9801/9800

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 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 $\text{M}{-2}^{11,11}_{5,5,7,7}$ Special properties square superparticular,reduced Tenney height (log2 nd) 26.5173 Weil height (log2 max(n, d)) 26.5174 Wilson height (sopfr (nd)) 64 Harmonic entropy(Shannon, $\sqrt{nd}$) ~1.19851 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.

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[1].