Wedgie/Archived version: Difference between revisions
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The '''wedgie''' is a way of defining and working with an [[abstract regular temperament]] (that is, a regular temperament where no tuning has been decided on). Wedgies are in a one-to-one relationship with abstract regular temperaments. | The '''wedgie''' is a way of defining and working with an [[abstract regular temperament]] (that is, a regular temperament where no tuning has been decided on). Wedgies are in a one-to-one relationship with abstract regular temperaments. | ||
A wedgie is defined by its values on the basis of the temperament's JI subgroup. Let a and b be non-[[contorted]] vals on a [[JI subgroup]] q<sub>1</sub>.[...].q<sub>n</sub> (where the q<sub>i</sub> need not be prime). Then the entries of the wedgie W corresponding to the rank-2 temperament a&b on the JI subgroup q<sub>1</sub>.[...].q<sub>n</sub> are: | A wedgie is defined by its values on the basis of the temperament's JI subgroup. Let a and b be (non-[[contorted]]) vals on a [[JI subgroup]] q<sub>1</sub>.[...].q<sub>n</sub> (where the q<sub>i</sub> need not be prime). Then the entries of the wedgie W corresponding to the rank-2 temperament a&b on the JI subgroup q<sub>1</sub>.[...].q<sub>n</sub> are: | ||
<math>W(q_i, q_j) = a(q_i)b(q_j) - a(q_j)b(q_i) \text{ for } i < j.</math> | <math>W(q_i, q_j) = a(q_i)b(q_j) - a(q_j)b(q_i) \text{ for } i < j.</math> | ||