Olympia

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.

Interval information

Ratio	131072/130977
Factorization	217 × 3-5 × 7-2 × 11-1
Monzo	[17 -5 0 -2 -1⟩
Size in cents	1.25524¢
Name	olympia
Color name	salururu unison, s1urr1
FJS name	[math]\displaystyle{ \text{P1}_{7,7,11} }[/math]
Special properties	reduced, reduced subharmonic
Tenney norm (log2 nd)	33.999
Weil norm (log2 max(n, d))	34
Wilson norm (sopfr(nd))	74
Comma size	unnoticeable
S-expression	S642⋅S65
Open this interval in xen-calc

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.

See also

• Unnoticeable comma