Wedgie/Archived version: Difference between revisions
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=== Example === | === Example === | ||
Consider the wedgie W = | Consider the wedgie W = {{wedgie|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 ''c''<sub>1</sub> = 1, ''c''<sub>2</sub> = 0 is one solution, and we can use 3<sup>1</sup>5<sup>0</sup> = 3/1 as our generator. | ||
Note that -3*W('''2''', '''3''') + 1*W('''2''', '''5''') = −3*1 + 1*4 = 1, so ''c''<sub>1</sub> = −3, ''c''<sub>2</sub> = 1 is another solution to the equation. Thus 5/27 is also a valid generator. This octave reduces to the [[40/27]] grave fifth, which is equated to 3/2 in meantone. | Note that -3*W('''2''', '''3''') + 1*W('''2''', '''5''') = −3*1 + 1*4 = 1, so ''c''<sub>1</sub> = −3, ''c''<sub>2</sub> = 1 is another solution to the equation. Thus 5/27 is also a valid generator. This octave reduces to the [[40/27]] grave fifth, which is equated to 3/2 in meantone. | ||