Olympia

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Interval information
Ratio 131072/130977
Factorization 217 × 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 (log2 n⋅d) 33.999
Weil height (max(n, d)) 131072
Benedetti height (n⋅d) 17167417344
Harmonic entropy
(Shannon, [math]\sqrt{n\cdot d}[/math])
~2.40482 bits
Comma size unnoticeable
S-expression S642 × 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.

See also