9801/9800: Difference between revisions

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'''9801/9800''', the '''kalisma''', sometimes described as ''Gauss' comma'', is an [[11-limit]] [[~~unnoticeable~~ comma]] measuring about 0.18{{cent}}. It is the smallest 11-limit [[superparticular]] interval.

'''9801/9800''', the '''kalisma''', sometimes described as ''Gauss' comma'', is an [[unnoticeable comma|unnoticeable]] [[11-limit]] [[comma]] measuring about 0.18{{cent}}. It is the smallest 11-limit [[superparticular]] interval.

It can be described as the difference between [[99/98]] and [[100/99]], and between [[99/70]] and its octave complement, [[140/99]]. It is also the difference between [[245/243]] and [[121/120]], and a stack of two 11/7's and 81/80 against 5/2~~. Tempering it out also means that [[10/9]] and [[11/7]] are 600 cents apart, as well as are [[11/10]] and [[14/9]]~~.

It can be described as the difference between [[99/98]] and [[100/99]], and between [[99/70]] and its octave complement, [[140/99]]. It is also the difference between [[245/243]] and [[121/120]], and a stack of two 11/7's and 81/80 against 5/2.

It factors into the two smallest 13-limit superparticular commas: 9801/9800 = 10648/10647 × 123201/123200.

It factors into the two smallest 13-limit superparticular commas: 9801/9800 = ([[10648/10647]])([[123201/123200]]).

== Temperaments ==

Tempering it out leads to the '''kalismic temperament''', which splits the [[octave]] into two equal parts, each representing 99/70~140/99. Odd-numbered edos cannot temper it out. See [[Rank-4 temperament #Kalismic (9801/9800)]] for some technical details.

[[Tempering out]] this comma leads to the '''kalismic temperament''', which splits the [[octave]] into two equal parts, each representing 99/70~140/99. Tempering it out also means that [[10/9]] and [[11/7]] are 1/2-octave apart, as well as are [[11/10]] and [[14/9]]. Odd-numbered edos cannot temper it out. See [[Rank-4 temperament #Kalismic (9801/9800)]] for some technical details. See [[Kalismic temperaments]] for a collection of rank-3 temperaments where it is tempered out.

== Etymology ==

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== See also ==

* [[Rank-4 temperament #Kalismic (9801/9800)]]

* [[Kalismic temperaments]], a collection of rank-3 temperaments where it is tempered out

* [[List of superparticular intervals]]

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[[Category:Kalismic]]

[[Category:Commas named by translating something into another language]]

[[Category:Commas named after ~~individuals~~]]

[[Category:Commas named after mathematicians]]

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 }}
-'''9801/9800''', the '''kalisma''', sometimes described as ''Gauss' comma'', is an [[11-limit]] [[unnoticeable comma]] measuring about 0.18{{cent}}. It is the smallest 11-limit [[superparticular]] interval.
+'''9801/9800''', the '''kalisma''', sometimes described as ''Gauss' comma'', is an [[unnoticeable comma|unnoticeable]] [[11-limit]] [[comma]] measuring about 0.18{{cent}}. It is the smallest 11-limit [[superparticular]] interval.
-It can be described as the difference between [[99/98]] and [[100/99]], and between [[99/70]] and its octave complement, [[140/99]]. It is also the difference between [[245/243]] and [[121/120]], and a stack of two 11/7's and 81/80 against 5/2. Tempering it out also means that [[10/9]] and [[11/7]] are 600 cents apart, as well as are [[11/10]] and [[14/9]].
+It can be described as the difference between [[99/98]] and [[100/99]], and between [[99/70]] and its octave complement, [[140/99]]. It is also the difference between [[245/243]] and [[121/120]], and a stack of two 11/7's and 81/80 against 5/2.
-It factors into the two smallest 13-limit superparticular commas: 9801/9800 = 10648/10647 × 123201/123200.
+It factors into the two smallest 13-limit superparticular commas: 9801/9800 = ([[10648/10647]])([[123201/123200]]).
 == Temperaments ==
-Tempering it out leads to the '''kalismic temperament''', which splits the [[octave]] into two equal parts, each representing 99/70~140/99. Odd-numbered edos cannot temper it out. See [[Rank-4 temperament #Kalismic (9801/9800)]] for some technical details.
+[[Tempering out]] this comma leads to the '''kalismic temperament''', which splits the [[octave]] into two equal parts, each representing 99/70~140/99. Tempering it out also means that [[10/9]] and [[11/7]] are 1/2-octave apart, as well as are [[11/10]] and [[14/9]]. Odd-numbered edos cannot temper it out. See [[Rank-4 temperament #Kalismic (9801/9800)]] for some technical details. See [[Kalismic temperaments]] for a collection of rank-3 temperaments where it is tempered out.
 == Etymology ==
@@ Line 18: / Line 18: @@
 == See also ==
-* [[Rank-4 temperament #Kalismic (9801/9800)]]
-* [[Kalismic temperaments]], a collection of rank-3 temperaments where it is tempered out
 * [[List of superparticular intervals]]
@@ Line 26: / Line 24: @@
 [[Category:Kalismic]]
 [[Category:Commas named by translating something into another language]]
-[[Category:Commas named after individuals]]
+[[Category:Commas named after mathematicians]]