100/99: Difference between revisions
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{{Infobox Interval | {{Infobox Interval | ||
| Ratio = 100/99 | | Ratio = 100/99 | ||
| Monzo = 2 -2 2 0 -1 | | Monzo = 2 -2 2 0 -1 | ||
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In [[just intonation]], '''100/99''', the '''Ptolemy's comma''' or '''ptolemisma''', is a [[superparticular]] interval of around 17.4¢ which makes the difference between [[11/10]], the greater undecimal neutral second of about 165¢, and [[10/9]], the 5-limit minor whole tone of about 182.4¢. Temperaments in which 100/99 is tempered out include [[22edo]], [[41edo]] and others; in such systems, 11/10 and 10/9 are equated. This is in contrast to the more familiar tempering out of [[81/80]], which results in meantone and other temperaments, in which 10/9 is equated, not with 11/10, but with [[9/8]]. Along with being the difference between 11/10 and 10/9, 100/99 is the amount by which an [[11/8]] and two [[6/5]]s fall short of an octave, so that tempering out 100/99 allows for the [[ptolemismic triad]] which has intervals of 11/8, 6/5, 6/5. | In [[just intonation]], '''100/99''', the '''Ptolemy's comma''' or '''ptolemisma''', is a [[superparticular]] interval of around 17.4¢ which makes the difference between [[11/10]], the greater undecimal neutral second of about 165¢, and [[10/9]], the 5-limit minor whole tone of about 182.4¢. Temperaments in which 100/99 is tempered out include [[22edo]], [[41edo]] and others; in such systems, 11/10 and 10/9 are equated. This is in contrast to the more familiar tempering out of [[81/80]], which results in meantone and other temperaments, in which 10/9 is equated, not with 11/10, but with [[9/8]]. Along with being the difference between 11/10 and 10/9, 100/99 is the amount by which an [[11/8]] and two [[6/5]]s fall short of an octave, so that tempering out 100/99 allows for the [[ptolemismic triad]] which has intervals of 11/8, 6/5, 6/5. | ||
== See | == See also == | ||
* [[Ptolemismic triad]] | |||
* [[Rank-4 temperament #Ptolemismic (100/99)]] | |||
* [[Ptolemismic clan]], the clan of rank-3 temperaments where it is tempered out | |||
* [[Small comma]] | |||
* [[List of superparticular intervals]] | |||
* [[Gallery of just intervals]] | * [[Gallery of just intervals]] | ||
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[[Category:Small comma]] | [[Category:Small comma]] | ||
[[Category:Superparticular]] | [[Category:Superparticular]] | ||
[[Category:Ptolemismic]] | |||