9801/9800: Difference between revisions
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== Etymology == | == Etymology == | ||
This comma was named ''kalisma'' by [[Margo Schulter]] in 2000 from the Greek root [[wiktionary:%CE%BA%CE%B1%CE%BB%CF%8C%CF%82 #Ancient Greek|''kal-'' ("beautiful")]]<ref>[https://yahootuninggroupsultimatebackup.github.io/tuning/topicId_12989.html Yahoo! Tuning Group | ''Re: Kalisma/xenisma (new names?) -- JI tuning and Scala file'']</ref>. [[Gene Ward Smith]], not aware of Margo's work, proposed ''gaussisma'' in 2004, reasoning that {{w|D. H. Lehmer}} claimed {{w|Carl Friedrich Gauss}} had mentioned the ratio<ref>[https://yahootuninggroupsultimatebackup.github.io/tuning-math/topicId_10130.html#10135 Yahoo! Tuning Group | ''Re: {{lbrack}}tuning-math{{rbrack}} Digest Number 1011'']</ref>. | |||
== See also == | == See also == | ||
Revision as of 10:22, 25 October 2024
| Interval information |
Gauss' comma
reduced
S33/S35
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
This comma was named kalisma by Margo Schulter in 2000 from the Greek root kal- ("beautiful")[1]. Gene Ward Smith, not aware of Margo's work, proposed gaussisma in 2004, reasoning that D. H. Lehmer claimed Carl Friedrich Gauss had mentioned the ratio[2].
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