99/80: Difference between revisions

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'''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''', also known as the '''cake 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]]. It is also [[100~~/99]] ~~flat of [[5/4]]. 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).~~

== 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 ==

* [[26edo]]

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

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

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+'''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''', also known as the '''cake 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]]. It is also [[100/99]] flat of [[5/4]]. 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).
+== 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 ==
-* [[26edo]]
 * [[160/99]] – its [[octave complement]]
 * [[40/33]] – its [[fifth complement]]