/45. As a further consequence, it equates [[161/144]], the "arithmetic meantone" (being the arithmetic mean of [[9/8]] and [[10/9]]) with [[180/161]] and splits [[5/4]] in half, providing a way to use hemithirds without equating 9/8 and 10/9 together.
+'''25921/25920''', the '''diarithmedia''', is a [[23-limit]] and 2.3.5.7.23-[[subgroup]] [[square superparticular]] comma of about 0.067 [[cent]]s. It is the difference between [[161/160]] and [[162/161]], and between [[49/45]] and ([[24/23]])<sup>2</sup>, and therefore tempering this comma out splits the syntonic comma, [[81/80]] into exact halves alongside 49/45. As a further consequence, it equates [[161/144]], the "arithmetic meantone" (being the arithmetic mean of [[9/8]] and [[10/9]]) with [[180/161]] and splits [[5/4]] in half, providing a way to use hemithirds without equating 9/8 and 10/9 together.
 == Etymology ==
@@ Line 14: / Line 15: @@
 * [[161/144]]
 * [[Meantone]]
+[[Category:Commas named for the intervals they stack]]