100/99: Difference between revisions
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In [[ | {{Infobox Interval | ||
| Icon = | |||
| Ratio = 100/99 | |||
| Monzo = 2 -2 2 0 -1 | |||
| Cents = 17.4 | |||
| Name = Ptolemy's comma, <br>ptolemisma | |||
| Color name = 1uyy1, luyoyo comma | |||
| Sound = | |||
}} | |||
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 == | ||
* [[Gallery of just intervals]] | |||
[[Category:11-limit]] | |||
[[Category:comma]] | |||
[[Category:superparticular]] | [[Category:superparticular]] | ||
Revision as of 13:14, 23 July 2020
| 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.