Meet and join: Difference between revisions

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Similarly, the '''kernel-meet''' or '''val-join''' of A and B is formed by taking the meet of the kernels of A and B, and thus equivalently, the join of the supporting vals of both. The resulting temperament, in terms of commas, tempers out only those commas tempered in both A ''and'' B, and in terms of vals, is supported by any linear combination of vals supporting either A ''or'' B. Dually to the above, we can compute this by taking the normal val lists for A and B, concatenating, and Hermite-reducing to another normal val list.

The kernel-join/val-meet of two temperaments A and B is the "simplest" temperament that supports both A and B, ~~and~~ kernel-meet/val-join is the "most complex" temperament that is supported by both A and B.

The kernel-join/val-meet of two temperaments A and B is the "simplest" temperament that supports both A and B, in the sense that it only tempers out the minimum set of commas required to support both. Similarly, the kernel-meet/val-join is the "most complex" temperament that is supported by both A and B, in the sense that it tempers out as many commas as possible that the kernels of A and B have in common.

This definition assumes both A and B have no torsion or contorsion.

This definition assumes both A and B have no torsion or contorsion, and that torsion/contorsion is removed after taking the meet/join; otherwise the definition is more complicated.

== Inter-Subgroup Temperament Meet and Join ==

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 Similarly, the '''kernel-meet''' or '''val-join''' of A and B is formed by taking the meet of the kernels of A and B, and thus equivalently, the join of the supporting vals of both. The resulting temperament, in terms of commas, tempers out only those commas tempered in both A ''and'' B, and in terms of vals, is supported by any linear combination of vals supporting either A ''or'' B. Dually to the above, we can compute this by taking the normal val lists for A and B, concatenating, and Hermite-reducing to another normal val list.
-The kernel-join/val-meet of two temperaments A and B is the "simplest" temperament that supports both A and B, and kernel-meet/val-join is the "most complex" temperament that is supported by both A and B.
+The kernel-join/val-meet of two temperaments A and B is the "simplest" temperament that supports both A and B, in the sense that it only tempers out the minimum set of commas required to support both. Similarly, the kernel-meet/val-join is the "most complex" temperament that is supported by both A and B, in the sense that it tempers out as many commas as possible that the kernels of A and B have in common.
-This definition assumes both A and B have no torsion or contorsion.
+This definition assumes both A and B have no torsion or contorsion, and that torsion/contorsion is removed after taking the meet/join; otherwise the definition is more complicated.
 == Inter-Subgroup Temperament Meet and Join ==