Temperament mapping matrix: Difference between revisions
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for which the rows are the patent vals for [[7-EDO|7-EDO]] and [[15-EDO|15-EDO]], respectively. Since the dual transformation is injective, these vals can be interpreted as the full-limit vals which are implied by the <7 1| and <15 2| tvals. Additionally, since the image of the dual transformation is the set of vals supporting porcupine, and since the above two vals are linearly independent, the resulting matrix '''V∙P''' is another valid mapping matrix for porcupine. We can confirm this by putting the matrix back into normal val list form and getting [<1 2 3 2 4|, <0 -3 -5 6 -4|] as a result again. | for which the rows are the patent vals for [[7-EDO|7-EDO]] and [[15-EDO|15-EDO]], respectively. Since the dual transformation is injective, these vals can be interpreted as the full-limit vals which are implied by the <7 1| and <15 2| tvals. Additionally, since the image of the dual transformation is the set of vals supporting porcupine, and since the above two vals are linearly independent, the resulting matrix '''V∙P''' is another valid mapping matrix for porcupine. We can confirm this by putting the matrix back into normal val list form and getting [<1 2 3 2 4|, <0 -3 -5 6 -4|] as a result again. | ||
[[Category:Regular temperament theory]] | |||
[[Category:Theory]] | [[Category:Theory]] | ||
[[Category:Math]] | [[Category:Math]] | ||
[[Category:Mapping]] | [[Category:Mapping]] | ||
[[Category:Temperament]] | [[Category:Temperament]] | ||