Wedgie/Archived version: Difference between revisions

Line 1:

__FORCETOC__

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). If one takes r independent [[vals]] V1, ..., Vr in a p-limit group of n primes, then the wedgie for the rank-r temperament V1& ...&Vr is defined by taking the [https://en.wikipedia.org/wiki/Wedge_product wedge product] of the vals (called a '''multival'''), and dividing out the greatest common divisior of the coefficients, to produce an r-multival. If the first non-zero coefficient of this multival is negative, it is then scalar multiplied by -1, changing the sign of the first non-zero coefficient to be positive. The result is the wedgie. 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). If one takes r independent [[vals]] V1, ..., Vr in a p-limit group of n primes, then the wedgie for the rank-r temperament V1& ...&Vr is defined by taking the [https://en.wikipedia.org/wiki/Wedge_product wedge product] of the vals (called a '''multival'''), and dividing out the greatest common divisior of the coefficients, to produce an r-multival. If the first non-zero coefficient of this multival is negative, the multival is then scalar multiplied by -1, changing the sign of the first non-zero coefficient to be positive. The result is the wedgie. Wedgies are in a one-to-one relationship with abstract regular temperaments.

==How the period and generator falls out of a rank-2 wedgie==

@@ Line 1: / Line 1: @@
 __FORCETOC__
-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). If one takes r independent [[vals]] V1, ..., Vr in a p-limit group of n primes, then the wedgie for the rank-r temperament V1& ...&Vr is defined by taking the [https://en.wikipedia.org/wiki/Wedge_product wedge product] of the vals (called a '''multival'''), and dividing out the greatest common divisior of the coefficients, to produce an r-multival. If the first non-zero coefficient of this multival is negative, it is then scalar multiplied by -1, changing the sign of the first non-zero coefficient to be positive. The result is the wedgie. 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). If one takes r independent [[vals]] V1, ..., Vr in a p-limit group of n primes, then the wedgie for the rank-r temperament V1& ...&Vr is defined by taking the [https://en.wikipedia.org/wiki/Wedge_product wedge product] of the vals (called a '''multival'''), and dividing out the greatest common divisior of the coefficients, to produce an r-multival. If the first non-zero coefficient of this multival is negative, the multival is then scalar multiplied by -1, changing the sign of the first non-zero coefficient to be positive. The result is the wedgie. Wedgies are in a one-to-one relationship with abstract regular temperaments.
 ==How the period and generator falls out of a rank-2 wedgie==