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 | 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 | * 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. | ||