Ptolemi-nicema: Difference between revisions

From Xenharmonic Wiki
Jump to navigation Jump to search
Eliora (talk | contribs)
No edit summary
Eliora (talk | contribs)
No edit summary
Line 4: Line 4:
| Comma = yes
| Comma = yes
}}
}}
'''Ptolemismic 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.
'''Ptolemismic 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 '''ptolemismic nice''' temperament is defined.

Revision as of 19:02, 9 January 2023

Interval information
Factorization 2137 × 3-138 × 5138 × 11-69
Monzo [137 -138 138 0 -69
Size in cents 0.5643708¢
Name ptolemismic nicema
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

Ptolemismic 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 ptolemismic nice temperament is defined.