Meet and join: Difference between revisions

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There is a partial order on the temperaments of G, given by A ≤ B iff A & B = A, or equivalently, A ≤ B iff A | B = B. Since A & G = G, G is the minimal temperament - it is JI and tempers out no commas. Similarly, if we denote G/G as the "rank-0" temperament of G in which ''everything'' is tempered out, we have that A | G/G = G/G, thus G/G is the maximal temperament.

A ≤ B may be expressed by "A is supported by B", in the sense that every comma tempered out by A is also tempered out by B, thus all of the [[essentially tempered chord]]s and [[comma ~~pumps~~]] from temperament A are also playable in B.

A ≤ B may be expressed by "A is supported by B", in the sense that every comma tempered out by A is also tempered out by B, thus all of the [[essentially tempered chord]]s and [[comma pump]]s from temperament A are also playable in B.

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.

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 There is a partial order on the temperaments of G, given by A ≤ B iff A & B = A, or equivalently, A ≤ B iff A | B = B. Since A & G = G, G is the minimal temperament - it is JI and tempers out no commas. Similarly, if we denote G/G as the "rank-0" temperament of G in which ''everything'' is tempered out, we have that A | G/G = G/G, thus G/G is the maximal temperament.
-A ≤ B may be expressed by "A is supported by B", in the sense that every comma tempered out by A is also tempered out by B, thus all of the [[essentially tempered chord]]s and [[comma pumps]] from temperament A are also playable in B.
+A ≤ B may be expressed by "A is supported by B", in the sense that every comma tempered out by A is also tempered out by B, thus all of the [[essentially tempered chord]]s and [[comma pump]]s from temperament A are also playable in B.
 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.