Xenharmonic Wiki

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

← Older editNewer edit →
VisualWikitext
Unque (talk | contribs)
217 edits
No edit summary
Unque (talk | contribs)
217 edits
Added 3L 4s.
Line 194: Line 194:
|+ style="font-size: 105%;" | Modes of 5L 2s
|+ style="font-size: 105%;" | Modes of 5L 2s
|-
|-
! UDP
! Gens Up
! Step Pattern
! Step Pattern
! Notation
! Notation
! Name
! Name
|-
|-
| 6{{pipe}}0
| 6
| LLLsLLs
| LLLsLLs
| C - D - E - F♯ - G - A - B - C
| C - D - E - F♯ - G - A - B - C
| Lydian
| Lydian
|-
|-
| 5{{pipe}}1
| 5
| LLsLLLs
| LLsLLLs
| C - D - E - F - G - A - B - C
| C - D - E - F - G - A - B - C
| Ionian
| Ionian
|-
|-
| 4{{pipe}}2
| 4
| LLsLLsL
| LLsLLsL
| C - D - E - F - G - A - B♭ - C
| C - D - E - F - G - A - B♭ - C
Line 219: Line 219:
| Dorian
| Dorian
|-
|-
| 2{{pipe}}4
| 2
| LsLLsLL
| LsLLsLL
| C - D - E♭ - F - G - A♭ - B♭ - C
| C - D - E♭ - F - G - A♭ - B♭ - C
| Aeolian
| Aeolian
|-
|-
| 1{{pipe}}5
| 1
| sLLLsLL
| sLLLsLL
| C - D♭ - E♭ - F - G - A♭ - B♭ - C
| C - D♭ - E♭ - F - G - A♭ - B♭ - C
| Phrygian
| Phrygian
|-
|-
| 0{{pipe}}6
| 0
| sLLsLLL
| sLLsLLL
| C - D♭ - E♭ - F - G♭ - A♭ - B♭ - C
| C - D♭ - E♭ - F - G♭ - A♭ - B♭ - C
Line 240: Line 240:
|+ style="font-size: 105%;" | Modes of 5L 7s
|+ style="font-size: 105%;" | Modes of 5L 7s
|-
|-
! UDP
! Gens Up
! Step Pattern
! Step Pattern
! Notation
! Notation
Line 246: Line 246:
! Notes
! Notes
|-
|-
| 11{{pipe}}0
| 11
| LsLsLssLsLss
| LsLsLssLsLss
| C - C♯ - D - D♯ - E - E♯ - F♯ - G - G♯ - A - A♯ - B - C
| C - C♯ - D - D♯ - E - E♯ - F♯ - G - G♯ - A - A♯ - B - C
Line 252: Line 252:
| Like the seven-note Lydian, lacks a Perfect Fourth over the root.
| Like the seven-note Lydian, lacks a Perfect Fourth over the root.
|-
|-
| 10{{pipe}}1
| 10
| LsLssLsLsLss
| LsLssLsLsLss
| C - C♯ - D - D♯ - E - F - F♯ - G - G♯ - A - A♯ - B - C
| C - C♯ - D - D♯ - E - F - F♯ - G - G♯ - A - A♯ - B - C
Line 258: Line 258:
|  
|  
|-
|-
| 9{{pipe}}2
| 9
| LsLssLsLssLs
| LsLssLsLssLs
| C - C♯ - D - D♯ - E - F - F♯ - G - G♯ - A - B♭ - B - C
| C - C♯ - D - D♯ - E - F - F♯ - G - G♯ - A - B♭ - B - C
Line 264: Line 264:
|  
|  
|-
|-
| 8{{pipe}}3
| 8
| LssLsLsLssLs
| LssLsLsLssLs
| C - C♯ - D - E♭ - E - F - F♯ - G - G♯ - A - B♭ - B - C
| C - C♯ - D - E♭ - E - F - F♯ - G - G♯ - A - B♭ - B - C
Line 270: Line 270:
|  
|  
|-
|-
| 7{{pipe}}4
| 7
| LssLsLssLsLs
| LssLsLssLsLs
| C - C♯ - D - E♭ - E - F - F♯ - G - A♭ - A - B♭ - B - C
| C - C♯ - D - E♭ - E - F - F♯ - G - A♭ - A - B♭ - B - C
Line 276: Line 276:
|  
|  
|-
|-
| 6{{pipe}}5
| 6
| sLsLsLssLsLs
| sLsLsLssLsLs
| C - D♭ - D - E♭ - E - F - F♯ - G - A♭ - A - B♭ - B - C
| C - D♭ - D - E♭ - E - F - F♯ - G - A♭ - A - B♭ - B - C
Line 282: Line 282:
| Also accounts for Acute Lydian
| Also accounts for Acute Lydian
|-
|-
| 5{{pipe}}6
| 5
| sLsLssLsLsLs
| sLsLssLsLsLs
| C - D♭ - D - E♭ - E - F - G♭ - G - A♭ - A - B♭ - B - C
| C - D♭ - D - E♭ - E - F - G♭ - G - A♭ - A - B♭ - B - C
Line 288: Line 288:
| Also accounts for Grave Locrian
| Also accounts for Grave Locrian
|-
|-
| 4{{pipe}}7
| 4
| sLsLssLsLssL
| sLsLssLsLssL
| C - D♭ - D - E♭ - E - F - G♭ - G - A♭ - A - B♭ - C♭ - C
| C - D♭ - D - E♭ - E - F - G♭ - G - A♭ - A - B♭ - C♭ - C
Line 294: Line 294:
|  
|  
|-
|-
| 3{{pipe}}8
| 3
| sLssLsLsLssL
| sLssLsLsLssL
| C - D♭ - D - E♭ - F♭ - F - G♭ - G - A♭ - A - B♭ - C♭ - C
| C - D♭ - D - E♭ - F♭ - F - G♭ - G - A♭ - A - B♭ - C♭ - C
Line 300: Line 300:
|  
|  
|-
|-
| 2{{pipe}}9
| 2
| sLssLsLssLsL
| sLssLsLssLsL
| C - D♭ - D - E♭ - F♭ - F - G♭ - G - A♭ - B𝄫 - B♭ - C♭ - C
| C - D♭ - D - E♭ - F♭ - F - G♭ - G - A♭ - B𝄫 - B♭ - C♭ - C
Line 306: Line 306:
|  
|  
|-
|-
| 1{{pipe}}10
| 1
| ssLsLsLssLsL
| ssLsLsLssLsL
| C - D♭ - E𝄫 - E♭ - F♭ - F - G♭ - G - A♭ - B𝄫 - B♭ - C♭ - C
| C - D♭ - E𝄫 - E♭ - F♭ - F - G♭ - G - A♭ - B𝄫 - B♭ - C♭ - C
Line 312: Line 312:
|  
|  
|-
|-
| 0{{pipe}}11
| 0
| ssLsLssLsLsL
| ssLsLssLsLsL
| C - D♭ - E𝄫 - E♭ - F♭ - F - G♭ - A𝄫 - A♭ - B𝄫 - B♭ - C♭ - C
| C - D♭ - E𝄫 - E♭ - F♭ - F - G♭ - A𝄫 - A♭ - B𝄫 - B♭ - C♭ - C
Line 328: Line 328:
|+ style="font-size: 105%;" | Modes of Right-hand 3L 2M 2s
|+ style="font-size: 105%;" | Modes of Right-hand 3L 2M 2s
|-
|-
! UDP
! Gens Up
! Step pattern
! Step pattern
! Notation
! Notation
Line 334: Line 334:
! Notes
! Notes
|-
|-
| 6{{pipe}}0
| 6
| LMLsLMs
| LMLsLMs
| C - D - vE - vF♯ - G - A - vB - C
| C - D - vE - vF♯ - G - A - vB - C
Line 340: Line 340:
| Tritone is precisely the semioctave
| Tritone is precisely the semioctave
|-
|-
| 5{{pipe}}1
| 5
| LsLMsLM
| LsLMsLM
| C - D - ^E♭ - ^F - G - ^A♭ - ^B♭ - C
| C - D - ^E♭ - ^F - G - ^A♭ - ^B♭ - C
Line 346: Line 346:
| Contains the Wolf fourth (^F)
| Contains the Wolf fourth (^F)
|-
|-
| 4{{pipe}}2
| 4
| LMsLMLs
| LMsLMLs
| C - D - vE - F - G - vA - vB - C
| C - D - vE - F - G - vA - vB - C
Line 358: Line 358:
|  
|  
|-
|-
| 2{{pipe}}4
| 2
| MLsLMsL
| MLsLMsL
| C - vD - vE - F - G - vA - B♭ - C
| C - vD - vE - F - G - vA - B♭ - C
Line 364: Line 364:
|  
|  
|-
|-
| 1{{pipe}}5
| 1
| sLMsLML
| sLMsLML
| C - ^D♭ - ^E♭ - F - ^G♭ - ^A♭ - B♭ - C
| C - ^D♭ - ^E♭ - F - ^G♭ - ^A♭ - B♭ - C
Line 370: Line 370:
| Tritone is precisely the semioctave
| Tritone is precisely the semioctave
|-
|-
| 0{{pipe}}6
| 0
| MsLMLsL
| MsLMLsL
| C - vD - E♭ - F - vG - vA - B♭ - C
| C - vD - E♭ - F - vG - vA - B♭ - C
Line 380: Line 380:
|+ style="font-size: 105%;" | Modes of Left-hand 3L 2M 2s
|+ style="font-size: 105%;" | Modes of Left-hand 3L 2M 2s
|-
|-
! UDP
! Gens Up
! Step pattern
! Step pattern
! Notation
! Notation
Line 386: Line 386:
! Notes
! Notes
|-
|-
| 6{{pipe}}0
| 6
| LsLMLsM
| LsLMLsM
| C - D - ^E♭ - ^F - G - A - ^B♭ - C
| C - D - ^E♭ - ^F - G - A - ^B♭ - C
Line 392: Line 392:
| Contains the Wolf fourth (^F)
| Contains the Wolf fourth (^F)
|-
|-
| 5{{pipe}}1
| 5
| LMLsMLs
| LMLsMLs
| C - D - vE - vF♯ - G - vA - vB - C
| C - D - vE - vF♯ - G - vA - vB - C
Line 398: Line 398:
| Tritone is precisely the semioctave
| Tritone is precisely the semioctave
|-
|-
| 4{{pipe}}2
| 4
| LsMLsLM
| LsMLsLM
| C - D - ^E♭ - F - G - ^A♭ - ^B♭ - C
| C - D - ^E♭ - F - G - ^A♭ - ^B♭ - C
Line 410: Line 410:
|  
|  
|-
|-
| 2{{pipe}}4
| 2
| sLMLsML
| sLMLsML
| C - ^D♭ - ^E♭ - F - G - ^A♭ - B♭ - C
| C - ^D♭ - ^E♭ - F - G - ^A♭ - B♭ - C
Line 416: Line 416:
|  
|  
|-
|-
| 1{{pipe}}5
| 1
| MLsMLsL
| MLsMLsL
| C - vD - vE - F - vG - vA - B♭ - C
| C - vD - vE - F - vG - vA - B♭ - C
Line 422: Line 422:
| Contains the Wolf fifth (vG)
| Contains the Wolf fifth (vG)
|-
|-
| 0{{pipe}}6
| 0
| sMLsLML
| sMLsLML
| C - ^D♭ - E♭ - F - ^G♭ - ^A♭ - B♭ - C
| C - ^D♭ - E♭ - F - ^G♭ - ^A♭ - B♭ - C
Line 438: Line 438:
|+ style="font-size: 105%;" | Modes of 5L 2m 3s (Grave)
|+ style="font-size: 105%;" | Modes of 5L 2m 3s (Grave)
|-
|-
! UDP
! Gens Up
! Step pattern
! Step pattern
! Notation
! Notation
Line 444: Line 444:
! Notes
! Notes
|-
|-
| 4{{pipe}}0
| 4
| LmLsLmLsLs
| LmLsLmLsLs
| C - C♯ - E♭ - E - F - F# - A♭ - A - B♭ - B - C
| C - C♯ - E♭ - E - F - F# - A♭ - A - B♭ - B - C
Line 450: Line 450:
| Contains the Wolf fifth (^G)
| Contains the Wolf fifth (^G)
|-
|-
| 3{{pipe}}1
| 3
| LmLsLsLmLs
| LmLsLsLmLs
| C - C♯ - E♭ - E - F - F# - G - G♯ - B♭ - B - C
| C - C♯ - E♭ - E - F - F# - G - G♯ - B♭ - B - C
Line 462: Line 462:
|  
|  
|-
|-
| 1{{pipe}}3
| 1
| LsLmLsLsLm
| LsLmLsLsLm
| C - C♯ - D - D♯ - F - F# - G - G♯ - A - A♯ - C
| C - C♯ - D - D♯ - F - F# - G - G♯ - A - A♯ - C
Line 468: Line 468:
|  
|  
|-
|-
| 0{{pipe}}4
| 0
| LsLsLmLsLm
| LsLsLmLsLm
| C - C♯ - D - D♯ - E - E♯ - G - G♯ - A - A♯ - C
| C - C♯ - D - D♯ - E - E♯ - G - G♯ - A - A♯ - C
Line 478: Line 478:
|+ style="font-size: 105%;" | Modes of 5L 2m 3s (Acute)
|+ style="font-size: 105%;" | Modes of 5L 2m 3s (Acute)
|-
|-
! UDP
! Gens Up
! Step pattern
! Step pattern
! Notation
! Notation
Line 484: Line 484:
! Notes
! Notes
|-
|-
| 4{{pipe}}0
| 4
| mLsLmLsLsL
| mLsLmLsLsL
| C - E𝄫 - E♭ - F♭ - F - A𝄫 - A♭ - B𝄫 - B♭ - C♭ - C
| C - E𝄫 - E♭ - F♭ - F - A𝄫 - A♭ - B𝄫 - B♭ - C♭ - C
Line 490: Line 490:
| Brightness is reversed - Locrian is the brightest acute mode!
| Brightness is reversed - Locrian is the brightest acute mode!
|-
|-
| 3{{pipe}}1
| 3
| mLsLsLmLsL
| mLsLsLmLsL
| C - E𝄫 - E♭ - F♭ - F - G♭ - G - B𝄫 - B♭ - C♭ - C
| C - E𝄫 - E♭ - F♭ - F - G♭ - G - B𝄫 - B♭ - C♭ - C
Line 502: Line 502:
|  
|  
|-
|-
| 1{{pipe}}3
| 1
| sLmLsLsLmL
| sLmLsLsLmL
| C - D♭ - D - F♭ - F - G♭ - G - A♭ - A - C♭ - C
| C - D♭ - D - F♭ - F - G♭ - G - A♭ - A - C♭ - C
Line 508: Line 508:
|  
|  
|-
|-
| 0{{pipe}}4
| 0
| sLsLmLsLmL
| sLsLmLsLmL
| C - D♭ - D - E♭ - E - G♭ - G - A♭ - A - C♭ - C
| C - D♭ - D - E♭ - E - G♭ - G - A♭ - A - C♭ - C
Line 531: Line 531:
! Notes
! Notes
|-
|-
| 8{{pipe}}0
| 8
| LssssLssss
| LssssLssss
| C - C♯ - ^D - D♯ - F - vF♯ - ^G - G♯ - ^A - A♯ - C
| C - C♯ - ^D - D♯ - F - vF♯ - ^G - G♯ - ^A - A♯ - C
Line 537: Line 537:
| Contains the wolf fifth (^G)
| Contains the wolf fifth (^G)
|-
|-
| 6{{pipe}}2
| 6
| sLssssLsss
| sLssssLsss
| C - vC♯ - ^D - D♯ - F - vF♯ - G - G♯ - ^A - A♯ - C
| C - vC♯ - ^D - D♯ - F - vF♯ - G - G♯ - ^A - A♯ - C
Line 549: Line 549:
| Laterally symmetrical
| Laterally symmetrical
|-
|-
| 2{{pipe}}6
| 2
| sssLssssLs
| sssLssssLs
| C - vC♯ - D - vD♯ - F - vF♯ - G - vG♯ - A - A♯ - C
| C - vC♯ - D - vD♯ - F - vF♯ - G - vG♯ - A - A♯ - C
Line 555: Line 555:
| Messiaen treated this rotation as the "default"
| Messiaen treated this rotation as the "default"
|-
|-
| 0{{pipe}}8
| 0
| ssssLssssL
| ssssLssssL
| C - vC♯ - D - vD♯ - vF - vF♯ - G - vG♯ - A - vA♯ - C
| C - vC♯ - D - vD♯ - vF - vF♯ - G - vG♯ - A - vA♯ - C
Line 573: Line 573:
! Notes
! Notes
|-
|-
| 8{{pipe}}0
| 8
| LsLsLsLss
| 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!
| ^F♯ is actually the Wolf Fifth in this context, and F♯ is the desirable interval!
|-
|-
| 7{{pipe}}1
| 7
| LsLsLssLs
| LsLsLssLs
| C - C♯ - E♭ - ^D♯ - G♭ - ^F♯ - ^A♭ - A - A♯ - C
| C - C♯ - E♭ - ^D♯ - G♭ - ^F♯ - ^A♭ - A - A♯ - C
|  
|  
|-
|-
| 6{{pipe}}2
| 6
| LsLssLsLs
| LsLssLsLs
| C - C♯ - E♭ - ^D♯ - G♭ - F♯ - ^A♭ - A - A♯ - C
| C - C♯ - E♭ - ^D♯ - G♭ - F♯ - ^A♭ - A - A♯ - C
|  
|  
|-
|-
| 5{{pipe}}3
| 5
| LssLsLsLs
| LssLsLsLs
| C - C♯ - E♭ - D♯ - G♭ - F♯ - ^A♭ - A - A♯ - C
| C - C♯ - E♭ - D♯ - G♭ - F♯ - ^A♭ - A - A♯ - C
Line 617: Line 617:
| C - vC♯ - vE♭ - D♯ - vG♭ - F♯ - A♭ - A - vA♯ - C
| C - vC♯ - vE♭ - D♯ - vG♭ - F♯ - A♭ - A - vA♯ - C
| Subminor third above the root is unavailable in this mode.
| Subminor third above the root is unavailable in this mode.
|}
=== 3L 4s ===
The [[3L 4s]] scale is a distant deviation from common-practice harmony.  The harmony in this scale is based primarily on Marvel triads (see below) rather than the typical major and minor triads that the other scales were quite generously accustomed to.  It is closely related to [[Magic]] temperament, and may be thought of as the functional opposite of the 4L5s due to their nature as leaning into augmented and diminished harmony respectively as their primary concordances.  The modes of 3L 4s are given names by [[Andrew Heathwaite]].
{| class="wikitable"
|+ style="font-size: 105%;" |Modes of 3L 4s
|-
! UDP
! Step Pattern
! Notation
! Name
!Notes
|-
| 6
| LsLsLss
| C - vD♯ - vE - ^F♯ - ^G - A♯ - B - C
| Dril
|^F♯ and ^G both act as fifths, so this mode contains no functional fourths.
|-
| 5
| LsLssLs
| C - vD♯ - vE - ^F♯ - ^G - ^A♭ - B - C
| Gil
|
|-
| 4
| LssLsLs
| C - vD♯ - vE - vF - ^G - ^A♭ - B - C
| Kleeth
|
|-
| 3
| sLsLsLs
| C - D♭ - vE - vF - ^G - ^A♭ - B - C
| Bish
|Contains the up- and down-leading tones, making it easy to root melodically.
|-
| 2
| sLsLssL
| C - D♭ - vE - vF - ^G - ^A♭ - ^B𝄫 - C
| Fish
|
|-
| 1
| sLssLsL
| C - D♭ - vE - vF - vG♭ - ^A♭ - ^B𝄫 - C
| Jwl
|vF and vG♭ both act as fourths, so this mode contains no functional fifths.
|-
| 0
| ssLsLsL
| C - D♭ - E𝄫 - vF - vG♭ - ^A♭ - ^B𝄫 - C
| Led
|
|}
|}


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