Olympia: Difference between revisions
S-expressions are encodings of interval relations. They don't make the interval relations trivial! Also don't discuss temps outside the Temperaments section! 1089/1024 is (33/32)^2 so it's always split in two, and it's split in four since 33/32 is split in two |
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[[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–[[1089/1024|(33/32)<sup>2</sup>]] to become equidistant. | [[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–[[1089/1024|(33/32)<sup>2</sup>]] 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. | 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. | ||
Olympian is also very close to undecimal [[gary]], which also tempers out the symbiotic comma and makes all the 2.3.7.11 reachable through the chain of fifths, thus equating [[64/63]] with a [[pythagorean comma]]. | |||
== Etymology == | == Etymology == | ||