Let's get this out of the other chain:)

Question:

Has anyone here studied any of these lattices, in relationship to
musical tuning?

1. A2.12 sublattice of the Leech Lattice (one of 23 Neimeier lattices)
2. A1.24 sublattice of the Leech Lattice
3. K12 Lattice
4. Barnes-Walls Lattice
5. Coxeter-Todd Lattice

There first two are based on M12 and M24 respectively, and of course
Leech is just a lattice of S(5,8,24) blown up, K12 I think is the
same as Coxeter-Todd?

Finally, is the A4 or D4 lattice discussed here based on the same
nomenclature as the Dynkin diagrams? (Used for Lie Algebras, et c)

Thanks

PGH