The heading is slightly deceptive, because it refers to adding wedge

invariants, which are only determined up to sign, but it gives the

idea.

The wedge invariant represents each 7-limit linear temperament by a

pair of 6-dimensional lattice points, of opposite sign. Hence, we can

add and subtract wedge invariants, or in general take linear

combinations, and produce new linear temperaments. I tried this with

Miracle and Meantone with the above result.

In particular, Meantone = [1,4,10,12,-13,4] and Miracle =

[6,-7,-2,14,20,-25]. The sum gives us [7,-3,8,27,7,-21] and the

difference [-5,11,12,-3,-33,29]. The sum is Orwell, but the

difference was not on my list; by finding a reduced set of commas

from the wedge invariant, I get that it is <225/224,50421/50000>,

where the second comma has a Tenney height too high to make the cut.

It seems like a pretty good system anyway; it is basically the

29+2 system (also 31+29) with a generator close to 7/5.