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22edo/Unque's compositional approach: Difference between revisions

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→Intervals: The Balzano temp is not as unnamed as previous versions of the page suggested.
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Unque (talk | contribs)
217 edits
Greatly expanded the "scales" section
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[[Ups and downs notation]] uses the accidentals ^ and v to modify a given note by one step of 22edo


=== The thirds of 22edo ===
=== The thirds of 22edo ===
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|<nowiki>6|0</nowiki>
|<nowiki>6|0</nowiki>
|LLLsLLs
|LLLsLLs
|C - D - E - F# - G - A - B - C
|C - D - E - F♯ - G - A - B - C
|Lydian
|Lydian
|-
|-
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|<nowiki>4|2</nowiki>
|<nowiki>4|2</nowiki>
|LLsLLsL
|LLsLLsL
|C - D - E - F - G - A - Bb - C
|C - D - E - F - G - A - B♭ - C
|Mixolydian
|Mixolydian
|-
|-
|<nowiki>3|3</nowiki>
|<nowiki>3|3</nowiki>
|LsLLLsL
|LsLLLsL
|C - D - Eb - F - G - A - Bb - C
|C - D - E♭ - F - G - A - B♭ - C
|Dorian
|Dorian
|-
|-
|<nowiki>2|4</nowiki>
|<nowiki>2|4</nowiki>
|LsLLsLL
|LsLLsLL
|C - D - Eb - F - G - Ab - Bb - C
|C - D - E♭ - F - G - A♭ - B♭ - C
|Aeolian
|Aeolian
|-
|-
|<nowiki>1|5</nowiki>
|<nowiki>1|5</nowiki>
|sLLLsLL
|sLLLsLL
|C - Db - Eb - F - G - Ab - Bb - C
|C - D♭ - E♭ - F - G - A♭ - B♭ - C
|Phrygian
|Phrygian
|-
|-
|<nowiki>0|6</nowiki>
|<nowiki>0|6</nowiki>
|sLLsLLL
|sLLsLLL
|C - Db - Eb - F - Gb - Ab - Bb - C
|C - D♭ - E♭ - F - G♭ - A♭ - B♭ - C
|Locrian
|Locrian
|}
|}


=== 5L 7s ===
=== 5L 7s ===
The [[5L 7s]] scale is an extension of 5L 2s created by continuing the generator sequence.  It has twelve unique rotations, which can be categorized as Grave and Acute forms of the seven diatonic modes.
The [[5L 7s]] scale is an extension of 5L 2s created by continuing the generator sequence.  Because the Circle of Fifths is bidirectional, the seven modes can be extended either by continuing the sequence upwards or downwards; those created by going up the chain are called grave modes, and those extended by going down the chain are called acute modes.
{| class="wikitable"
{| class="wikitable"
|+Modes of 5L 7s
|+Modes of 5L 7s
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=== 3L 2M 2s ===
=== 3L 2M 2s ===
The [[Nicetone|3L 2M 2s]] scale is the other type of Diatonic scale represented in 22edo; this one represents the 5-limit shade of Diatonic popularized by musicians and theorists such as Ptolemy and Zarlino.  It is generated by alternating intervals 6\22 and 7\22, and as such yields two different forms ("left-hand" and "right-hand") based on which generator is comes first and which comes second.
The [[Nicetone|3L 2M 2s]] scale is the other type of Diatonic scale represented in 22edo; this one represents the 5-limit shade of Diatonic popularized by musicians and theorists such as Ptolemy and Zarlino.  It is generated by alternating intervals 6\22 and 7\22, and as such yields two different forms ("left-hand" and "right-hand") based on which generator comes first and which comes second.


The 5-limit harmony of this scale is much more reminiscent of the familiar harmony used in common-practice music, so popular music translated into this scale will be much more faithful to the harmony of the original piece than it would be using 5L 2s.
The 5-limit harmony of this scale is much more reminiscent of the familiar harmony used in common-practice music, so popular music translated into this scale will be much more faithful to the harmony of the original piece than it would be using 5L 2s.
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|<nowiki>6|0</nowiki>
|<nowiki>6|0</nowiki>
|LMLsLMs
|LMLsLMs
|C - D - Ev - F#v - G - A - Bv - C
|C - D - vE - vF♯ - G - A - vB - C
|Lydian
|Lydian
|Tritone is precisely the semioctave
|Tritone is precisely the semioctave
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|<nowiki>5|1</nowiki>
|<nowiki>5|1</nowiki>
|LsLMsLM
|LsLMsLM
|C - D - Eb^ - F^ - G - Ab^ - Bb^ - C
|C - D - ^E♭ - ^F - G - ^A♭ - ^B♭ - C
|Aeolian
|Aeolian
|Contains the Wolf fourth
|Contains the Wolf fourth (^F)
|-
|-
|<nowiki>4|2</nowiki>
|<nowiki>4|2</nowiki>
|LMsLMLs
|LMsLMLs
|C - D - Ev - F - G - Av - Bv - C
|C - D - vE - F - G - vA - vB - C
|Ionian
|Ionian
|
|
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|<nowiki>3|3</nowiki>
|<nowiki>3|3</nowiki>
|sLMLsLM
|sLMLsLM
|C - Db^ - Eb^ - F - G - Ab^ - Bb^ - C
|C - ^D♭ - ^E♭ - F - G - vA♭ - ^B♭ - C
|Phrygian
|Phrygian
|
|
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|<nowiki>2|4</nowiki>
|<nowiki>2|4</nowiki>
|MLsLMsL
|MLsLMsL
|C - Dv - Ev - F - G - Av - Bb - C
|C - vD - vE - F - G - vA - B♭ - C
|Mixolydian
|Mixolydian
|
|
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|<nowiki>1|5</nowiki>
|<nowiki>1|5</nowiki>
|sLMsLML
|sLMsLML
|C - Db^ - Eb^ - F - Gb^ - Ab^ - Bb - C
|C - ^D♭ - ^E♭ - F - ^G♭ - ^A♭ - B♭ - C
|Locrian
|Locrian
|Tritone is precisely the semioctave
|Tritone is precisely the semioctave
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|<nowiki>0|6</nowiki>
|<nowiki>0|6</nowiki>
|MsLMLsL
|MsLMLsL
|C - Dv - Eb - F - Gv - Av - Bb - C
|C - vD - E♭ - F - vG - vA - B♭ - C
|Dorian
|Dorian
|Contains the Wolf fifth
|Contains the Wolf fifth (vG)
|}
|}
{| class="wikitable"
{| class="wikitable"
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|<nowiki>6|0</nowiki>
|<nowiki>6|0</nowiki>
|LsLMLsM
|LsLMLsM
|C - D - Eb^ - F^ - G - A - Bb^ - C
|C - D - ^E♭ - ^F - G - A - ^B♭ - C
|Dorian
|Dorian
|Contains the Wolf fourth
|Contains the Wolf fourth (^F)
|-
|-
|<nowiki>5|1</nowiki>
|<nowiki>5|1</nowiki>
|LMLsMLs
|LMLsMLs
|C - D - Ev - F#v - G - Av - Bv - C
|C - D - vE - vF♯ - G - vA - vB - C
|Lydian
|Lydian
|Tritone is precisely the semioctave
|Tritone is precisely the semioctave
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|<nowiki>4|2</nowiki>
|<nowiki>4|2</nowiki>
|LsMLsLM
|LsMLsLM
|C - D - Eb^ - F - G - Ab^ - Bb^ - C
|C - D - ^E♭ - F - G - ^A♭ - ^B♭ - C
|Aeolian
|Aeolian
|
|
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|<nowiki>3|3</nowiki>
|<nowiki>3|3</nowiki>
|MLsLMLs
|MLsLMLs
|C - Dv - Ev - F - G - Av - Bv - C
|C - vD - vE - F - G - vA - vB - C
|Ionian
|Ionian
|
|
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|<nowiki>2|4</nowiki>
|<nowiki>2|4</nowiki>
|sLMLsML
|sLMLsML
|C - Db^ - Eb^ - F - G - Ab^ - Bb - C
|C - ^D♭ - ^E♭ - F - G - ^A♭ - B♭ - C
|Phrygian
|Phrygian
|
|
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|<nowiki>1|5</nowiki>
|<nowiki>1|5</nowiki>
|MLsMLsL
|MLsMLsL
|C - Dv - Ev - F - Gv - Av - Bb - C
|C - vD - vE - F - vG - vA - B♭ - C
|Mixolydian
|Mixolydian
|Contains the Wolf fifth
|Contains the Wolf fifth (vG)
|-
|-
|<nowiki>0|6</nowiki>
|<nowiki>0|6</nowiki>
|sMLsLML
|sMLsLML
|C - Db^ - Eb - F - Gb^ - Ab^ - Bb - C
|C - ^D♭ - E♭ - F - ^G♭ - ^A♭ - B♭ - C
|Locrian
|Locrian
|Tritone is precisely the semioctave
|Tritone is precisely the semioctave
|}
|}
When disambiguation is needed between the modes of 5L 2s and 3L 2M 2s, the former can be described as e.g. "Superpyth Ionian" or "Superpyth Aeolian," and the latter as e.g. "Nice Ionian" or "Nice Aeolian."
When disambiguation is needed between the modes of 5L 2s and 3L 2M 2s, the former can be described as "Superpyth" or "Archy," while the latter can be called "Nicetone" or "Zarlino"
 
=== 5L 2m 3s ===
The [[Blackdye|5L 2m 3s]] scale functions as an extension to 3L 2M 2s, created by adding a commatic step into each large step of that Diatonic scale.  This provides the scale with three new modes in addition to the seven already present.  Due to the commatic step, this scale does not distinguish the left-hand from the right-hand variants.
 
While there is no singular generator sequence used to create this scale, it can be thought of as two pentatonic scales offset by a neutral second, which is coincidentally the amount by which a sharp or flat alters a note; this makes the scale easy to notate as a pentatonic scale and its sharp/flat counterpart. This splits the modes into five "grave" modes and five "acute" modes, where the grave modes place the root on the flattened pentatonic, and the acute modes place the root on the sharpened one.
{| class="wikitable"
|+Modes of 5L 2m 3s (Grave)
!UDP
!Step pattern
!Notation
!Name
!Notes
|-
|<nowiki>4|0</nowiki>
|LmLsLmLsLs
|C - C♯ - E♭ - E - F - F# - A♭ - A - B♭ - B - C
|Aeolian
|Contains the Wolf fifth (A♭)
|-
|<nowiki>3|1</nowiki>
|LmLsLsLmLs
|C - C♯ - E♭ - E - F - F# - G - G♯ - B♭ - B - C
|Dorian
|
|-
|<nowiki>2|2</nowiki>
|LsLmLsLmLs
|C - C♯ - D - D♯ - F - F# - G - G♯ - B♭ - B - C
|Mixolydian
|
|-
|<nowiki>1|3</nowiki>
|LsLmLsLsLm
|C - C♯ - D - D♯ - F - F# - G - G♯ - A - A♯ - C
|Ionian
|
|-
|<nowiki>0|4</nowiki>
|LsLsLmLsLm
|C - C♯ - D - D♯ - E - E♯ - G - G♯ - A - A♯ - C
|Lydian
|Brightness is reversed - Lydian is the darkest grave mode!
|}
{| class="wikitable"
|+Modes of 5L 2m 3s (Acute)
!UDP
!Step pattern
!Notation
!Name
!Notes
|-
|<nowiki>4|0</nowiki>
|mLsLmLsLsL
|C - E𝄫 - E♭ - F♭ - F - A𝄫 - A♭ - B𝄫 - B♭ - C♭ - C
|Locrian
|Brightness is reversed - Locrian is the brightest acute mode!
|-
|<nowiki>3|1</nowiki>
|mLsLsLmLsL
|C - E𝄫 - E♭ - F♭ - F - G♭ - G - B𝄫 - B♭ - C♭ - C
|Phrygian
|
|-
|<nowiki>2|2</nowiki>
|sLmLsLmLsL
|C - D♭ - D - F♭ - F - G♭ - G - B𝄫 - B♭ - C♭ - C
|Aeolian
|
|-
|<nowiki>1|3</nowiki>
|sLmLsLsLmL
|C - D♭ - D - F♭ - F - G♭ - G - A♭ - A - C♭ - C
|Dorian
|
|-
|<nowiki>0|4</nowiki>
|sLsLmLsLmL
|C - D♭ - D - E♭ - E - G♭ - G - A♭ - A - C♭ - C
|Mixolydian
|E is used as a Wolf fourth, not a Supermajor Third
|}
Where disambiguation is needed between the modes of 5L 7s and 5L 2M 2s, the former can be described as "chromatic," and the latter as "blackdye."
 
=== 2L 8s ===
The [[2L 8s]] scale is another characteristic scale of 22edo, which was discovered independently by [[Paul Erlich]], [[Gene Ward Smith]], and Olivier Messiaen (though the latter theorist documented [https://ianring.com/musictheory/scales/3055 the scale's analog in 12edo] rather than in 22).
 
This scale is a mode of limited transposition, which means that it has some amount of rotational symmetry. In this case, the semioctave is the axis of symmetry, and transposing a mode up by 11 steps of 22edo (or 6 steps of 12edo in the case of Messiaen's works) yields the same set of pitches as the mode on which you started.
 
Erlich divides four of the five unique rotations into a 2x2 grid, categorized by how many thirds it contains (one third is "static," two is "dynamic,") and which type of third falls on the fourth degree of the scale (major or minor).  The brightest mode does not appear to have been considered by Erlich, due to lacking a perfect fifth above the root.
{| class="wikitable"
|+Modes of 2L 8s
!UDP
!Step pattern
!Notation
!Name
!Notes
|-
|<nowiki>8|0</nowiki>
|LssssLssss
|
|Wolf Minor
|Contains the wolf fifth
|-
|<nowiki>6|2</nowiki>
|sLssssLsss
|
|Dynamic Major
|Dual thirds are subminor and major
|-
|<nowiki>4|4</nowiki>
|ssLssssLss
|
|Static Major
|Laterally symmetrical (flipping the scale upside-down yields the same pitches)
|-
|<nowiki>2|6</nowiki>
|sssLssssLs
|
|Static Minor
|Messiaen treated this rotation as the "default"
|-
|<nowiki>0|8</nowiki>
|ssssLssssL
|
|Dynamic Minor
|Dual thirds are minor and supermajor
|}
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