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

(2 intermediate revisions by 2 users not shown)

Line 1:

{{mos scalesig|8L 3s<3/1>}} scale pattern includes the well-known {{mos scalesig|5L 2s|link=1}} pattern within it.

Line 7:

=== Intervals ===

=== Generator chain ===

=== Modes ===

== 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 ==

=== Simple tunings ===

{{MOS tunings~~|Scale Signature=8L 3s<3/1>~~|Step Ratios=2/1; 3/1; 3/2}}

=== Soft-of-basic tunings ===

{{MOS tunings~~|Scale Signature=8L 3s<3/1>~~|Step Ratios=5/4; 4/3; 3/2; 5/3}}

=== Hard-of-basic tunings ===

{{MOS tunings~~|Scale Signature=8L 3s<3/1>~~|Step Ratios=5/2; 3/1; 4/1; 5/1}}

== Scale tree ==

{{MOS tuning spectrum~~|Scale Signature=8L 3s<3/1>~~|9/4=Pythagorean tuning is around here}}

@@ Line 1: / Line 1: @@
-{{Infobox MOS|Scale Signature=8L 3s<3/1>}}
+{{Infobox MOS}}
-{{MOS intro|Scale Signature=8L 3s<3/1>}}
+{{MOS intro}}
 {{mos scalesig|8L 3s<3/1>}} scale pattern includes the well-known {{mos scalesig|5L 2s|link=1}} pattern within it.
@@ Line 7: / Line 7: @@
 === Intervals ===
-{{MOS intervals|Scale Signature=8L 3s<3/1>}}
+{{MOS intervals}}
 === Generator chain ===
-{{MOS genchain|Scale Signature=8L 3s<3/1>}}
+{{MOS genchain}}
 === Modes ===
-{{MOS mode degrees|Scale Signature=8L 3s<3/1>}}
+{{MOS mode degrees}}
 == 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 ==
 === Simple tunings ===
-{{MOS tunings|Scale Signature=8L 3s<3/1>|Step Ratios=2/1; 3/1; 3/2}}
+{{MOS tunings|Step Ratios=2/1; 3/1; 3/2}}
 === Soft-of-basic tunings ===
-{{MOS tunings|Scale Signature=8L 3s<3/1>|Step Ratios=5/4; 4/3; 3/2; 5/3}}
+{{MOS tunings|Step Ratios=5/4; 4/3; 3/2; 5/3}}
 === Hard-of-basic tunings ===
-{{MOS tunings|Scale Signature=8L 3s<3/1>|Step Ratios=5/2; 3/1; 4/1; 5/1}}
+{{MOS tunings|Step Ratios=5/2; 3/1; 4/1; 5/1}}
 == Scale tree ==
-{{MOS tuning spectrum|Scale Signature=8L 3s<3/1>|9/4=Pythagorean tuning is around here}}
+{{MOS tuning spectrum|9/4=Pythagorean tuning is around here}}