Olympia
Ratio | 131072/130977 |
Factorization | 2^{17} × 3^{-5} × 7^{-2} × 11^{-1} |
Monzo | [17 -5 0 -2 -1⟩ |
Size in cents | 1.2552404¢ |
Name | olympia |
Color name | salururu unison, s1urr1 |
FJS name | [math]\text{P1}_{7,7,11}[/math] |
Special properties | reduced, reduced subharmonic |
Tenney height (log_{2} nd) | 33.999 |
Weil height (log_{2} max(n, d)) | 34 |
Wilson height (sopfr (nd)) | 74 |
Harmonic entropy (Shannon, [math]\sqrt{n\cdot d}[/math]) |
~2.40482 bits |
Comma size | unnoticeable |
S-expression | S64^{2} × S65 |
open this interval in xen-calc |
The olympia (monzo: [17 -5 0 -2 -1⟩, ratio: 131072/130977) is an 11-limit (also 2.3.7.11 subgroup) unnoticeable comma measuring about 1.26 cents. It is the difference between the undecimal quartertone (33/32) and a stack of two septimal commas (64/63). Even more interesting is the possible factorization into two 13-limit superparticular ratios: 2080/2079 × 4096/4095. In fact, the olympia is the default interval represented by three minas in the Olympian level of Sagittal notation, from which it gets its name.
Temperaments
Tempering out this comma in the full 11-limit results in the rank-4 olympic temperament , with a very natural 13-limit extension {2080/2079, 4096/4095} (→Rank-4 temperament #Olympic (131072/130977)).
As its order of 11 is one, any 7-limit temperament can be immediately extended to the 11-limit in theory by tempering out this comma. To make practical sense, however, it requires low complexity and high accuracy of 64/63, which is less common.