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

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* 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).

* 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, obtained by adding the weights of the intervals along all the chains of intervals that generate it.

* The classes are then sorted from highest to lowest score; only the best-scoring ones for each cardinality are shown in the tables.

Each small inner table groups the inversions (rotations) of a single chord class. In every row, the left cell names the chord by listing its intervals above the root note of that inversion, and the right cell gives the same information as a set of degrees modulo 17.

The first row of each inner table is a distinguished representative: it is the inversion whose pitch classes, when ordered along the 17-EDO circle of fifths (0–10–3–13–6–16–9–2–12–5–15–8–1–11–4–14–7), give the lexicographically smallest sequence. The remaining rows list the other inversions of the same chord, in the order obtained by successive rotations.

@@ Line 133: / Line 133: @@
 * 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).
-* 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, obtained by adding the weights of the intervals along all the chains of intervals that generate it.
 * The classes are then sorted from highest to lowest score; only the best-scoring ones for each cardinality are shown in the tables.
 Each small inner table groups the inversions (rotations) of a single chord class. In every row, the left cell names the chord by listing its intervals above the root note of that inversion, and the right cell gives the same information as a set of degrees modulo 17.
 The first row of each inner table is a distinguished representative: it is the inversion whose pitch classes, when ordered along the 17-EDO circle of fifths (0–10–3–13–6–16–9–2–12–5–15–8–1–11–4–14–7), give the lexicographically smallest sequence. The remaining rows list the other inversions of the same chord, in the order obtained by successive rotations.