9801/9800: Difference between revisions

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'''9801/9800''', the '''kalisma''' or '''Gauss' comma''', is an [[11-limit]] [[unnoticeable comma]] measuring about 0.18 cents. It is the difference between [[99/70]] and [[140/99]].  
'''9801/9800''', the '''kalisma''' or '''Gauss' comma''', is an [[11-limit]] [[unnoticeable comma]] measuring about 0.18 cents. 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]].  


Tempering it out leads to [[kalismic temperaments]], which splits the [[octave]] into two equal parts, each representing 99/70~140/99.  
Tempering it out leads to [[kalismic temperaments]], which splits the [[octave]] into two equal parts, each representing 99/70~140/99. Odd edos cannot be tempering it out.
 
It factors into two 13-limit superparticular commas which are also the smallest: 9801/9800 = 10648/10647 × 123201/123200.  


== See also ==
== See also ==

Revision as of 03:26, 18 November 2020

Interval information
Ratio 9801/9800
Factorization 2-3 × 34 × 5-2 × 7-2 × 112
Monzo [-3 4 -2 -2 2
Size in cents 0.1766475¢
Names kalisma,
Gauss' comma
FJS name [math]\displaystyle{ \text{M}{-2}^{11,11}_{5,5,7,7} }[/math]
Special properties square superparticular,
reduced
Tenney norm (log2 nd) 26.5173
Weil norm (log2 max(n, d)) 26.5174
Wilson norm (sopfr(nd)) 64
Open this interval in xen-calc

9801/9800, the kalisma or Gauss' comma, is an 11-limit unnoticeable comma measuring about 0.18 cents. 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.

Tempering it out leads to kalismic temperaments, which splits the octave into two equal parts, each representing 99/70~140/99. Odd edos cannot be tempering it out.

It factors into two 13-limit superparticular commas which are also the smallest: 9801/9800 = 10648/10647 × 123201/123200.

See also