100/99: Difference between revisions

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[[de:100/99]]

In [[~~Just_intonation|Just Intonation~~]],100/99 is a [[~~superparticular|~~superparticular]] interval ~~(the ptolemisma)~~ of around 17.4¢ which makes the difference between [[~~11/10|~~11/10]], the greater undecimal neutral second of about 165¢, and [[~~10/9|~~10/9]], the 5-limit minor whole tone of about 182.4¢. Temperaments in which 100/99 is tempered out include [[~~22edo|~~22edo]], [[~~41edo|~~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|~~81/80]], which results in meantone and other temperaments, in which 10/9 is equated, not with 11/10, but with [[~~9/8|~~9/8]]. Along with being the difference between 11/10 and 10/9, 100/99 is the amount by which an [[~~11/8|~~11/8]] and two [[~~6/5|~~6/5]]s fall short of an octave, so that tempering out 100/99 allows for the [[~~ptolemismic_triad|~~ptolemismic triad]] which has intervals of 11/8, 6/5, 6/5.

{{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: [[~~Gallery_of_Just_Intervals|Galley~~ of ~~Just Intervals~~]] [[Category:11-limit]]

== See Also ==

* [[Gallery of just intervals]]

[[Category:11-limit]]

[[Category:comma]]

[[Category:superparticular]]

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 [[de:100/99]]
-In [[Just_intonation|Just Intonation]],100/99 is a [[superparticular|superparticular]] interval (the ptolemisma) of around 17.4¢ which makes the difference between [[11/10|11/10]], the greater undecimal neutral second of about 165¢, and [[10/9|10/9]], the 5-limit minor whole tone of about 182.4¢. Temperaments in which 100/99 is tempered out include [[22edo|22edo]], [[41edo|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|81/80]], which results in meantone and other temperaments, in which 10/9 is equated, not with 11/10, but with [[9/8|9/8]]. Along with being the difference between 11/10 and 10/9, 100/99 is the amount by which an [[11/8|11/8]] and two [[6/5|6/5]]s fall short of an octave, so that tempering out 100/99 allows for the [[ptolemismic_triad|ptolemismic triad]] which has intervals of 11/8, 6/5, 6/5.
+{{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: [[Gallery_of_Just_Intervals|Galley of Just Intervals]]      [[Category:11-limit]]
+== See Also ==
+* [[Gallery of just intervals]]
+[[Category:11-limit]]
+[[Category:comma]]
 [[Category:superparticular]]