# Olympia

 Ratio 131072/130977 Factorization 217 × 3-5 × 7-2 × 11-1 Monzo [17 -5 0 -2 -1⟩ Size in cents 1.2552404¢ Names olympia,olympic comma Color name salururu unison, s1urr1 FJS name $\text{P1}_{7,7,11}$ Special properties reduced Tenney height (log2 nd) 33.999 Weil height (log2 max(n, d)) 34 Wilson height (sopfr (nd)) 74 Harmonic entropy(Shannon, $\sqrt{nd}$) ~1.21294 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), otherwise known as the olympic comma, 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.

## Etymology

The olympia was named by Flora Canou in 2021, referring to the Olympian level of Sagittal notation.