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 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]]. | '''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. | ||
== 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. | It factors into the two smallest 13-limit superparticular commas: 9801/9800 = 10648/10647 × 123201/123200. | ||