Meet and join: Difference between revisions

Mike Battaglia (talk | contribs)
Intro
Mike Battaglia (talk | contribs)
Poset Properties: add link to wikipedia
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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, nothing is tempered out, and we may also call it [[Trivial temperament|'''OM'''<sub>G</sub>]].  
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 ===