Wedgie/Archived version: Difference between revisions
| Line 49: | Line 49: | ||
=== Example === | === Example === | ||
Consider the wedgie W = <<1 4 4|| for 2.3.5 meantone (the 12&19 temperament). We have W(2,3) = 1 and W(2,5) = 4, so d = 1, and our period is 1\1. Further, | Consider the wedgie W = <<1 4 4|| for 2.3.5 meantone (the 12&19 temperament). We have W(2,3) = 1 and W(2,5) = 4, so d = 1, and our period is 1\1. Further, we have that 1*W(2,3) + 0*W(2,5) = 1, so we can use 3^1 * 5^0 = 3/1 as our generator. | ||
Note that -3*(2,3) + 1*W(2,5) = -3*1 + 1*4 = 1, so 5/27 is also a valid generator. This octave reduces to the [[40/27]] grave fifth, which is equated to 3/2 in meantone. | |||
=== Proof (a bit technical) === | === Proof (a bit technical) === | ||