Xenharmonic Wiki

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

← Older editNewer edit →
VisualWikitext
Unque (talk | contribs)
217 edits
m Notated quartal inversions
ArrowHead294 (talk | contribs)
14,512 edits
mNo edit summary
Line 191: Line 191:
=== 5L 2s ===
=== 5L 2s ===
The [[5L 2s]] scale is one of two types of Diatonic scales represented in 22edo, and represents the shade of Diatonic popularized by the Greek mathematician Archytas, which uses the 2.3.7 subgroup of Just Intonation.  It is generated by the Circle of Fifths just as in common practice tunings, though the perfect fifth of 22edo is significantly sharper than any tuning attested in common practice, which makes the scale and its chords behave somewhat differently from standard Diatonic functionality.  Notably, suspended chords feel less tense and more restful, while typical tertian triads tend to sound tenser and more energetic; this is the opposite of how these chords behave in Meantone tunings, and as such Western music translated into 22edo's Diatonic may sound strange if it is not adjusted to account for its unique properties.
The [[5L 2s]] scale is one of two types of Diatonic scales represented in 22edo, and represents the shade of Diatonic popularized by the Greek mathematician Archytas, which uses the 2.3.7 subgroup of Just Intonation.  It is generated by the Circle of Fifths just as in common practice tunings, though the perfect fifth of 22edo is significantly sharper than any tuning attested in common practice, which makes the scale and its chords behave somewhat differently from standard Diatonic functionality.  Notably, suspended chords feel less tense and more restful, while typical tertian triads tend to sound tenser and more energetic; this is the opposite of how these chords behave in Meantone tunings, and as such Western music translated into 22edo's Diatonic may sound strange if it is not adjusted to account for its unique properties.
{| class="wikitable"
{| class="wikitable"
|+Modes of 5L 2s
|+ style="font-size: 105%;" | Modes of 5L 2s
!UDP
!Step Pattern
!Notation
!Name
|-
|-
|<nowiki>6|0</nowiki>
! UDP
|LLLsLLs
! Step Pattern
|C - D - E - F♯ - G - A - B - C
! Notation
|Lydian
! Name
|-
|-
|<nowiki>5|1</nowiki>
| 6{{pipe}}0
|LLsLLLs
| LLLsLLs
|C - D - E - F - G - A - B - C
| C - D - E - F♯ - G - A - B - C
|Ionian
| Lydian
|-
|-
|<nowiki>4|2</nowiki>
| 5{{pipe}}1
|LLsLLsL
| LLsLLLs
|C - D - E - F - G - A - B♭ - C
| C - D - E - F - G - A - B - C
|Mixolydian
| Ionian
|-
|-
|<nowiki>3|3</nowiki>
| 4{{pipe}}2
|LsLLLsL
| LLsLLsL
|C - D - E♭ - F - G - A - B♭ - C
| C - D - E - F - G - A - B♭ - C
|Dorian
| Mixolydian
|-
|-
|<nowiki>2|4</nowiki>
| 3{{pipe}}3
|LsLLsLL
| LsLLLsL
|C - D - E♭ - F - G - A♭ - B♭ - C
| C - D - E♭ - F - G - A - B♭ - C
|Aeolian
| Dorian
|-
|-
|<nowiki>1|5</nowiki>
| 2{{pipe}}4
|sLLLsLL
| LsLLsLL
|C - D♭ - E♭ - F - G - A♭ - B♭ - C
| C - D - E♭ - F - G - A♭ - B♭ - C
|Phrygian
| Aeolian
|-
|-
|<nowiki>0|6</nowiki>
| 1{{pipe}}5
|sLLsLLL
| sLLLsLL
|C - D♭ - E♭ - F - G♭ - A♭ - B♭ - C
| C - D♭ - E♭ - F - G - A♭ - B♭ - C
|Locrian
| Phrygian
|-
| 0{{pipe}}6
| sLLsLLL
| C - D♭ - E♭ - F - G♭ - A♭ - B♭ - C
| Locrian
|}
|}


Line 237: Line 239:
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.
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
|+ style="font-size: 105%;" | Modes of 5L 7s
!UDP
!Step Pattern
!Notation
!Name
!Notes
|-
|-
|<nowiki>11|0</nowiki>
! UDP
|LsLsLssLsLss
! Step Pattern
|C - C♯ - D - D♯ - E - E♯ - F♯ - G - G♯ - A - A♯ - B - C
! Notation
|Grave Lydian
! Name
|Like the seven-note Lydian, lacks a Perfect Fourth over the root.
! Notes
|-
|-
|<nowiki>10|1</nowiki>
| 11{{pipe}}0
|LsLssLsLsLss
| LsLsLssLsLss
|C - C♯ - D - D♯ - E - F - F♯ - G - G♯ - A - A♯ - B - C
| C - C♯ - D - D♯ - E - E♯ - F♯ - G - G♯ - A - A♯ - B - C
|Grave Ionian
| Grave Lydian
|
| Like the seven-note Lydian, lacks a Perfect Fourth over the root.
|-
|-
|<nowiki>9|2</nowiki>
| 10{{pipe}}1
|LsLssLsLssLs
| LsLssLsLsLss
|C - C♯ - D - D♯ - E - F - F♯ - G - G♯ - A - B♭ - B - C
| C - C♯ - D - D♯ - E - F - F♯ - G - G♯ - A - A♯ - B - C
|Grave Mixolydian
| Grave Ionian
|
|  
|-
|-
|<nowiki>8|3</nowiki>
| 9{{pipe}}2
|LssLsLsLssLs
| LsLssLsLssLs
|C - C♯ - D - E♭ - E - F - F♯ - G - G♯ - A - B♭ - B - C
| C - C♯ - D - D♯ - E - F - F♯ - G - G♯ - A - B♭ - B - C
|Grave Dorian
| Grave Mixolydian
|
|  
|-
|-
|<nowiki>7|4</nowiki>
| 8{{pipe}}3
|LssLsLssLsLs
| LssLsLsLssLs
|C - C♯ - D - E♭ - E - F - F♯ - G - A♭ - A - B♭ - B - C
| C - C♯ - D - E♭ - E - F - F♯ - G - G♯ - A - B♭ - B - C
|Grave Aeolian
| Grave Dorian
|
|  
|-
|-
|<nowiki>6|5</nowiki>
| 7{{pipe}}4
|sLsLsLssLsLs
| LssLsLssLsLs
|C - D♭ - D - E♭ - E - F - F♯ - G - A♭ - A - B♭ - B - C
| C - C♯ - D - E♭ - E - F - F♯ - G - A♭ - A - B♭ - B - C
|Grave Phrygian
| Grave Aeolian
|Also accounts for Acute Lydian
|  
|-
|-
|<nowiki>5|6</nowiki>
| 6{{pipe}}5
|sLsLssLsLsLs
| sLsLsLssLsLs
|C - D♭ - D - E♭ - E - F - G♭ - G - A♭ - A - B♭ - B - C
| C - D♭ - D - E♭ - E - F - F♯ - G - A♭ - A - B♭ - B - C
|Acute Ionian
| Grave Phrygian
|Also accounts for Grave Locrian
| Also accounts for Acute Lydian
|-
|-
|<nowiki>4|7</nowiki>
| 5{{pipe}}6
|sLsLssLsLssL
| sLsLssLsLsLs
|C - D♭ - D - E♭ - E - F - G♭ - G - A♭ - A - B♭ - C♭ - C
| C - D♭ - D - E♭ - E - F - G♭ - G - A♭ - A - B♭ - B - C
|Acute Mixolydian
| Acute Ionian
|
| Also accounts for Grave Locrian
|-
|-
|<nowiki>3|8</nowiki>
| 4{{pipe}}7
|sLssLsLsLssL
| sLsLssLsLssL
|C - D♭ - D - E♭ - F♭ - F - G♭ - G - A♭ - A - B♭ - C♭ - C
| C - D♭ - D - E♭ - E - F - G♭ - G - A♭ - A - B♭ - C♭ - C
|Acute Dorian
| Acute Mixolydian
|
|  
|-
|-
|<nowiki>2|9</nowiki>
| 3{{pipe}}8
|sLssLsLssLsL
| sLssLsLsLssL
|C - D♭ - D - E♭ - F♭ - F - G♭ - G - A♭ - B𝄫 - B♭ - C♭ - C
| C - D♭ - D - E♭ - F♭ - F - G♭ - G - A♭ - A - B♭ - C♭ - C
|Acute Aeolian
| Acute Dorian
|
|  
|-
|-
|<nowiki>1|10</nowiki>
| 2{{pipe}}9
|ssLsLsLssLsL
| sLssLsLssLsL
|C - D♭ - E𝄫 - E♭ - F♭ - F - G♭ - G - A♭ - B𝄫 - B♭ - C♭ - C
| C - D♭ - D - E♭ - F♭ - F - G♭ - G - A♭ - B𝄫 - B♭ - C♭ - C
|Acute Phrygian
| Acute Aeolian
|
|  
|-
|-
|<nowiki>0|11</nowiki>
| 1{{pipe}}10
|ssLsLssLsLsL
| ssLsLsLssLsL
|C - D♭ - E𝄫 - E♭ - F♭ - F - G♭ - A𝄫 - A♭ - B𝄫 - B♭ - C♭ - C
| C - D♭ - E𝄫 - E♭ - F♭ - F - G♭ - G - A♭ - B𝄫 - B♭ - C♭ - C
|Acute Locrian
| Acute Phrygian
|Like the seven-note Locrian, lacks a Perfect Fifth over the root.
|
|-
| 0{{pipe}}11
| ssLsLssLsLsL
| C - D♭ - E𝄫 - E♭ - F♭ - F - G♭ - A𝄫 - A♭ - B𝄫 - B♭ - C♭ - C
| Acute Locrian
| Like the seven-note Locrian, lacks a Perfect Fifth over the root.
|}
|}


Line 321: Line 324:


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.
{| class="wikitable"
{| class="wikitable"
|+Modes of Right-hand 3L 2M 2s
|+ style="font-size: 105%;" | Modes of Right-hand 3L 2M 2s
!UDP
!Step pattern
!Notation
!Name
!Notes
|-
|-
|<nowiki>6|0</nowiki>
! UDP
|LMLsLMs
! Step pattern
|C - D - vE - vF♯ - G - A - vB - C
! Notation
|Lydian
! Name
|Tritone is precisely the semioctave
! Notes
|-
|-
|<nowiki>5|1</nowiki>
| 6{{pipe}}0
|LsLMsLM
| LMLsLMs
|C - D - ^E♭ - ^F - G - ^A♭ - ^B♭ - C
| C - D - vE - vF♯ - G - A - vB - C
|Aeolian
| Lydian
|Contains the Wolf fourth (^F)
| Tritone is precisely the semioctave
|-
|-
|<nowiki>4|2</nowiki>
| 5{{pipe}}1
|LMsLMLs
| LsLMsLM
|C - D - vE - F - G - vA - vB - C
| C - D - ^E♭ - ^F - G - ^A♭ - ^B♭ - C
|Ionian
| Aeolian
|
| Contains the Wolf fourth (^F)
|-
|-
|<nowiki>3|3</nowiki>
| 4{{pipe}}2
|sLMLsLM
| LMsLMLs
|C - ^D♭ - ^E♭ - F - G - vA♭ - ^B♭ - C
| C - D - vE - F - G - vA - vB - C
|Phrygian
| Ionian
|
|  
|-
|-
|<nowiki>2|4</nowiki>
| 3{{pipe}}3
|MLsLMsL
| sLMLsLM
|C - vD - vE - F - G - vA - B♭ - C
| C - ^D♭ - ^E♭ - F - G - vA♭ - ^B♭ - C
|Mixolydian
| Phrygian
|
|  
|-
|-
|<nowiki>1|5</nowiki>
| 2{{pipe}}4
|sLMsLML
| MLsLMsL
|C - ^D♭ - ^E♭ - F - ^G♭ - ^A♭ - B♭ - C
| C - vD - vE - F - G - vA - B♭ - C
|Locrian
| Mixolydian
|Tritone is precisely the semioctave
|  
|-
|-
|<nowiki>0|6</nowiki>
| 1{{pipe}}5
|MsLMLsL
| sLMsLML
|C - vD - E♭ - F - vG - vA - B♭ - C
| C - ^D♭ - ^E♭ - F - ^G♭ - ^A♭ - B♭ - C
|Dorian
| Locrian
|Contains the Wolf fifth (vG)
| Tritone is precisely the semioctave
|-
| 0{{pipe}}6
| MsLMLsL
| C - vD - E♭ - F - vG - vA - B♭ - C
| Dorian
| Contains the Wolf fifth (vG)
|}
|}
{| class="wikitable"
{| class="wikitable"
|+Modes of Left-hand 3L 2M 2s
|+ style="font-size: 105%;" | Modes of Left-hand 3L 2M 2s
!UDP
|-
!Step pattern
! UDP
!Notation
! Step pattern
!Name
! Notation
!Notes
! Name
! Notes
|-
|-
|<nowiki>6|0</nowiki>
| 6{{pipe}}0
|LsLMLsM
| LsLMLsM
|C - D - ^E♭ - ^F - G - A - ^B♭ - C
| C - D - ^E♭ - ^F - G - A - ^B♭ - C
|Dorian
| Dorian
|Contains the Wolf fourth (^F)
| Contains the Wolf fourth (^F)
|-
|-
|<nowiki>5|1</nowiki>
| 5{{pipe}}1
|LMLsMLs
| LMLsMLs
|C - D - vE - vF♯ - G - vA - vB - C
| C - D - vE - vF♯ - G - vA - vB - C
|Lydian
| Lydian
|Tritone is precisely the semioctave
| Tritone is precisely the semioctave
|-
|-
|<nowiki>4|2</nowiki>
| 4{{pipe}}2
|LsMLsLM
| LsMLsLM
|C - D - ^E♭ - F - G - ^A♭ - ^B♭ - C
| C - D - ^E♭ - F - G - ^A♭ - ^B♭ - C
|Aeolian
| Aeolian
|
|  
|-
|-
|<nowiki>3|3</nowiki>
| 3{{pipe}}3
|MLsLMLs
| MLsLMLs
|C - vD - vE - F - G - vA - vB - C
| C - vD - vE - F - G - vA - vB - C
|Ionian
| Ionian
|
|  
|-
|-
|<nowiki>2|4</nowiki>
| 2{{pipe}}4
|sLMLsML
| sLMLsML
|C - ^D♭ - ^E♭ - F - G - ^A♭ - B♭ - C
| C - ^D♭ - ^E♭ - F - G - ^A♭ - B♭ - C
|Phrygian
| Phrygian
|
|  
|-
|-
|<nowiki>1|5</nowiki>
| 1{{pipe}}5
|MLsMLsL
| MLsMLsL
|C - vD - vE - F - vG - vA - B♭ - C
| C - vD - vE - F - vG - vA - B♭ - C
|Mixolydian
| Mixolydian
|Contains the Wolf fifth (vG)
| Contains the Wolf fifth (vG)
|-
|-
|<nowiki>0|6</nowiki>
| 0{{pipe}}6
|sMLsLML
| sMLsLML
|C - ^D♭ - E♭ - F - ^G♭ - ^A♭ - B♭ - 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 "Superpyth" or "Archy," while the latter can be called "Nicetone" or "Zarlino"
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"


Line 428: Line 436:
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.
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"
{| class="wikitable"
|+Modes of 5L 2m 3s (Grave)
|+ style="font-size: 105%;" | Modes of 5L 2m 3s (Grave)
!UDP
|-
!Step pattern
! UDP
!Notation
! Step pattern
!Name
! Notation
!Notes
! Name
! Notes
|-
|-
|<nowiki>4|0</nowiki>
| 4{{pipe}}0
|LmLsLmLsLs
| LmLsLmLsLs
|C - C♯ - E♭ - E - F - F# - A♭ - A - B♭ - B - C
| C - C♯ - E♭ - E - F - F# - A♭ - A - B♭ - B - C
|Aeolian
| Aeolian
|Contains the Wolf fifth (^G)
| Contains the Wolf fifth (^G)
|-
|-
|<nowiki>3|1</nowiki>
| 3{{pipe}}1
|LmLsLsLmLs
| LmLsLsLmLs
|C - C♯ - E♭ - E - F - F# - G - G♯ - B♭ - B - C
| C - C♯ - E♭ - E - F - F# - G - G♯ - B♭ - B - C
|Dorian
| Dorian
|
|  
|-
|-
|<nowiki>2|2</nowiki>
| 2{{pipe}}2
|LsLmLsLmLs
| LsLmLsLmLs
|C - C♯ - D - D♯ - F - F# - G - G♯ - B♭ - B - C
| C - C♯ - D - D♯ - F - F# - G - G♯ - B♭ - B - C
|Mixolydian
| Mixolydian
|
|  
|-
|-
|<nowiki>1|3</nowiki>
| 1{{pipe}}3
|LsLmLsLsLm
| LsLmLsLsLm
|C - C♯ - D - D♯ - F - F# - G - G♯ - A - A♯ - C
| C - C♯ - D - D♯ - F - F# - G - G♯ - A - A♯ - C
|Ionian
| Ionian
|
|  
|-
|-
|<nowiki>0|4</nowiki>
| 0{{pipe}}4
|LsLsLmLsLm
| LsLsLmLsLm
|C - C♯ - D - D♯ - E - E♯ - G - G♯ - A - A♯ - C
| C - C♯ - D - D♯ - E - E♯ - G - G♯ - A - A♯ - C
|Lydian
| Lydian
|Brightness is reversed - Lydian is the darkest grave mode!
| Brightness is reversed - Lydian is the darkest grave mode!
|}
|}
{| class="wikitable"
{| class="wikitable"
|+Modes of 5L 2m 3s (Acute)
|+ style="font-size: 105%;" | Modes of 5L 2m 3s (Acute)
!UDP
!Step pattern
!Notation
!Name
!Notes
|-
|-
|<nowiki>4|0</nowiki>
! UDP
|mLsLmLsLsL
! Step pattern
|C - E𝄫 - E♭ - F♭ - F - A𝄫 - A♭ - B𝄫 - B♭ - C♭ - C
! Notation
|Locrian
! Name
|Brightness is reversed - Locrian is the brightest acute mode!
! Notes
|-
|-
|<nowiki>3|1</nowiki>
| 4{{pipe}}0
|mLsLsLmLsL
| mLsLmLsLsL
|C - E𝄫 - E♭ - F♭ - F - G♭ - G - B𝄫 - B♭ - C♭ - C
| C - E𝄫 - E♭ - F♭ - F - A𝄫 - A♭ - B𝄫 - B♭ - C♭ - C
|Phrygian
| Locrian
|
| Brightness is reversed - Locrian is the brightest acute mode!
|-
|-
|<nowiki>2|2</nowiki>
| 3{{pipe}}1
|sLmLsLmLsL
| mLsLsLmLsL
|C - D♭ - D - F♭ - F - G♭ - G - B𝄫 - B♭ - C♭ - C
| C - E𝄫 - E♭ - F♭ - F - G♭ - G - B𝄫 - B♭ - C♭ - C
|Aeolian
| Phrygian
|
|  
|-
|-
|<nowiki>1|3</nowiki>
| 2{{pipe}}2
|sLmLsLsLmL
| sLmLsLmLsL
|C - D♭ - D - F♭ - F - G♭ - G - A♭ - A - C♭ - C
| C - D♭ - D - F♭ - F - G♭ - G - B𝄫 - B♭ - C♭ - C
|Dorian
| Aeolian
|
|  
|-
|-
|<nowiki>0|4</nowiki>
| 1{{pipe}}3
|sLsLmLsLmL
| sLmLsLsLmL
|C - D♭ - D - E♭ - E - G♭ - G - A♭ - A - C♭ - C
| C - D♭ - D - F♭ - F - G♭ - G - A♭ - A - C♭ - C
|Mixolydian
| Dorian
|Contains the Wolf fourth (vF)
|
|-
| 0{{pipe}}4
| sLsLmLsLmL
| C - D♭ - D - E♭ - E - G♭ - G - A♭ - A - C♭ - C
| Mixolydian
| Contains the Wolf fourth (vF)
|}
|}
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."
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."
Line 512: Line 523:
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.
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"
{| class="wikitable"
|+Modes of 2L 8s
|+ style="font-size: 105%;" | Modes of 2L 8s
!UDP
!Step pattern
!Notation
!Name
!Notes
|-
|-
|<nowiki>8|0</nowiki>
! UDP
|LssssLssss
! Step pattern
|C - C♯ - ^D - D♯ - F - vF♯ - ^G - G♯ - ^A - A♯ - C
! Notation
|Wolf Minor
! Name
|Contains the wolf fifth (^G)
! Notes
|-
|-
|<nowiki>6|2</nowiki>
| 8{{pipe}}0
|sLssssLsss
| LssssLssss
|C - vC♯ - ^D - D♯ - F - vF♯ - G - G♯ - ^A - A♯ - C
| C - C♯ - ^D - D♯ - F - vF♯ - ^G - G♯ - ^A - A♯ - C
|Dynamic Major
| Wolf Minor
|Dual thirds are subminor and major
| Contains the wolf fifth (^G)
|-
|-
|<nowiki>4|4</nowiki>
| 6{{pipe}}2
|ssLssssLss
| sLssssLsss
|C - vC♯ - D - D♯ - F - vF♯ - G - vG♯ - ^A - A♯ - C
| C - vC♯ - ^D - D♯ - F - vF♯ - G - G♯ - ^A - A♯ - C
|Static Major
| Dynamic Major
|Laterally symmetrical
| Dual thirds are subminor and major
|-
|-
|<nowiki>2|6</nowiki>
| 4{{pipe}}4
|sssLssssLs
| ssLssssLss
|C - vC♯ - D - vD♯ - F - vF♯ - G - vG♯ - A - A♯ - C
| C - vC♯ - D - D♯ - F - vF♯ - G - vG♯ - ^A - A♯ - C
|Static Minor
| Static Major
|Messiaen treated this rotation as the "default"
| Laterally symmetrical
|-
|-
|<nowiki>0|8</nowiki>
| 2{{pipe}}6
|ssssLssssL
| sssLssssLs
|C - vC♯ - D - vD♯ - vF - vF♯ - G - vG♯ - A - vA♯ - C
| C - vC♯ - D - vD♯ - F - vF♯ - G - vG♯ - A - A♯ - C
|Dynamic Minor
| Static Minor
|Dual thirds are minor and supermajor
| Messiaen treated this rotation as the "default"
|-
| 0{{pipe}}8
| ssssLssssL
| C - vC♯ - D - vD♯ - vF - vF♯ - G - vG♯ - A - vA♯ - C
| Dynamic Minor
| Dual thirds are minor and supermajor
|}
|}


=== 4L 5s ===
=== 4L 5s ===
The [[4L 5s]] scale is another quite useful scale available in 22edo <s>and a perfect example of 22edo being better than 31</s>; it is closely associated with [[Orwell]] temperament, and as such is best utilized alongside Orwell Chords for functional harmony (see below).
The [[4L 5s]] scale is another quite useful scale available in 22edo <s>and a perfect example of 22edo being better than 31</s>; it is closely associated with [[Orwell]] temperament, and as such is best utilized alongside Orwell Chords for functional harmony (see below).
{| class="wikitable"
{| class="wikitable"
|+Modes of 4L 5s
|+ style="font-size: 105%;" | Modes of 4L 5s
!UDP
!Step Pattern
!Notation
!Notes
|-
|-
|<nowiki>8|0</nowiki>
! UDP
|LsLsLsLss
! Step Pattern
|C - C♯ - E♭ - ^D♯ - G♭ - ^F♯ - ^A♭ - ^A - A♯ - C
! Notation
|^F♯ is actually the Wolf Fifth in this context, and F♯ is the desirable interval!
! Notes
|-
|-
|<nowiki>7|1</nowiki>
| 8{{pipe}}0
|LsLsLssLs
| LsLsLsLss
|C - C♯ - E♭ - ^D♯ - G♭ - ^F♯ - ^A♭ - A - A♯ - C
| C - C♯ - E♭ - ^D♯ - G♭ - ^F♯ - ^A♭ - ^A - A♯ - C
|
| ^F♯ is actually the Wolf Fifth in this context, and F♯ is the desirable interval!
|-
|-
|<nowiki>6|2</nowiki>
| 7{{pipe}}1
|LsLssLsLs
| LsLsLssLs
|C - C♯ - E♭ - ^D♯ - G♭ - F♯ - ^A♭ - A - A♯ - C
| C - C♯ - E♭ - ^D♯ - G♭ - ^F♯ - ^A♭ - A - A♯ - C
|
|  
|-
|-
|<nowiki>5|3</nowiki>
| 6{{pipe}}2
|LssLsLsLs
| LsLssLsLs
|C - C♯ - E♭ - D♯ - G♭ - F♯ - ^A♭ - A - A♯ - C
| C - C♯ - E♭ - ^D♯ - G♭ - F♯ - ^A♭ - A - A♯ - C
|
|  
|-
|-
|<nowiki>4|4</nowiki>
| 5{{pipe}}3
|sLsLsLsLs
| LssLsLsLs
|C - vC♯ - E♭ - D♯ - G♭ - F♯ - ^A♭ - A - A♯ - C
| C - C♯ - E♭ - D♯ - G♭ - F♯ - ^A♭ - A - A♯ - C
|
|  
|-
|-
|<nowiki>3|5</nowiki>
| 4{{pipe}}4
|sLsLsLssL
| sLsLsLsLs
|C - vC♯ - E♭ - D♯ - G♭ - F♯ - ^A♭ - A - vA♯ - C
| C - vC♯ - E♭ - D♯ - G♭ - F♯ - ^A♭ - A - A♯ - C
|
|  
|-
|-
|<nowiki>2|6</nowiki>
| 3{{pipe}}5
|sLsLssLsL
| sLsLsLssL
|C - vC♯ - E♭ - D♯ - G♭ - F♯ - A♭ - A - vA♯ - C
| C - vC♯ - E♭ - D♯ - G♭ - F♯ - ^A♭ - A - vA♯ - C
|
|  
|-
|-
|<nowiki>1|7</nowiki>
| 2{{pipe}}6
|sLssLsLsL
| sLsLssLsL
|C - vC♯ - E♭ - D♯ - vG♭ - F♯ - A♭ - A - vA♯ - C
| C - vC♯ - E♭ - D♯ - G♭ - F♯ - A♭ - A - vA♯ - C
|vG♭ is actually the Wolf Fourth in this context, and G♭ is the desirable interval!
|  
|-
|-
|<nowiki>0|8</nowiki>
| 1{{pipe}}7
|ssLsLsLsL
| sLssLsLsL
|C - vC♯ - vE♭ - D♯ - vG♭ - F♯ - A♭ - A - vA♯ - C
| C - vC♯ - E♭ - D♯ - vG♭ - F♯ - A♭ - A - vA♯ - C
|Subminor third above the root is unavailable in this mode.
| vG♭ is actually the Wolf Fourth in this context, and G♭ is the desirable interval!
|-
| 0{{pipe}}8
| ssLsLsLsL
| C - vC♯ - vE♭ - D♯ - vG♭ - F♯ - A♭ - A - vA♯ - C
| Subminor third above the root is unavailable in this mode.
|}
|}


Line 612: Line 626:


Additionally, there are four distinct types of diminished triads that can be formed using the two types of minor thirds; due to the [[225/224|Marvel comma]] being tempered out in 22edo, however, there are only two distinct types of augmented triads that can be formed using the two types of major thirds, as 7 + 7 + 8 = 22.
Additionally, there are four distinct types of diminished triads that can be formed using the two types of minor thirds; due to the [[225/224|Marvel comma]] being tempered out in 22edo, however, there are only two distinct types of augmented triads that can be formed using the two types of major thirds, as 7 + 7 + 8 = 22.
{| class="wikitable"
{| class="wikitable"
|+Tertiary Chords
|+ style="font-size: 105%;" | Tertiary Chords
!Name
|-
!Symbol
! Name
!Notation
! Symbol
!Formula
! Notation
!Otonal
! Formula
!Utonal
! Otonal
! Utonal
|-
|-
|Major
| Major
|C maj
| C maj
|C - vE - G
| C - vE - G
|7\22 + 6\22
| 7\22 + 6\22
|4:5:6
| 4:5:6
|1/(15:12:10)
| 1/(15:12:10)
|-
|-
|Minor
| Minor
|c min
| c min
|C - ^E♭ - G
| C - ^E♭ - G
|6\22 + 7\22
| 6\22 + 7\22
|10:12:15
| 10:12:15
|1/(6:5:4)
| 1/(6:5:4)
|-
|-
|Supermajor
| Supermajor
|C saj
| C saj
|C - E - G
| C - E - G
|8\22 + 5\22
| 8\22 + 5\22
|14:18:21
| 14:18:21
|1/(9:7:1)
| 1/(9:7:1)
|-
|-
|Subminor
| Subminor
|c sin
| c sin
|C - E♭ - G
| C - E♭ - G
|5\22 + 8\22
| 5\22 + 8\22
|6:7:9
| 6:7:9
|1/(21:18:14)
| 1/(21:18:14)
|-
|-
|Orwell Dim.
| Orwell Dim.
|c<sup>ow</sup>
| c<sup>ow</sup>
|C - E♭ - G♭
| C - E♭ - G♭
|5\22 + 5\22
| 5\22 + 5\22
|36:32:49
| 36:32:49
|1/(49:32:36)
| 1/(49:32:36)
|-
|-
|Utonal Dim.
| Utonal Dim.
|c<sup>ut</sup>
| c<sup>ut</sup>
|C - E♭ - ^G♭
| C - E♭ - ^G♭
|5\22 + 6\22
| 5\22 + 6\22
|30:35:42
| 30:35:42
|1/(7:6:5)
| 1/(7:6:5)
|-
|-
|Otonal Dim.
| Otonal Dim.
|c<sup>ot</sup>
| c<sup>ot</sup>
|C - ^E♭ - ^G♭
| C - ^E♭ - ^G♭
|6\22 + 5\22
| 6\22 + 5\22
|5:6:7
| 5:6:7
|1/(42:35:30)
| 1/(42:35:30)
|-
|-
|Orgone Dim.
| Orgone Dim.
|c<sup>og</sup>
| c<sup>og</sup>
|C - ^E♭ - vG
| C - ^E♭ - vG
|6\22 + 6\22
| 6\22 + 6\22
|25:30:36
| 25:30:36
|1/(36:30:25)
| 1/(36:30:25)
|-
|-
|Marvel
| Marvel
|C+
| C+
|C - vE - ^G
| C - vE - ^G
|7\22 + 7\22
| 7\22 + 7\22
|16:20:25
| 16:20:25
|1/(25:20:16)
| 1/(25:20:16)
|-
|-
|Marvel (1st inv.)
| Marvel (1st inv.)
|vE+/C
| vE+/C
|C - vE - vG♯
| C - vE - vG♯
|7\22 + 8\22
| 7\22 + 8\22
|20:25:32
| 20:25:32
|1/(40:32:25)
| 1/(40:32:25)
|-
|-
|Marvel (2nd inv.)
| Marvel (2nd inv.)
|vG♯+/C
| vG♯+/C
|C - E - vG♯
| C - E - vG♯
|8\22 + 7\22
| 8\22 + 7\22
|25:32:40
| 25:32:40
|1/(32:25:20)
| 1/(32:25:20)
|-
|-
|Sensamagic
| Sensamagic
|C×
| C×
|C - E - G♯
| C - E - G♯
|8\22 + 8\22
| 8\22 + 8\22
|21:27:35
| 21:27:35
|1/(45:35:27)
| 1/(45:35:27)
|}
|}


=== Quartal Inversions ===
=== Quartal Inversions ===
In diatonic tunings with a sharp-tempered 3/2, such as the [[Superpyth]] diatonic found in 22edo, quartal harmony is often more concordant than tertian harmony; as such, musicians interested in using Superpyth should familiarize themselves with the Quartal Triad and its inversions.
In diatonic tunings with a sharp-tempered 3/2, such as the [[Superpyth]] diatonic found in 22edo, quartal harmony is often more concordant than tertian harmony; as such, musicians interested in using Superpyth should familiarize themselves with the Quartal Triad and its inversions.
{| class="wikitable"
{| class="wikitable"
|+Quartal Inversions
|+ style="font-size: 105%;" | Quartal Inversions
!UDP
|-
!Symbol
! UDP
!Notation
! Symbol
!Formula
! Notation
!3-limit JI
! Formula
!7-limit JI
! 3-limit JI
! 7-limit JI
|-
|-
|<nowiki>2|0</nowiki>
| 2{{pipe}}0
|C<sup>4</sup>
| C<sup>4</sup>
|C - F - B♭
| C - F - B♭
|9\22 + 9\22
| 9\22 + 9\22
|9:12:16
| 9:12:16
|16:21:28
| 16:21:28
|-
|-
|<nowiki>1|1</nowiki>
| 1{{pipe}}1
|Csus4
| Csus4
|C - F - G
| C - F - G
|9\22 + 4\22
| 9\22 + 4\22
|6:8:9
| 6:8:9
|16:21:24
| 16:21:24
|-
|-
|<nowiki>0|2</nowiki>
| 0{{pipe}}2
|Csus2
| Csus2
|C - D - G
| C - D - G
|4\22 + 9\22
| 4\22 + 9\22
|8:9:12
| 8:9:12
|14:16:21
| 14:16:21
|}
|}


Retrieved from "https://en.xen.wiki/w/22edo/Unque%27s_compositional_approach"