9801/9800: Difference between revisions
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'''9801/9800''', the '''kalisma''' or '''Gauss' comma''', is an [[11-limit]] [[unnoticeable comma]] measuring about 0.18 cents. 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]]. | '''9801/9800''', the '''kalisma''' or '''Gauss' comma''', is an [[11-limit]] [[unnoticeable comma]] measuring about 0.18 cents. 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 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. | |||
== See also == | == See also == | ||
* [[Kalismic temperaments]] | * [[Rank-4 temperament #Kalismic (9801/9800)]] | ||
* [[Kalismic temperaments]], a collection of rank-3 temperaments where it is tempered out | |||
* [[Unnoticeable comma]] | * [[Unnoticeable comma]] | ||
* [[List of superparticular intervals]] | * [[List of superparticular intervals]] | ||
Revision as of 14:59, 6 October 2021
| Interval information |
Gauss' comma
reduced
9801/9800, the kalisma or Gauss' comma, is an 11-limit unnoticeable comma measuring about 0.18 cents. 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 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.
See also
- Rank-4 temperament #Kalismic (9801/9800)
- Kalismic temperaments, a collection of rank-3 temperaments where it is tempered out
- Unnoticeable comma
- List of superparticular intervals