9801/9800
Ratio | 9801/9800 |
Factorization | 2^{-3} × 3^{4} × 5^{-2} × 7^{-2} × 11^{2} |
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 (log_{2} nd) | 26.5173 |
Weil height (log_{2} max(n, d)) | 26.5174 |
Wilson height (sopfr (nd)) | 64 |
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
- Rank-4 temperament #Kalismic (9801/9800)
- Kalismic temperaments, a collection of rank-3 temperaments where it is tempered out
- List of superparticular intervals