Ptolemi-nicema

Interval information

Factorization	2137 × 3-138 × 5138 × 11-69
Monzo	[137 -138 138 0 -69⟩
Size in cents	0.5643708¢
Name	ptolemi-nicema
Color name	s101u69y138-8, quinbisa-twethetriluyoyo negative octave
Special properties	reduced
Tenney norm (log2 nd)	914.852
Weil norm (log2 max(n, d))	914.852
Wilson norm (sopfr(nd))	2137
Comma size	unnoticeable
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Ptolemi-nicema is an unnoticeable 11-limit comma which marks the difference between 69 intervals of 100/99 and the octave. For EDOs N up to ~20000, it is tempered if and only if 69 divides N.

Tempering it out means that 11/10 and 10/9 are set exactly 1/69th of the octave apart.

Temperaments

By tempering it out, rank-4 ptolemi-nicemic temperament and in the 2.3.5.11 subgroup, rank-3 ptolemi-nice temperament is defined. See 69th-octave temperaments.