15edo/Unque's compositional approach: Difference between revisions

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Elaborated on how 3L 2M 2s works, and reanalyzed Right-Hand as the "default" form.
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|C# = Db
|C# = Db
|B# = Db
|B# = Db
|C# = Db
|C#
|-
|-
|2\15
|2\15
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|D
|D
|C#
|C#
|D
|Db
|-
|-
|3\15
|3\15
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|D# = Eb
|D# = Eb
|D
|D
|D#
|D
|-
|-
|4\15
|4\15
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|E
|E
|Eb
|Eb
|Eb
|D# = Eb
|-
|-
|5\15
|5\15
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=== 3L 2M 2s ===
=== 3L 2M 2s ===
The [[Nicetone|3L 2M 2s]] scale is often used as an analog to Diatonic in 15edo, as its step pattern resembles that of the Zarlino scale that was historically used as a ternary version of Diatonic that was considered to have more consonant thirds.  Whereas the true Zarlino scale was made by alternating 5/4 and 6/5 as generators, 15edo's 3L2M2s scale can be made by alternating 5\15 and 4\15 generators.
The [[Nicetone|3L 2M 2s]] scale is often used as an analog to Diatonic in 15edo, as its step pattern resembles that of the Zarlino scale that was historically used as a ternary version of Diatonic that was considered to have more consonant thirds.  Whereas the true Zarlino scale was made by alternating 5/4 and 6/5 as generators, 15edo's 3L2M2s scale can be made by alternating 5\15 and 4\15 generators.  Rather than tempering out the [[81/80|syntonic comma]] (the difference between the two types of whole tone) as in common-practice Western music, 15edo tempers the scale such that the syntonic comma is equal to the semitone.


There are two versions of this scale; the left hand version results when the number of minor third generators outnumber the major third generators, and the right hand version results when the opposite is true.  Each of these versions has seven unique modes.
There are two versions of the 3L 2M 2s scale; the left hand version results when the number of minor third generators outnumber the major third generators, and the right hand version results when the opposite is true.  Each of these versions has seven unique modes.
{| class="wikitable"
{| class="wikitable"
|+Modes of Left-hand 3L2M2s
|+Modes of Right-hand 3L 2M 2s
!UDP
!UDP
!Step pattern
!Step pattern
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|-
|-
|<nowiki>6|0</nowiki>
|<nowiki>6|0</nowiki>
|LsLMLsM
|LMLsLMs
|C - D# - Eb - F# - G - A# - Bb - C
|C - D - E - Fx - G - A# - B - C
|Dorian
|Pat 2
|-
|<nowiki>5|1</nowiki>
|LMLsMLs
|C - D# - E - Fx - G - A - B - C
|Lydian
|Lydian
|Pat 3
|Pat 3
|-
|-
|<nowiki>4|2</nowiki>
|<nowiki>5|1</nowiki>
|LsMLsLM
|LsLMsLM
|C - D# - Ebb - F - G - Ab - Bb - C
|C - D - Ebb - F# - G - Ab - Bb - C
|Aeolian
|Aeolian
|Pat 1
|Pat 1
|-
|-
|<nowiki>3|3</nowiki>
|<nowiki>4|2</nowiki>
|MLsLMLs
|LMsLMLs
|C - D - E - F - G - A - B - C
|C - D - E - F - G - A - B - C
|Ionian
|Ionian
|Pat 3
|Pat 3
|-
|-
|<nowiki>2|4</nowiki>
|<nowiki>3|3</nowiki>
|sLMLsML
|sLMLsLM
|C - D - Ebb - F - G - Ab - Bbb - C
|C - Db - Ebb - F - G - Ab - Bb - C
|Phrygian
|Phrygian
|Pat 1
|Pat 1
|-
|<nowiki>2|4</nowiki>
|MLsLMsL
|C - Db - E - F - G - A - Bbb - C
|Mixolydian
|Pat 3
|-
|-
|<nowiki>1|5</nowiki>
|<nowiki>1|5</nowiki>
|MLsMLsL
|sLMsLML
|C - D - E - F - Gb - A - Bbb - C
|C - Dbb - Eb - F - Gbb - Ab - Bbb - C
|Mixolydian
|Locrian
|Patdim 3
|Susaug 2
|-
|-
|<nowiki>0|6</nowiki>
|<nowiki>0|6</nowiki>
|sMLsLML
|MsLMLsL
|C - Db - Ebb - F - Gbb - Ab - Bbb - C
|C - Db - Ebb - F - Gb - A - Bbb - C
|Locrian
|Dorian
|Susaug 1
|Patdim 1
|}
|}
{| class="wikitable"
{| class="wikitable"
|+Modes of Right-hand 3L2M2s
|+Modes of Left-hand 3L 2M 2s
!UDP
!UDP
!Step pattern
!Step pattern
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|-
|-
|<nowiki>6|0</nowiki>
|<nowiki>6|0</nowiki>
|LMLsLMs
|LsLMLsM
|C - D# - E - Fx - G - A# - B - C
|C - D - Eb - F# - G - A# - Bb - C
|Dorian
|Pat 2
|-
|<nowiki>5|1</nowiki>
|LMLsMLs
|C - D - E - Fx - G - A - B - C
|Lydian
|Lydian
|Pat 3
|Pat 3
|-
|-
|<nowiki>5|1</nowiki>
|<nowiki>4|2</nowiki>
|LsLMsLM
|LsMLsLM
|C - D# - Ebb - F# - G - Ab - Bb - C
|C - D - Ebb - F - G - Ab - Bb - C
|Aeolian
|Aeolian
|Pat 1
|Pat 1
|-
|-
|<nowiki>4|2</nowiki>
|<nowiki>3|3</nowiki>
|LMsLMLs
|MLsLMLs
|C - D# - E - F - G - A - B - C
|C - Db - E - F - G - A - B - C
|Ionian
|Ionian
|Pat 3
|Pat 3
|-
|-
|<nowiki>3|3</nowiki>
|<nowiki>2|4</nowiki>
|sLMLsLM
|sLMLsML
|C - D - Ebb - F - G - Ab - Bb - C
|C - Db - Ebb - F - G - Ab - Bbb - C
|Phrygian
|Phrygian
|Pat 1
|Pat 1
|-
|-
|<nowiki>2|4</nowiki>
|<nowiki>1|5</nowiki>
|MLsLMsL
|MLsMLsL
|C - D - E - F - G - A - Bbb - C
|C - Db - E - F - Gb - A - Bbb - C
|Mixolydian
|Mixolydian
|Pat 3
|Patdim 3
|-
|-
|<nowiki>1|5</nowiki>
|<nowiki>0|6</nowiki>
|sLMsLML
|sMLsLML
|C - Db - Eb - F - Gbb - Ab - Bbb - C
|C - Dbb - Ebb - F - Gbb - Ab - Bbb - C
|Locrian
|Locrian
|Susaug 2
|Susaug 1
|-
|<nowiki>0|6</nowiki>
|MsLMLsL
|C - D - Ebb - F - Gb - A - Bbb - C
|Dorian
|Patdim 1
|}
|}