9801/9800: Difference between revisions

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{{Infobox Interval

| Name = kalisma~~, Gauss' comma~~

| Name = kalisma

| Color name = 1oorrgg-2, Bilorugu comma

| Comma = yes

}}

'''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 [[99/70]] and its [[octave complement]] [[140/99]], between ([[35/33]])<sup>2</sup> and [[9/8]], or between ([[176/175]])<sup>2</sup> and [[2048/2025]].

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

In terms of superparticular commas, it is the difference between:

* [[99/98]] and [[100/99]]

* [[351/350]] and [[364/363]]

* [[1716/1715]] and [[2080/2079]]

* [[3025/3024]] and [[4375/4374]]

~~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 is also the difference between the following notable non-superparticular commas:

* [[245/243]] and [[121/120]]

* [[245/242]] and [[81/80]]

* [[176/175]] and [[896/891]]

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

It also 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 the [[pythagorean comma]] is split into two [[2835/2816]] halves, [[10/9]] and [[11/7]] are a semioctave apart, as well as are [[11/10]] and [[14/9]]. Odd-numbered edos cannot temper it out, as they do not have a semioctave.

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]]

== ~~Notes~~ ==

== References ==

[[Category:Kalismic]]

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

[[Category:Commas named after mathematicians]]

@@ Line 1: / Line 1: @@
 {{Infobox Interval
-| Name = kalisma, Gauss' comma
+| Name = kalisma
 | Color name = 1oorrgg-2, Bilorugu comma
 | Comma = yes
 }}
+'''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 [[99/70]] and its [[octave complement]] [[140/99]], between ([[35/33]])<sup>2</sup> and [[9/8]], or between ([[176/175]])<sup>2</sup> and [[2048/2025]].
-'''9801/9800''', the '''kalisma''' or '''Gauss' comma''', is an [[11-limit]] [[unnoticeable comma]] measuring about 0.18{{cent}}. It is the smallest 11-limit [[superparticular]] interval.
+In terms of superparticular commas, it is the difference between:
+* [[99/98]] and [[100/99]]
+* [[351/350]] and [[364/363]]
+* [[1716/1715]] and [[2080/2079]]
+* [[3025/3024]] and [[4375/4374]]
-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 is also the difference between the following notable non-superparticular commas:
+* [[245/243]] and [[121/120]]
+* [[245/242]] and [[81/80]]
+* [[176/175]] and [[896/891]]
-It factors into the two smallest 13-limit superparticular commas: 9801/9800 = 10648/10647 × 123201/123200.
+It also 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 the [[pythagorean comma]] is split into two [[2835/2816]] halves, [[10/9]] and [[11/7]] are a semioctave apart, as well as are [[11/10]] and [[14/9]]. Odd-numbered edos cannot temper it out, as they do not have a semioctave.
+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 28: @@
 == 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]]
-== Notes ==
+== References ==
 [[Category:Kalismic]]
+[[Category:Commas named by translating something into another language]]
+[[Category:Commas named after mathematicians]]