100/99: Difference between revisions

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<span style="display: block; text-align: right;">[[:de:100/99 Deutsch]]</span>

<span style="display: block; text-align: right;">[[:de:100/99|Deutsch]]</span>

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.

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	<span style="display: block; text-align: right;">[[:de:100/99 Deutsch]]</span>		<span style="display: block; text-align: right;">[[:de:100/99\|Deutsch]]</span>

	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.