9801/9800

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Interval information
Ratio 9801/9800
Factorization 2-3 × 34 × 5-2 × 7-2 × 112
Monzo [-3 4 -2 -2 2
Size in cents 0.17664752¢
Names kalisma,
Gauss' comma
Color name 1oorrgg-2, Bilorugu comma
FJS name [math]\text{M}{-2}^{11,11}_{5,5,7,7}[/math]
Special properties square superparticular,
reduced
Tenney height (log2 n⋅d) 26.5173
Weil height (max(n, d)) 9801
Benedetti height (n⋅d) 96049800
Harmonic entropy
(Shannon, [math]\sqrt{n\cdot d}[/math])
~2.39763 bits
Comma size unnoticeable
S-expressions S99,
S33 / S35
open this interval in xen-calc

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.

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 11/7s 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.

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