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KingHyperio

Joined 18 July 2020
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If intervals are used solely for their 3-limit role, such as the M2 or in some cases the M6, the names Ro and Lo may be used, for perfect second or perfect sixth, as Ra can be thought of to imply 10/9, while Ro would imply 9/8, similarly to Lo and 27/16. In other cases, Mo would be 32/27 and To would be 16/9. A situation where this naming scheme may be used would be in a scale of P1 M2 ^M3 P4 P5 M6 ^M7 P8, where the M6 is used so that the ii chord has a perfect fifth, while the vi chord has a wolf fifth in order to be used as a "wolf tonic" to prevent tonicization.
If intervals are used solely for their 3-limit role, such as the M2 or in some cases the M6, the names Ro and Lo may be used, for perfect second or perfect sixth, as Ra can be thought of to imply 10/9, while Ro would imply 9/8, similarly to Lo and 27/16. In other cases, Mo would be 32/27 and To would be 16/9. A situation where this naming scheme may be used would be in a scale of P1 M2 ^M3 P4 P5 M6 ^M7 P8, where the M6 is used so that the ii chord has a perfect fifth, while the vi chord has a wolf fifth in order to be used as a "wolf tonic" to prevent tonicization.
== 31edo Functional Harmony ==
My personal view of harmony in 12edo is that each note in a key has a role in any chord, which I use the names Stable, Modal, Hollow, Unstable, Leading, and Odd for. Stable describes the P1 and P5, Modal describes the m3 and M3, Hollow describes the M6 and m7, Unstable describes the M2 and P4, Leading describes the m6 and M7, and Odd describes the m2 and A4. The summary is that a chord having unstable and leading notes in it makes it a Dominant, a chord having just unstable notes in it makes it a Subdominant, a chord having just leading notes in it makes it a Mediant, and a chord having neither makes it a Tonic or Substitute Tonic. It works best for triads and tetrads, and can extend reasonably well to 31edo, and I use the follow classifications for the notes: S: P1,P5, M: s3,m3,M3,S3, H: M6,S6,s7,m7, U: ~2,M2,S2,~3,v4,P4,^4,~6,~7, L: s6,m6,M7,S7, O: ^1,s2,m2,A4,d5,v5,^5,v8. Some notes, like the ~2 and ^4, can change roles depending on the chord, but in general the system works well. This is useful when trying to compose using microtonal scales in 31, so a table below will list some important chords (mainly triads) for each role (O means Orwell tetrad, h means harmonic):
{| class="wikitable"
|+Example Scales
!
!Tonic
!Subdominant
!Dominant
!Mediant
|-
!Major
|I, VIm
|IIm, IV
|V, VII*
|IIIm
|-
!Orwell[9] 1
|Ih11(no5,9), Is, IS, dbIIIS
|dIIO, dbIIIs
|dbIIIO, tIVO, bVIO
|VIIO
|-
!Squares[8] 5
|
|
|
|
|-
!Dylathian
|
|
|
|
|-
!Harrison Major
|
|
|
|
|-
!Graham Orwell
|
|
|
|
|-
!Neutral Lydian
|
|finishing later
|
|
|-
!Greeley[8] 8
|
|
|
|probably
|-
!Mode 8
|
|
|might add blackwood
oh yeah that exists
if a suboctave counts to you
|
|}


== 31edo Keyboard Setup ==
== 31edo Keyboard Setup ==
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The look of the keyboard with these chosen color roles is shown to the right.
The look of the keyboard with these chosen color roles is shown to the right.
[http://terpstrakeyboard.com/web-app/keys.htm?fundamental=263.09212&right=5&upright=2&size=50&rotation=343.897886248&instrument=piano&enum=false&equivSteps=31&spectrum_colors=false&fundamental_color=55FF55&no_labels=false&scale=!%2031-ed2%20Bosanquet%20Wilson%20Terpstra.scl%0A!%2031-tone%20equal%20tempered%20scale%20consisting%20of%2031%20sonically%20equal%20divisions%20per%20frequency%20halving%2Fdoubling%20in%20standard%20meantone%20notation%2C%20mapped%20on%20a%20Bosanquet%20%2F%20Wilson%20%2F%20Terpstra%20layout.%0A!%0ATerpstra%20Keyboard%20WebApp%20%7C%2031-ed2%20Bosanquet%20%2F%20Wilson%20%2F%20Terpstra%0A31%0A!%0A38.70968%0A77.41935%0A116.12903%0A154.83871%0A193.54839%0A232.25806%0A270.96774%0A309.67742%0A348.38710%0A387.09677%0A425.80645%0A464.51613%0A503.22581%0A541.93548%0A580.64516%0A619.35484%0A658.06452%0A696.77419%0A735.48387%0A774.19355%0A812.90323%0A851.61290%0A890.32258%0A929.03226%0A967.74194%0A1006.45161%0A1045.16129%0A1083.87097%0A1122.58065%0A1161.29032%0A1200.00000&names=C%0ACt%0AC%23%0ADb%0ADd%0AD%0ADt%0AD%23%0AEb%0AEd%0AE%0AEt%0AFd%0AF%0AFt%0AF%23%0AGb%0AGd%0AG%0AGt%0AG%23%0AAb%0AAd%0AA%0AAt%0AA%23%0ABb%0ABd%0AB%0ABt%0ACd%0AC&note_colors=ffffff%0Affcbcb%0Affffba%0Aff939a%0Ad3eeff%0Affffff%0Affcbcb%0A9ac1ff%0Abaffc9%0Ad3eeff%0Affffff%0Aff939a%0A9ac1ff%0Abaffc9%0Acfcfcf%0Affffba%0Aff939a%0Ad3eeff%0Affffff%0Affcbcb%0Affffba%0Abaffc9%0Ad3eeff%0Affffff%0Affcbcb%0A9ac1ff%0Abaffc9%0Acfcfcf%0Affffba%0Aff939a%0A9ac1ff%0Affffff Keyboard shown], [http://terpstrakeyboard.com/web-app/keys.htm?fundamental=263.09212&right=5&upright=2&size=50&rotation=343.897886248&instrument=piano&enum=false&equivSteps=31&spectrum_colors=false&fundamental_color=55FF55&no_labels=false&scale=!%2031-ed2%20Bosanquet%20Wilson%20Terpstra.scl%0A!%2031-tone%20equal%20tempered%20scale%20consisting%20of%2031%20sonically%20equal%20divisions%20per%20frequency%20halving%2Fdoubling%20in%20standard%20meantone%20notation%2C%20mapped%20on%20a%20Bosanquet%20%2F%20Wilson%20%2F%20Terpstra%20layout.%0A!%0ATerpstra%20Keyboard%20WebApp%20%7C%2031-ed2%20Bosanquet%20%2F%20Wilson%20%2F%20Terpstra%0A31%0A!%0A38.70968%0A77.41935%0A116.12903%0A154.83871%0A193.54839%0A232.25806%0A270.96774%0A309.67742%0A348.38710%0A387.09677%0A425.80645%0A464.51613%0A503.22581%0A541.93548%0A580.64516%0A619.35484%0A658.06452%0A696.77419%0A735.48387%0A774.19355%0A812.90323%0A851.61290%0A890.32258%0A929.03226%0A967.74194%0A1006.45161%0A1045.16129%0A1083.87097%0A1122.58065%0A1161.29032%0A1200.00000&names=C%0ACt%0AC%23%0ADb%0ADd%0AD%0ADt%0AD%23%0AEb%0AEd%0AE%0AEt%0AFd%0AF%0AFt%0AF%23%0AGb%0AGd%0AG%0AGt%0AG%23%0AAb%0AAd%0AA%0AAt%0AA%23%0ABb%0ABd%0AB%0ABt%0ACd%0AC&note_colors=ffffff%0Affd7ff%0Affffba%0Affbaff%0Ad3ffee%0Affffff%0Affd7ff%0Abaffc9%0Affdfba%0Ad3ffee%0Affffff%0Affbaff%0Abaffc9%0Affdfba%0Ae7e7e7%0Affffba%0Affbaff%0Ad3ffee%0Affffff%0Affd7ff%0Affffba%0Affdfba%0Ad3ffee%0Affffff%0Affd7ff%0Abaffc9%0Affdfba%0Ae7e7e7%0Affffba%0Affbaff%0Abaffc9%0Affffff keyboard shown with same roles but more pleasing colors].
[[File:31kitebasedlumatone.png|thumb|543x543px|Black outline shows dimensions of Lumatone keyboard.]]
[[File:31kitebasedlumatone.png|thumb|543x543px|Black outline shows dimensions of Lumatone keyboard.]]


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