Meet and join: Difference between revisions
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== Poset Properties == | == Poset Properties == | ||
The operations of join and meet give the set of temperaments the structure of a partially ordered set, sometimes called a [[Wikipedia:Partially_ordered_set|poset]]. | |||
=== Same Subgroup === | === Same Subgroup === | ||
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If we had gone with the other convention for meet and join, we would have gotten the same result, except this would be flipped: G would now be the maximal temperament and G/G the minimal. | If we had gone with the other convention for meet and join, we would have gotten the same result, except this would be flipped: G would now be the maximal temperament and G/G the minimal. | ||
In the temperament defined by G, nothing is tempered out, and we may also call it '''JI'''; and in the temperament defined by G/G, | In the temperament defined by G, nothing is tempered out, and we may also call it '''JI'''; and in the temperament defined by G/G, everything is tempered out, and we may also call it [[Trivial temperament|'''OM'''<sub>G</sub>]]. | ||
=== Different Subgroups === | === Different Subgroups === | ||