4L 3s: Difference between revisions

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== Name==

[[TAMNAMS]] suggests the temperament-agnostic name '''smitonic''' ''smy-TON-ik'' /smaɪˈtɒnɪk/ for this scale. The name is derived from 'sharp minor third', since the central range for the dark generator (320¢ to 333.3¢) is significantly sharp of [[6/5]] (just minor 3rd, 315.6¢).

== ~~Notation~~==

== Intervals==

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

:''This article assumes [[TAMNAMS]] for naming step ratios, intervals, and scale degrees.''

~~=== 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.

~~Being a moment-of-symmetry scale, every [[interval class]] of 4L 3s, 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~~.

Except for the unison and octave, all [[Interval class|interval classes]] have two [[Interval variety|varieties]] or sizes, denoted using the terms ''major'' and ''minor'' for the large and small sizes, respectively. The exception to this rule are the generators, which use the terms ''augmented'', ''perfect'', and ''diminished'' instead.

{~~{MOS~~ intervals}}

{| class="wikitable"

===~~Note names~~===

!Interval class

!Specific intervals

!Size (in ascending order)

|-

|'''0-smistep'''

|'''Perfect 0-smistep (unison)'''

|0

|-

| rowspan="2" |1-smistep

|Minor 1-smistep

|s

|-

|Major 1-smistep

|L

|-

| rowspan="2" |'''2-smistep'''

|Perfect 2-smistep

|L + s

|-

|Augmented 2-smistep

|2L

|-

| rowspan="2" |3-smistep

|Minor 3-smistep

|L + 2s

|-

|Major 3-smistep

|2L + s

|-

| rowspan="2" |4-smistep

|Minor 4-smistep

|2L + 2s

|-

|Major 4-smistep

|3L + s

|-

| rowspan="2" |'''5-smistep'''

|Diminished 5-smistep

|2L + 3s

|-

|Perfect 5-smistep

|3L + 2s

|-

| rowspan="2" |6-smistep

|Minor 6-smistep

|3L + 3s

|-

|Major 6-smistep

|4L + 2s

|-

|'''7-smistep (octave)'''

|'''Perfect 7-smistep (octave)'''

|4L + 3s

|}

A 7-note scale using these intervals will typically use scale degrees that represents one size from each interval class, with the true MOS upholding the step pattern of LLsLsLs, or some rotation thereof. MODMOS scales may be formed this way without upholding the step pattern, thereby creating a non-MOS pattern such as LLLssLs, or may include alterations that exceed the two varieties typical of a MOS scale.

==Notation==

For this article, note names are based on diamond-MOS notation, where the naturals JKLMNOP are applied to the step pattern LsLsLsL and the accidentals & (pronounced "am" or "amp") and @ (pronounced "at") are used to represent sharps and flats respectively. Thus, the basic gamut for 4L 3s is the following:

@@ Line 13: / Line 13: @@
 == Name==
 [[TAMNAMS]] suggests the temperament-agnostic name '''smitonic''' ''smy-TON-ik'' /smaɪˈtɒnɪk/ for this scale. The name is derived from 'sharp minor third', since the central range for the dark generator (320¢ to 333.3¢) is significantly sharp of [[6/5]] (just minor 3rd, 315.6¢).
-== Notation==
+== Intervals==
-:''This article assumes [[TAMNAMS]] for naming step ratios, intervals, and scale degrees, and [[Diamond-mos notation|diamond-MOS notation]] for note names.''
+:''This article assumes [[TAMNAMS]] for naming step ratios, intervals, and scale degrees.''
-=== 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.
-Being a moment-of-symmetry scale, every [[interval class]] of 4L 3s, 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.
+Except for the unison and octave, all [[Interval class|interval classes]] have two [[Interval variety|varieties]] or sizes, denoted using the terms ''major'' and ''minor'' for the large and small sizes, respectively. The exception to this rule are the generators, which use the terms ''augmented'', ''perfect'', and ''diminished'' instead.
-{{MOS intervals}}
+{| class="wikitable"
-===Note names===
+!Interval class
+!Specific intervals
+!Size (in ascending order)
+|-
+|'''0-smistep'''
+|'''Perfect 0-smistep (unison)'''
+|0
+|-
+| rowspan="2" |1-smistep
+|Minor 1-smistep
+|s
+|-
+|Major 1-smistep
+|L
+|-
+| rowspan="2" |'''2-smistep'''
+|Perfect 2-smistep
+|L + s
+|-
+|Augmented 2-smistep
+|2L
+|-
+| rowspan="2" |3-smistep
+|Minor 3-smistep
+|L + 2s
+|-
+|Major 3-smistep
+|2L + s
+|-
+| rowspan="2" |4-smistep
+|Minor 4-smistep
+|2L + 2s
+|-
+|Major 4-smistep
+|3L + s
+|-
+| rowspan="2" |'''5-smistep'''
+|Diminished 5-smistep
+|2L + 3s
+|-
+|Perfect 5-smistep
+|3L + 2s
+|-
+| rowspan="2" |6-smistep
+|Minor 6-smistep
+|3L + 3s
+|-
+|Major 6-smistep
+|4L + 2s
+|-
+|'''7-smistep (octave)'''
+|'''Perfect 7-smistep (octave)'''
+|4L + 3s
+|}
+A 7-note scale using these intervals will typically use scale degrees that represents one size from each interval class, with the true MOS upholding the step pattern of LLsLsLs, or some rotation thereof. MODMOS scales may be formed this way without upholding the step pattern, thereby creating a non-MOS pattern such as LLLssLs, or may include alterations that exceed the two varieties typical of a MOS scale.
+==Notation==
 For this article, note names are based on diamond-MOS notation, where the naturals JKLMNOP are applied to the step pattern LsLsLsL and the accidentals & (pronounced "am" or "amp") and @ (pronounced "at") are used to represent sharps and flats respectively. Thus, the basic gamut for 4L 3s is the following: