Ptolemi-nicema
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| Factorization | 2137 × 3-138 × 5138 × 11-69 |
| Monzo | [137 -138 138 0 -69⟩ |
| Size in cents | 0.56437076¢ |
| 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.