9801/9800: Difference between revisions

Line 7:

'''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.

~~== Theory ==~~

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 11/7s and 81/80 against a 5/4. 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 factors into the two smallest 13-limit superparticular commas: 9801/9800 = 10648/10647 × 123201/123200.

Line 14:

Line 13:

== Temperaments ==

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

== Etymology ==

The kalisma was named by [[Margo Schulter]] in 2000<ref>[https://yahootuninggroupsultimatebackup.github.io/tuning/topicId_12989.html Yahoo! Tuning Group | ''Re: Kalisma/xenisma (new names?) -- JI tuning and Scala file'']</ref>.

== See also ==

Line 19:

Line 21:

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

* [[List of superparticular intervals]]

== Notes ==

[[Category:Kalismic]]

@@ Line 7: / Line 7: @@
 '''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.
-== Theory ==
+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 11/7s and 81/80 against a 5/4. 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 factors into the two smallest 13-limit superparticular commas: 9801/9800 = 10648/10647 × 123201/123200.
@@ Line 14: / Line 13: @@
 == Temperaments ==
 Tempering it out leads to the '''kalismic temperament''', which splits the [[octave]] into two equal parts, each representing 99/70~140/99. Odd edos cannot temper it out. See [[Rank-4 temperament #Kalismic (9801/9800)]] for some technical details.
+== Etymology ==
+The kalisma was named by [[Margo Schulter]] in 2000<ref>[https://yahootuninggroupsultimatebackup.github.io/tuning/topicId_12989.html Yahoo! Tuning Group | ''Re: Kalisma/xenisma (new names?) -- JI tuning and Scala file'']</ref>.
 == See also ==
@@ Line 19: / Line 21: @@
 * [[Kalismic temperaments]], a collection of rank-3 temperaments where it is tempered out
 * [[List of superparticular intervals]]
+== Notes ==
 [[Category:Kalismic]]