Temperament addition: Difference between revisions

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==== How it looks with multivectors ====

We've now observed the outcome when adding non-addable temperaments using the matrix approach. It's instructive to observe how it works with multivectors as well. The canonical multicommas for septimal meantone and septimal blackwood are {{multicomma|12 -13 4 10 -4 1}} and {{multicomma|14 0 -8 0 5 0}}, respectively. When we add these, we get {{multicomma|26 -13 -4 10 1 1}}. What temperament is this — does it match with any of the four comma bases we've already found? Let's check by converting it back to matrix form. Oh, wait — we can't. This is what we call a [[decomposability|~~nondecomposable~~]] multivector. In other words, there is no set of vectors that could be wedged together to produce this multivector. This is the way that multivectors convey to us that there is no true temperament sum of these two temperaments.

We've now observed the outcome when adding non-addable temperaments using the matrix approach. It's instructive to observe how it works with multivectors as well. The canonical multicommas for septimal meantone and septimal blackwood are {{multicomma|12 -13 4 10 -4 1}} and {{multicomma|14 0 -8 0 5 0}}, respectively. When we add these, we get {{multicomma|26 -13 -4 10 1 1}}. What temperament is this — does it match with any of the four comma bases we've already found? Let's check by converting it back to matrix form. Oh, wait — we can't. This is what we call a [[decomposability|indecomposable]] multivector. In other words, there is no set of vectors that could be wedged together to produce this multivector. This is the way that multivectors convey to us that there is no true temperament sum of these two temperaments.

=== Further explanations ===

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 ==== How it looks with multivectors ====
-We've now observed the outcome when adding non-addable temperaments using the matrix approach. It's instructive to observe how it works with multivectors as well. The canonical multicommas for septimal meantone and septimal blackwood are {{multicomma|12 -13 4 10 -4 1}} and {{multicomma|14 0 -8 0 5 0}}, respectively. When we add these, we get {{multicomma|26 -13 -4 10 1 1}}. What temperament is this — does it match with any of the four comma bases we've already found? Let's check by converting it back to matrix form. Oh, wait — we can't. This is what we call a [[decomposability|nondecomposable]] multivector. In other words, there is no set of vectors that could be wedged together to produce this multivector. This is the way that multivectors convey to us that there is no true temperament sum of these two temperaments.
+We've now observed the outcome when adding non-addable temperaments using the matrix approach. It's instructive to observe how it works with multivectors as well. The canonical multicommas for septimal meantone and septimal blackwood are {{multicomma|12 -13 4 10 -4 1}} and {{multicomma|14 0 -8 0 5 0}}, respectively. When we add these, we get {{multicomma|26 -13 -4 10 1 1}}. What temperament is this — does it match with any of the four comma bases we've already found? Let's check by converting it back to matrix form. Oh, wait — we can't. This is what we call a [[decomposability|indecomposable]] multivector. In other words, there is no set of vectors that could be wedged together to produce this multivector. This is the way that multivectors convey to us that there is no true temperament sum of these two temperaments.
 === Further explanations ===