9801/9800
| Ratio | 9801/9800 |
| Monzo | [-3 4 -2 -2 2⟩ |
| Size in cents | 0.17665 |
| Name(s) | kalisma, Gauss' comma |
| 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