9801/9800: Difference between revisions
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In terms of superparticular commas, it is the difference between: | In terms of superparticular commas, it is the difference between: | ||
* [[99/98]] and [[100/99]] | * [[99/98]] and [[100/99]] | ||
* [[1716/1715]] and [[2080/2079]] | |||
* [[3025/3024]] and [[4375/4374]] | * [[3025/3024]] and [[4375/4374]] | ||
Revision as of 00:32, 28 February 2026
| Interval information |
reduced
S33/S35
9801/9800, the kalisma, sometimes described as Gauss' comma, is an unnoticeable 11-limit comma measuring about 0.18 ¢. It is the smallest 11-limit superparticular interval. It can be described as the difference between 99/70 and its octave complement 140/99, or between (35/33)2 and 9/8.
In terms of superparticular commas, it is the difference between:
It is also the difference between the following notable non-superparticular commas:
It also factors into the two smallest 13-limit superparticular commas: 9801/9800 = (10648/10647)⋅(123201/123200).
Temperaments
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, 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
This comma was named kalisma by Margo Schulter in 2000 from the Greek root kal- ("beautiful")[1]. Gene Ward Smith, not aware of Margo's work, proposed gaussisma in 2004, reasoning that D. H. Lehmer claimed Carl Friedrich Gauss had mentioned the ratio[2].