8L 3s (3/1-equivalent): Difference between revisions

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== Theory ==

By dividing the {{mos scalesig|5L 2s}} of LLsLLLs into A=LLs and B=LLLs, and combining them as ABBABB..., it becomes {{mos scalesig|8L 3s<3/1>}}. This scale has octaves that are too frequent for the listener to feel a tritave equivalence. The range of possible dark generators will likely feel sufficiently pseudo-octave. Similar to [[Angel]], it would be good to utilize a finite-length chain of octaves and make use of existing diatonic music theory.

By dividing the {{mos scalesig|5L 2s}} of LLsLLLs into A=LLs and B=LLLs, and combining them as ABBABB..., it becomes {{mos scalesig|8L 3s<3/1>}}. This scale has octaves that are too frequent for the listener to feel a tritave equivalence. The range of possible dark generators will likely feel sufficiently pseudo-octave. Similar to [[Angel]], it would be good to utilize a finite-length chain of octaves and make use of existing diatonic music theory. Markus Schmidmeier has written extensively on this in his paper [https://arxiv.org/abs/1709.00375 2:3:4-Harmony within the Tritave].

=== Low harmonic entropy scales ===

* Pythagorean tuning (period = 3/1, generator = 3/2): L/s = 2.260

* Tritave-equivalent meantone tunings:

** 1/6-comma ~~3eantone{{idiosyncratic}}~~ tuning ([[unchanged-interval]]s: {3/1, 5/4}): L/s = 1.625

** 1/6-comma pure-tritave meantone tuning ([[unchanged-interval]]s: {3/1, 5/4}): L/s = 1.625

== Tuning ranges ==

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 == Theory ==
-By dividing the {{mos scalesig|5L 2s}} of LLsLLLs into A=LLs and B=LLLs, and combining them as ABBABB..., it becomes {{mos scalesig|8L 3s<3/1>}}. This scale has octaves that are too frequent for the listener to feel a tritave equivalence. The range of possible dark generators will likely feel sufficiently pseudo-octave. Similar to [[Angel]], it would be good to utilize a finite-length chain of octaves and make use of existing diatonic music theory.
+By dividing the {{mos scalesig|5L 2s}} of LLsLLLs into A=LLs and B=LLLs, and combining them as ABBABB..., it becomes {{mos scalesig|8L 3s<3/1>}}. This scale has octaves that are too frequent for the listener to feel a tritave equivalence. The range of possible dark generators will likely feel sufficiently pseudo-octave. Similar to [[Angel]], it would be good to utilize a finite-length chain of octaves and make use of existing diatonic music theory. Markus Schmidmeier has written extensively on this in his paper [https://arxiv.org/abs/1709.00375 2:3:4-Harmony within the Tritave].
 === Low harmonic entropy scales ===
 * Pythagorean tuning (period = 3/1, generator = 3/2): L/s = 2.260
 * Tritave-equivalent meantone tunings:
-** 1/6-comma 3eantone{{idiosyncratic}} tuning ([[unchanged-interval]]s: {3/1, 5/4}): L/s = 1.625
+** 1/6-comma pure-tritave meantone tuning ([[unchanged-interval]]s: {3/1, 5/4}): L/s = 1.625
 == Tuning ranges ==