9801/9800

Interval information

Ratio	9801/9800
Factorization	2-3 × 34 × 5-2 × 7-2 × 112
Monzo	[-3 4 -2 -2 2⟩
Size in cents	0.1766475¢
Names	kalisma, Gauss' comma
Color name	1oorrgg-2, Bilorugu comma
FJS name	[math]\displaystyle{ \text{M}{-2}^{11,11}_{5,5,7,7} }[/math]
Special properties	square superparticular, reduced
Tenney height (log2 nd)	26.5173
Weil height (log2 max(n, d))	26.5174
Wilson height (sopfr(nd))	64
Comma size	unnoticeable
S-expressions	S99, S33 / S35
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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-numbered 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.

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