100/99: Difference between revisions
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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. | 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. | ||
See: [[Gallery_of_Just_Intervals|Galley of Just Intervals]] [[Category:11-limit]] | See: [[Gallery_of_Just_Intervals|Galley of Just Intervals]] [[Category:11-limit]] | ||
[[Category:superparticular]] | [[Category:superparticular]] | ||
Revision as of 07:48, 23 July 2020
In Just Intonation,100/99 is a superparticular interval (the ptolemisma) 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.