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

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= Some chords =

=== 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.

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.

* Each interval carries a weight (its Height): more “simple” intervals get larger weights than more remote ones.

* All unordered pitch-class sets obtained this way, modulo the 17-step equave, are grouped into chord classes (up to transposition).

* Each chord class receives a score, computed from the weights of 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 rotations (inversions) 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 contain the largest number of degrees from the 17-EDO circle of fifths (0–10–3–13–6–16–9–2–12–5–15–8–1–11–4–14–7). The remaining rows list the other inversions of the same chord, in the order obtained by successive rotations.

== Dyads ==

@@ Line 121: / Line 121: @@
 = Some chords =
+=== 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.
+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.
+* Each interval carries a weight (its Height): more “simple” intervals get larger weights than more remote ones.
+* All unordered pitch-class sets obtained this way, modulo the 17-step equave, are grouped into chord classes (up to transposition).
+* Each chord class receives a score, computed from the weights of 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 rotations (inversions) 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 contain the largest number of degrees from the 17-EDO circle of fifths (0–10–3–13–6–16–9–2–12–5–15–8–1–11–4–14–7). The remaining rows list the other inversions of the same chord, in the order obtained by successive rotations.
 == Dyads ==