100/99: Difference between revisions
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{{Infobox Interval | {{Infobox Interval | ||
| Ratio = 100/99 | | Ratio = 100/99 | ||
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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]] | |||
Revision as of 10:28, 1 March 2022
| Interval information |
ptolemisma
reduced
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 6/5s 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 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