Meet and join: Difference between revisions

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The second is found by extending the two subgroups to the simplest subgroup which includes both, and then repeating with the two kernels. This is the '''meet''' of the two subgroup temperaments. The meet is the "smallest" temperament that supports both A and B, in the sense that if any other temperament also supports both A and B, it supports the meet. Every comma tempered out by ''either'' A or B is also tempered out in the meet, and vice versa.

=== A note on terminology ===

It may seem somewhat strange that the "join" of two subgroup temperaments is the "meet" of their kernels and subgroups independently, and vice versa. This is due to a quirk from when the initial definition was proposed [https://yahootuninggroupsultimatebackup.github.io/tuning-math/topicId_19399.html on the tuning-math list]. If the two temperaments are on the same subgroup, one can think about "joining" or "meeting" either their kernels, or the subgroups of supporting vals (the "join" in one convention is the "meet" in the other and so forth). It makes no difference either way if one is in the same subgroup, but when looking at temperaments on different subgroups, it probably would have been more natural to go with the other convention, since then the "join" of two temperaments would been the "join" of kernels and subgroups independently. However, for backwards-compatibility, the definition above was chosen so as to agree with the original if the two temperaments are on the same subgroup, so that we have the "join" of the two subgroup temperaments is the "meet" of the subgroups and kernels, and vice versa.

== Examples ==

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 The second is found by extending the two subgroups to the simplest subgroup which includes both, and then repeating with the two kernels. This is the '''meet''' of the two subgroup temperaments. The meet is the "smallest" temperament that supports both A and B, in the sense that if any other temperament also supports both A and B, it supports the meet. Every comma tempered out by ''either'' A or B is also tempered out in the meet, and vice versa.
+=== A note on terminology ===
+It may seem somewhat strange that the "join" of two subgroup temperaments is the "meet" of their kernels and subgroups independently, and vice versa. This is due to a quirk from when the initial definition was proposed [https://yahootuninggroupsultimatebackup.github.io/tuning-math/topicId_19399.html on the tuning-math list]. If the two temperaments are on the same subgroup, one can think about "joining" or "meeting" either their kernels, or the subgroups of supporting vals (the "join" in one convention is the "meet" in the other and so forth). It makes no difference either way if one is in the same subgroup, but when looking at temperaments on different subgroups, it probably would have been more natural to go with the other convention, since then the "join" of two temperaments would been the "join" of kernels and subgroups independently. However, for backwards-compatibility, the definition above was chosen so as to agree with the original if the two temperaments are on the same subgroup, so that we have the "join" of the two subgroup temperaments is the "meet" of the subgroups and kernels, and vice versa.
 == Examples ==