Plücker coordinates: Difference between revisions
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note about duality |
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The usual way to write down an abstract temperament is via its mapping matrix, but Plücker coordinates give us a unique description that is useful for some calculations. | The usual way to write down an abstract temperament is via its mapping matrix, but Plücker coordinates give us a unique description that is useful for some calculations. | ||
The definition here is given in terms of temperament matrices, but by duality, we can also embed interval spaces in the same way. | |||
More specifically, the interval subspace spanned by the commas of some temperament can also be used to give unique coordinates to that temperament. | |||
These two representations are related via the [[Hodge dual]]. | |||
== Definition == | == Definition == | ||