Olympia

Interval information

Ratio	131072/130977
Factorization	217 × 3-5 × 7-2 × 11-1
Monzo	[17 -5 0 -2 -1⟩
Size in cents	1.25524¢
Names	olympia, olympic comma
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
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The olympia (monzo: [17 -5 0 -2 -1⟩, ratio: 131072/130977), otherwise known as the olympic comma, is an unnoticeable 11-limit (specifically 2.3.7.11-subgroup) 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)²), which gives rise to its S-expression as S64²⋅S65. Equivalently, it is the difference between 22/21 and a stack of three septimal commas.

It factors into two 13-limit superparticular ratios: (2080/2079)⋅(4096/4095). These ratios and the olympia itself are the default intervals represented by one, two, and 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 (→ Rank-4 temperament #Olympic (131072/130977)), or in the 2.3.7.11 subgroup, the rank-3 olympian temperament. In either case, it sets 1–64/63–33/32–22/21–(33/32)² to become equidistant.

Olympic has a very natural 13-limit extension {2080/2079, 4096/4095}. As the comma's order of 11 is one, any 7-limit temperament can be extended to the 11-limit by tempering out this comma, but it works best for temperaments with low complexity and high accuracy in the septimal comma.

Etymology

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