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 height (log2 nd)	914.852
Weil height (log2 max(n, d))	914.852
Wilson height (sopfr(nd))	2137
Harmonic entropy (Shannon, [math]\sqrt{nd}[/math])	~1.20119 bits
Comma size	unnoticeable
open this interval in xen-calc

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.