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'''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. | '''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. | ||
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/ | |||
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. | ||
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== Temperaments == | == 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. | 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 == | == See also == | ||
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* [[Kalismic temperaments]], a collection of rank-3 temperaments where it is tempered out | * [[Kalismic temperaments]], a collection of rank-3 temperaments where it is tempered out | ||
* [[List of superparticular intervals]] | * [[List of superparticular intervals]] | ||
== Notes == | |||
[[Category:Kalismic]] | [[Category:Kalismic]] | ||
Revision as of 12:01, 10 May 2023
| Interval information |
Gauss' comma
reduced
S33 / S35
9801/9800, the kalisma or Gauss' comma, is an 11-limit unnoticeable comma measuring about 0.18 ¢. 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 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 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[1].
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