User:Contribution/17-EDO resources: Difference between revisions

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=== What these chord tables show ===
=== What these chord tables show ===


For each set cardinality, the tables list the first members of the chord classes ranked by the interval "height" values defined in the previous section.
For each set cardinality, the tables list the first members of the chord classes ranked by the interval weight values defined in the previous section.


The ranking is obtained with a simple generative model on the 17-note circle:
The ranking is obtained with a simple generative model on the 17-note circle:


* Starting from degree 0, the algorithm successively extends the set by applying one of the 17 possible intervals above every degree that has already been generated.
* Starting from degree 0, the algorithm successively extends the set by applying one of the 17 possible intervals above every degree that has already been generated.
* Each interval carries a weight (its Height): more “simple” intervals get larger weights than more remote ones.
* Each interval carries a weight: more “simple” intervals get larger weights than more remote ones.
* All pitch-class sets obtained this way, modulo the 17-step equave, are grouped into chord classes (up to inversion and transposition).
* All pitch-class sets obtained this way, modulo the 17-step equave, are grouped into chord classes (up to inversion and transposition).
* Each chord class receives a score, computed from the weights of all the chains of intervals that generate it.
* Each chord class receives a score, computed from the weights of all the chains of intervals that generate it.