99/80: Difference between revisions

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{{interwiki

| ro = 99/80 (ro)

| de =

| es =

| ja =

| ko =

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{{Infobox Interval

| Name = undecimal submajor third

| Name = undecimal submajor third,<br>cake third

| Color name = logu 3rd, 1og3

}}

'''99/80''', the '''undecimal submajor third''', also known as the '''cake third''', is [[45/44]] flat of the [[81/64|Pythagorean major third (81/64)]], and also [[100/99]] flat of the [[5/4|classical major third (5/4)]], while being [[8019/8000]] sharp of the [[100/81|grave major third (100/81)]]. The alternate name, ''cake third'', refers to the fact that tempering out 45/44, the cake comma, leads to a temperament that slices 99/80 exactly in half (into two [[11/10]]'s). It arises in [[just intonation]] as the sum of a [[9/8]] whole tone and an [[11/10]] submajor second. It is also [[2080/2079]] flat of [[26/21]].

~~'''99/80''', the '''undecimal submajor third''',~~ is exactly [[8/7]] flat of the very accurate half-octave of [[99/70]], and so is accurately represented in any even edo with a good ~~7, of which the first truly good example is~~ [[~~26edo]].~~

== Approximation ==

This interval is exactly [[8/7]] flat of the very accurate half-octave of [[99/70]], and so is accurately represented in any even edo with a good [[7/1|7]], such as [[26edo]].

~~It is the sum of a [[9~~/8]] ~~whole tone and an [[11/10]] submajor second~~, ~~and so is~~ [[~~8019/8000]] sharp of [[100/81~~]].

== See also ==

* [[160/99]] – its [[octave complement]]

* [[40/33]] – its [[fifth complement]]

* [[320/297]] – its [[fourth complement]]

* [[Gallery of just intervals]]

[[Category:Third]]

[[Category:Submajor third]]

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+{{interwiki
+| ro = 99/80 (ro)
+| de =
+| es =
+| ja =
+| ko =
+}}
 {{Infobox Interval
-| Name = undecimal submajor third
+| Name = undecimal submajor third,<br>cake third
 | Color name = logu 3rd, 1og3
 }}
+'''99/80''', the '''undecimal submajor third''', also known as the '''cake third''', is [[45/44]] flat of the [[81/64|Pythagorean major third (81/64)]], and also [[100/99]] flat of the [[5/4|classical major third (5/4)]], while being [[8019/8000]] sharp of the [[100/81|grave major third (100/81)]]. The alternate name, ''cake third'', refers to the fact that tempering out 45/44, the cake comma, leads to a temperament that slices 99/80 exactly in half (into two [[11/10]]'s). It arises in [[just intonation]] as the sum of a [[9/8]] whole tone and an [[11/10]] submajor second. It is also [[2080/2079]] flat of [[26/21]].
-'''99/80''', the '''undecimal submajor third''', is exactly [[8/7]] flat of the very accurate half-octave of [[99/70]], and so is accurately represented in any even edo with a good 7, of which the first truly good example is [[26edo]].
+== Approximation ==
+This interval is exactly [[8/7]] flat of the very accurate half-octave of [[99/70]], and so is accurately represented in any even edo with a good [[7/1|7]], such as [[26edo]].
-It is the sum of a [[9/8]] whole tone and an [[11/10]] submajor second, and so is [[8019/8000]] sharp of [[100/81]].
+== See also ==
+* [[160/99]] – its [[octave complement]]
+* [[40/33]] – its [[fifth complement]]
+* [[320/297]] – its [[fourth complement]]
+* [[Gallery of just intervals]]
 [[Category:Third]]
 [[Category:Submajor third]]