Names for "join" and "meet" operations on temperaments

Abstract temperaments of all ranks form a lattice structure (the partially ordered set kind, not the Z-module kind), where any two temperaments have a unique "join" and "meet". The "join" of two temperaments is of equal or greater rank, and its set of commas is the intersection of those of its operands. The "meet" of two temperaments is of equal or lesser rank, and its set of commas is the direct sum of those of its operands.

For example, the "join" of meantone and pajara is marvel, because they both temper out 225/224, so if you want something to work in both meantone and pajara it has to work in marvel (but it can still have marvel comma pumps). The "meet" of meantone and pajara is 12-equal, because that's the only temperament that supports both.

(It's possible I swapped "join" and "meet" in the preceding, so don't get hung up on that.)

Are there specific names for these operations in the context of temperaments?

They're analogous to LCM and GCD. Names that would make sense to me are "simplest common supertemperament" and "most accurate common subtemperament", but those are sort of long.

Keenan

--- In tuning-math@yahoogroups.com, "Keenan Pepper" <keenanpepper@...> wrote:

> They're analogous to LCM and GCD. Names that would make sense to me are "simplest common supertemperament" and "most accurate common subtemperament", but those are sort of long.

What about "overtemperament" and "undertemperament"?