Ptolemi-nicema: Difference between revisions

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== Temperaments ==
== 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.
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]].
 
[[Category:Commas named after polymaths]]

Latest revision as of 02:39, 4 November 2024

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
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.