3L 2s (3/1-equivalent): Difference between revisions

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* [[8/3]]

* [[3/1]]

~~Their version of the MOS~~ scale has a [[hardness]] somewhere around 2.45. From an octave-[[equivalent]] point of view, ~~is a just version~~ of the familiar 7sus4 chord from [[12edo]] jazz harmony, ~~but in an open voicing~~.

Hilarion's just scale has a [[hardness]] somewhere around 2.45. It has [[generator]]s 3/1 and 2/1 (bright) or 3/1 and 3/2 (dark). From an octave-[[equivalent]] point of view, its first [[tritave]] resembles an open voicing of the familiar 7sus4 chord from [[12edo]] jazz harmony. Hilarion's just scale is especially well approximated in [[19edt]] and [[46edt]]. EDTs {{EDTs|27, 30, 35, 41 and 49}} also approximate it decently.

~~Hilarion's~~ just ~~scale is especially well approximated in [[19edt]] and [[46edt]]. EDTs {{EDTs|27, 30, 35, 41 and 49}} also approximate it somewhat.~~

A non-just 3L 2s⟨3/1⟩ scale occurs in [[13edt]] (equal tempered [[Bohlen-Pierce]]), where it is generated by 8\13 with a hardness of exactly 1.5. Though that iteration of the scale is very different to Hilarion's version, as it completely avoids both the perfect fifth and the octave, and is much more dissonant but also much more tritave-equivalent in character.

~~The~~ 3L 2s⟨3/1⟩ scale occurs in ~~many important [[EDT]]s, including~~ [[13edt]] (equal tempered [[Bohlen-Pierce]]), where it is generated by 8\13 with a hardness of exactly 1.5. Though that iteration of the scale is very different to Hilarion's version, as it completely avoids both the perfect fifth and the octave, and is much more dissonant but also much more tritave-equivalent in character.

== Theory ==

@@ Line 8: / Line 8: @@
 * [[8/3]]
 * [[3/1]]
-Their version of the MOS scale has a [[hardness]] somewhere around 2.45. From an octave-[[equivalent]] point of view, is a just version of the familiar 7sus4 chord from [[12edo]] jazz harmony, but in an open voicing.
+Hilarion's just scale has a [[hardness]] somewhere around 2.45. It has [[generator]]s 3/1 and 2/1 (bright) or 3/1 and 3/2 (dark). From an octave-[[equivalent]] point of view, its first [[tritave]] resembles an open voicing of the familiar 7sus4 chord from [[12edo]] jazz harmony. Hilarion's just scale is especially well approximated in [[19edt]] and [[46edt]]. EDTs {{EDTs|27, 30, 35, 41 and 49}} also approximate it decently.
-Hilarion's just scale is especially well approximated in [[19edt]] and [[46edt]]. EDTs {{EDTs|27, 30, 35, 41 and 49}} also approximate it somewhat.
+A non-just 3L 2s⟨3/1⟩ scale occurs in [[13edt]] (equal tempered [[Bohlen-Pierce]]), where it is generated by 8\13 with a hardness of exactly 1.5. Though that iteration of the scale is very different to Hilarion's version, as it completely avoids both the perfect fifth and the octave, and is much more dissonant but also much more tritave-equivalent in character.
-The 3L 2s⟨3/1⟩ scale occurs in many important [[EDT]]s, including [[13edt]] (equal tempered [[Bohlen-Pierce]]), where it is generated by 8\13 with a hardness of exactly 1.5. Though that iteration of the scale is very different to Hilarion's version, as it completely avoids both the perfect fifth and the octave, and is much more dissonant but also much more tritave-equivalent in character.
 == Theory ==