Wedgie: Difference between revisions
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== Derivation from edo joins == | == Derivation from edo joins == | ||
{{See also|Wedge product }} | {{See also|Wedge product }} | ||
[[File:Wedgediagram .png|thumb|504x504px|Wedge product diagram]] | |||
Two [[vals]] can be combined into a wedgie representing the rank-2 temperament they both support using the wedge product. For example, wedging {{val| 5 8 12 }} and {{val| 7 11 16 }} (the patent vals for 5edo and 7edo) yields {{multival| (5×11 - 8×7) (5×16 - 12×7) (8×16 - 12×11) }}, which simplifies to {{multival| (55 - 56) (80 - 84) (128 - 132) }} and thus to {{multival| -1 -4 -4 }}. Note that we generally assume the first entry of the wedgie should be positive, for which we flip all the signs of it to obtain {{multival| 1 4 4 }}, which is the wedgie for 5 & 7, a.k.a. meantone. | Two [[vals]] can be combined into a wedgie representing the rank-2 temperament they both support using the wedge product. For example, wedging {{val| 5 8 12 }} and {{val| 7 11 16 }} (the patent vals for 5edo and 7edo) yields {{multival| (5×11 - 8×7) (5×16 - 12×7) (8×16 - 12×11) }}, which simplifies to {{multival| (55 - 56) (80 - 84) (128 - 132) }} and thus to {{multival| -1 -4 -4 }}. Note that we generally assume the first entry of the wedgie should be positive, for which we flip all the signs of it to obtain {{multival| 1 4 4 }}, which is the wedgie for 5 & 7, a.k.a. meantone. | ||