3L 4s: Difference between revisions

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 {{MOS intro}}
-== Standing assumptions ==
+==Name==
-The [[TAMNAMS]] system is used in this article to name 3L 4s intervals and step size ratios and step ratio ranges.
+[[TAMNAMS]] suggests the temperament-agnostic name '''mosh''' for this scale, adopted from an older [[Graham Breed's MOS naming scheme|MOS naming scheme]] by Graham Breed. The name is a contraction of "mohajira-ish".
+==Notation==
+:''This article assumes [[TAMNAMS]] for naming step ratios, intervals, and scale degrees, and [[Diamond-mos notation|diamond-MOS notation]] for note names.''
+===Intervals and degrees===
+Names for this scale's intervals (mossteps) and scale degrees (mosdegrees) are based on the number of large and small steps from the root, starting at 0 (0-mosstep and 0-mosdegree) for the unison, per TAMNAMS. Ordinal names, such as mos-1st for the unison, are discouraged for non-diatonic MOS scales.
-The notation used in this article is sLsLsLs = JKLMNOPJ unless specified otherwise. We denote raising and lowering by a chroma (L − s) by & "amp" and @ "at". (Mnemonics: & "and" means additional pitch. @ "at" rhymes with "flat".) The 10edo gamut would thus be notated as follows:
+Being a moment-of-symmetry scale, every [[interval class]] of 3L 4s, except for the unison and octave, has two [[Interval variety|varieties]] – large and small – whose [[Interval quality|relative qualities]] are denoted as major or minor, or augmented, perfect, and diminished for the generators.
+{| class="wikitable"
+|+
+Interval varieties of 3L 4s
+! rowspan="2" |Interval class
+! colspan="2" |Large variety
+! colspan="2" | Small variety
+|-
+!Size
+!Quality
+!Size
+! Quality
+|-
+|'''0-mosstep (unison)'''
+|0
+|Perfect
+| 0
+|Perfect
+|-
+| 1-mosstep
+|L
+|Major
+|s
+|Minor
+|-
+| 2-mosstep
+|L + s
+| Perfect
+|2s
+|Diminished
+|-
+|3-mosstep
+|2L + s
+|Major
+|L + 2s
+| Minor
+|-
+|4-mosstep
+| 2L + 2s
+|Major
+| L + 3s
+| Minor
+|-
+|5-mosstep
+|3L + 2s
+|Augmented
+|2L + 3s
+| Perfect
+|-
+| 6-mosstep
+|3L + 3s
+| Major
+|2L + 4s
+|Minor
+|-
+|'''7-mosstep (octave)'''
+|3L + 4s
+|Perfect
+|3L + 4s
+|Perfect
+|}
+===Note names===
+For this article, note names are based on diamond-MOS notation, where the naturals JKLMNOP are applied to the step pattern sLsLsLs and the accidentals & (pronounced "am" or "amp") and @ (pronounced "at") are used to represent sharps and flats respectively. Thus, the basic gamut for 3L 4s is the following:
-'''J''' '''K''' K&/L@ '''L''' '''M''' M&/N@ '''N''' '''O''' O&/P@ '''P''' '''J'''
+{{MOS gamut}}
-== Names ==
+== Theory ==
-[[TAMNAMS]] (used by this article) uses the name '''mosh''' for this pattern. This is taken from an older [[MOS naming]] scheme by Graham Breed.
-== Intervals ==
+=== Low harmonic entropy scales ===
-Note: In TAMNAMS, a k-step interval class in mosh may be called a "k-step", "k-mosstep", or "k-moshstep". 1-indexed terms such as "mos(k+1)th" are discouraged for non-diatonic mosses.
+There are two notable harmonic entropy minima:
-== Low-harmonic-entropy scales ==
+* [[Neutral third scales]], such as dicot, hemififth, and mohajira, in which the generator is a neutral 3rd (around 350¢) and two of them make a 3/2 (702¢).
-The two notable harmonic entropy minima with this pattern are neutral third scales ("dicot" / "hemififth" / "mohajira") where two generators make a 3/2, and magic, where the generator is a 5/4 but five of them make a 3/1.
+* [[Magic]], in which the generator is 5/4 (386¢) and 5 of them make a 3/1 (1902¢).
 == Tuning ranges ==