Bipentatonic scale: Difference between revisions

Line 1:

A '''dipentatonic scale''' is a 10-note octave-equivalent scale where every other note gives an [[MOS]] pentatonic scale. Following from this, dipentatonic scales have a maximum of two sizes for intervals that are an even number of steps. Many dipentatonic scales are generated by a diatonic-sized fifth (between the 7edo fifth and the 5edo fifth) of a fixed size. Some dipentatonic scales are MOSes, such as the Erlich decatonic in [[22edo]]. Modulating by fifths is easy in dipentatonic scales where the interleaved pentatonics are generated by a fifth (i.e. [[2L 3s]] and [[3L 2s]], depending on tuning).

~~Abstract~~ dipentatonic scales ~~can be classified~~ by the pentatonics they interleave and by their rank (whether they are mosses or rank-3). The second part of this article surveys dipentatonic scales in [[JI]]. Dipentatonic scales also exist in [[regular temperaments]] of course, but exploration of such scales is not included in the article for now at least.

The first part of this article classifies abstract dipentatonic scales by the pentatonics they interleave and by their rank (whether they are mosses or rank-3). The second part of this article surveys dipentatonic scales in [[JI]]. Dipentatonic scales also exist in [[regular temperaments]] of course, but exploration of such scales is not included in the article for now at least.

== Dipentatonic mosses ==

== Abstract dipentatonic scales ==

== Dipentatonic ~~abstract~~ rank-3 scale patterns ==

=== Dipentatonic mosses ===

=== Dipentatonic rank-3 scale patterns ===

A rank-3 dipentatonic scale with step sizes ''5x ay (5-a)z'' has the form ''xYxYxYxYxY'' where the ''Y'''s are the ''y'' and ''z'' arranged in the [[MOS]] pattern ay (5-a)z. The interlocking pentatonics are copies of the mos ''aL (5-a)s'' if ''y > z'' and ''(5-a)L as'' if ''z > y''. The following is a complete list of such abstract patterns, assuming octave equivalence:

* 1L 4M 5s, LsMsMsMsMs

@@ Line 1: / Line 1: @@
 A '''dipentatonic scale''' is a 10-note octave-equivalent scale where every other note gives an [[MOS]] pentatonic scale. Following from this, dipentatonic scales have a maximum of two sizes for intervals that are an even number of steps. Many dipentatonic scales are generated by a diatonic-sized fifth (between the 7edo fifth and the 5edo fifth) of a fixed size. Some dipentatonic scales are MOSes, such as the Erlich decatonic in [[22edo]]. Modulating by fifths is easy in dipentatonic scales where the interleaved pentatonics are generated by a fifth (i.e. [[2L 3s]] and [[3L 2s]], depending on tuning).
-Abstract dipentatonic scales can be classified by the pentatonics they interleave and by their rank (whether they are mosses or rank-3). The second part of this article surveys dipentatonic scales in [[JI]]. Dipentatonic scales also exist in [[regular temperaments]] of course, but exploration of such scales is not included in the article for now at least.
+The first part of this article classifies abstract dipentatonic scales by the pentatonics they interleave and by their rank (whether they are mosses or rank-3). The second part of this article surveys dipentatonic scales in [[JI]]. Dipentatonic scales also exist in [[regular temperaments]] of course, but exploration of such scales is not included in the article for now at least.
-== Dipentatonic mosses ==
+== Abstract dipentatonic scales ==
-== Dipentatonic abstract rank-3 scale patterns ==
+=== Dipentatonic mosses ===
+=== Dipentatonic rank-3 scale patterns ===
 A rank-3 dipentatonic scale with step sizes ''5x ay (5-a)z'' has the form ''xYxYxYxYxY'' where the ''Y'''s are the ''y'' and ''z'' arranged in the [[MOS]] pattern ay (5-a)z. The interlocking pentatonics are copies of the mos ''aL (5-a)s'' if ''y > z'' and ''(5-a)L as'' if ''z > y''. The following is a complete list of such abstract patterns, assuming octave equivalence:
 * 1L 4M 5s, LsMsMsMsMs