100/99

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Interval information
Ratio 100/99
Factorization 22 × 3-2 × 52 × 11-1
Monzo [2 -2 2 0 -1
Size in cents 17.399484¢
Names Ptolemy's comma,
ptolemisma
Color name 1uyy1, luyoyo 1sn,
Luyoyo comma
FJS name [math]\text{A1}^{5,5}_{11}[/math]
Special properties square superparticular,
reduced
Tenney height (log2 nd) 13.2732
Weil height (log2 max(n, d)) 13.2877
Wilson height (sopfr (nd)) 31
Harmonic entropy
(Shannon, [math]\sqrt{nd}[/math])
~3.37611 bits
Comma size small
S-expression S10
open this interval in xen-calc

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. However, meantone and ptolemismic are not necessarily mutually exclusive–the flattone temperament merges both and has 11/10, 10/9 and 9/8 all tempered to a 10/9-like interval. 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. It is also the difference between 25/24 and 33/32.

See also