Transversal: Difference between revisions
m Changed protection level for "Transversal" ([Edit=Allow only administrators] (expires 17:03, 17 February 2025 (UTC)) [Move=Allow only administrators] (expires 17:03, 17 February 2025 (UTC))) |
deploying new cat |
||
| Line 1: | Line 1: | ||
{{Legacy}} | |||
In the language of mathematics, a '''transversal''' is a selection of one representative element from each set of a collection of sets. Transversals may be used to define scales tempered by a [[regular temperament]] in a way which is precise, useful for several purposes, and independent of the exact tuning used by the temperament. For each note of a scale which is defined in ''p''-limit temperament, there is a set of ''p''-limit rational intervals which is tempered by the temperament to that note. This gives us a collection of sets, and selecting a representative element from each set gives us a transversal. Transversals may also be used to denote all of the intervals of a regular temperament, usually by confining the intervals of the transversal to a subgroup of the group tempered by the temperament. For instance, Pythagorean tuning provides a transversal for meantone. | In the language of mathematics, a '''transversal''' is a selection of one representative element from each set of a collection of sets. Transversals may be used to define scales tempered by a [[regular temperament]] in a way which is precise, useful for several purposes, and independent of the exact tuning used by the temperament. For each note of a scale which is defined in ''p''-limit temperament, there is a set of ''p''-limit rational intervals which is tempered by the temperament to that note. This gives us a collection of sets, and selecting a representative element from each set gives us a transversal. Transversals may also be used to denote all of the intervals of a regular temperament, usually by confining the intervals of the transversal to a subgroup of the group tempered by the temperament. For instance, Pythagorean tuning provides a transversal for meantone. | ||
Revision as of 16:16, 17 February 2025
Template:Legacy In the language of mathematics, a transversal is a selection of one representative element from each set of a collection of sets. Transversals may be used to define scales tempered by a regular temperament in a way which is precise, useful for several purposes, and independent of the exact tuning used by the temperament. For each note of a scale which is defined in p-limit temperament, there is a set of p-limit rational intervals which is tempered by the temperament to that note. This gives us a collection of sets, and selecting a representative element from each set gives us a transversal. Transversals may also be used to denote all of the intervals of a regular temperament, usually by confining the intervals of the transversal to a subgroup of the group tempered by the temperament. For instance, Pythagorean tuning provides a transversal for meantone.