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

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This MOS was first explored by hilarious_hilarion on the [[Xenharmonic Alliance]] Discord server in September 2026. Specifically they discovered a [[just intonation]] version of this ~~mos~~:

This MOS was first explored by hilarious_hilarion on the [[Xenharmonic Alliance]] Discord server in September 2026. Specifically they discovered a [[just intonation]] version of this MOS in the [[3-limit]]:

* [[4/3]]

* [[16/9]]

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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.

~~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.

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.

== Theory ==

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 {{MOS intro}}
-This MOS was first explored by hilarious_hilarion on the [[Xenharmonic Alliance]] Discord server in September 2026. Specifically they discovered a [[just intonation]] version of this mos:
+This MOS was first explored by hilarious_hilarion on the [[Xenharmonic Alliance]] Discord server in September 2026. Specifically they discovered a [[just intonation]] version of this MOS in the [[3-limit]]:
 * [[4/3]]
 * [[16/9]]
@@ 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.
-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.
+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.
 == Theory ==