User:Ganaram inukshuk/4L 3s: Difference between revisions

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== Notation ==

: ''This article assumes [[TAMNAMS]] and [[Diamond-mos notation|diamond-MOS notation]] for naming intervals, scale degrees, and note names.''

=== Interval names ===

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== Theory ==

~~''RTT-related stuff here?''~~

== ~~Tunings~~ ==

=== Low harmonic entropy scales ===

There are two notable harmonic entropy minima: [[Kleismic family|kleismic temperament]], in which the generator is 6/5 and 6 of them make a 3/1 ((6/5)^6, tempered, equals 3/1), and [[myna]], in which the generator is also 6/5 but 10 of them make a 6/1 ((6/5)^10, tempered, equals 6/1), resulting in the intervals 4/3 and 3/2 being absent.

=== Temperament interpretations ===

: ''Main article: [[4L 3s/Temperaments]]''

4L 3s has the following temperament interpretations:

# With generator size between 5\18 (333.3c) and 11\39 (338.5c): [[Sixix]], corresponding to a step ratio between 3/2 and 6/5.

# With generator size between 4\15 (320.0c) and 3\11 (327.3c): [[Orgone]], corresponding to a step ratio between 3/1 and 2/1.

# With generator size between 5\19 (315.8c) and 4\15 (320.0c): [[Kleismic]], corresponding to a step ratio between 4/1 and 3/1.

There are also other temperaments in the 4L 3s range, particularly [[amity]] and [[myna]], but 7 pitches are not enough to contain the concordant chords optimized by these temperaments; a [[MODMOS]] or a larger MOS gamut is necessary to access these pitches, if restricted to a rank-2 approach.

== Step ratios ==

The basic tuning for 4L 3s has a large and small step size of 2 and 1 respectively, which is supported by 11edo. Raising or lowering certain nominals by a [[chroma]] produces the following scale degrees.

@@ Line 10: / Line 10: @@
 == Notation ==
+: ''This article assumes [[TAMNAMS]] and [[Diamond-mos notation|diamond-MOS notation]] for naming intervals, scale degrees, and note names.''
 === Interval names ===
@@ Line 81: / Line 83: @@
 == Theory ==
-''RTT-related stuff here?''
-== Tunings ==
+=== Low harmonic entropy scales ===
+There are two notable harmonic entropy minima: [[Kleismic family|kleismic temperament]], in which the generator is 6/5 and 6 of them make a 3/1 ((6/5)^6, tempered, equals 3/1), and [[myna]], in which the generator is also 6/5 but 10 of them make a 6/1 ((6/5)^10, tempered, equals 6/1), resulting in the intervals 4/3 and 3/2 being absent.
+=== Temperament interpretations ===
+: ''Main article: [[4L 3s/Temperaments]]''
+L 3s has the following temperament interpretations:
+# With generator size between 5\18 (333.3c) and 11\39 (338.5c): [[Sixix]], corresponding to a step ratio between 3/2 and 6/5.
+# With generator size between 4\15 (320.0c) and 3\11 (327.3c): [[Orgone]], corresponding to a step ratio between 3/1 and 2/1.
+# With generator size between 5\19 (315.8c) and 4\15 (320.0c): [[Kleismic]], corresponding to a step ratio between 4/1 and 3/1.
+There are also other temperaments in the 4L 3s range, particularly [[amity]] and [[myna]], but 7 pitches are not enough to contain the concordant chords optimized by these temperaments; a [[MODMOS]] or a larger MOS gamut is necessary to access these pitches, if restricted to a rank-2 approach.
+== Step ratios ==
 The basic tuning for 4L 3s has a large and small step size of 2 and 1 respectively, which is supported by 11edo. Raising or lowering certain nominals by a [[chroma]] produces the following scale degrees.
 {{MOS degrees|Scale Signature=4L 3s|Step Ratio=2/1}}