Subgroup temperament families, relationships, and genes: Difference between revisions
m Mike Battaglia moved page Subgroup Temperament Relationships and Genes to Subgroup Temperament Families, Relationships, and Genes |
m →Extensions and Restrictions: tiny edit to fix a 'lil error |
||
| Line 40: | Line 40: | ||
Suppose that we have some subgroup temperament A for which temperament B is a retraction to some subgroup. If B is the same rank as A, then it is said to be a ''restriction'' of A, and A is said to be an ''extension'' of B. We will again assume contorsion is being removed. | Suppose that we have some subgroup temperament A for which temperament B is a retraction to some subgroup. If B is the same rank as A, then it is said to be a ''restriction'' of A, and A is said to be an ''extension'' of B. We will again assume contorsion is being removed. | ||
Restrictions (and retractions) can be easily computed using [[Subgroup basis matrices]]. For instance, if <math>M</math> is some mapping matrix for the temperament <math>A</math>, and <math>N<math> is a subgroup basis matrix representing some basis for <math>R</math> (expressed in the coordinate system of <math>S</math>), then we can easily compute the restriction of <math>A</math> to <math>R</math> by first taking the matrix product | Restrictions (and retractions) can be easily computed using [[Subgroup basis matrices]]. For instance, if <math>M</math> is some mapping matrix for the temperament <math>A</math>, and <math>N</math> is a subgroup basis matrix representing some basis for <math>R</math> (expressed in the coordinate system of <math>S</math>), then we can easily compute the restriction of <math>A</math> to <math>R</math> by first taking the matrix product | ||
<math> | <math> | ||