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User:Contribution/Exploring Selected Modes in 12-EDO: Difference between revisions

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Line 384: Line 384:
|2048/2025
|2048/2025
|-
|-
|1 2 2 1 1 2 2 1
|1 1 2 2 1 1 2 2
|81/80, 648/625, 2048/2025
|81/80, 648/625, 2048/2025
|-
|-
Line 446: Line 446:
|1 2 2 2 1 3 1
|1 2 2 2 1 3 1
|128/125
|128/125
|-
|Diaschisma
|2 2 1 2 1 1 2 1
|81/80, 128/125, 648/625, 2048/2025
|-
|-
|Schisma
|Schisma
Line 452: Line 456:
|}
|}


=== Blues scales ===
=== Pajara and Blues scales ===
 
{| class="wikitable"
|+
Pajara
!Truncation
!Modes
! Distinctly tempered commas
|-
|Pajara[10]
|1 1 1 1 1 2 1 1 1 2
|81/80, 128/125, 648/625, 2048/2025, 6561/6250, 32805/32768, 82944/78125, 262144/253125
|-
|Pajara[8]
|1 1 1 1 3 1 1 3
|81/80, 648/625, 2048/2025
|-
|Pajara[8] mod
|1 1 1 2 2 1 2 2
|81/80
|-
|Pajara[6]
|1 1 1 4 1 4
|None
|}


{| class="wikitable"
{| class="wikitable"
Line 493: Line 521:


== Scales notes ==
== Scales notes ==
{| class="wikitable center-all"
|+style=white-space:nowrap|
Pentatonic modes
|+
!Penta MOS
!Penta dom
!Penta app
|-
|F# G# A# C# D#
|E# G# B C# D#
|F# G# A# B# E
|-
|B C# D# F# G#
|A# C# E F# G#
|B C# D# E# A
|-
|E F# G# B C#
|D# F# A B C#
|E F# G# A# D
|-
|A B C# E F#
|G# B D E F#
|A B C# D# G
|-
|D E F# A B
|C# E G A B
|D E F# G# C
|-
|G A B D E
|F# A C D E
|G A B C# F
|-
|C D E G A
|B D F G A
|C D E F# Bb
|-
|F G A C D
|E G Bb C D
|F G A B Eb
|-
|Bb C D F G
|A C Eb F G
|Bb C D E Ab
|-
|Eb F G Bb C
|D F Ab Bb C
|Eb F G A Db
|-
|Ab Bb C Eb F
|G Bb Db Eb F
|Ab Bb C D Gb
|-
|Db Eb F Ab Bb
|C Eb Gb Ab Bb
|Db Eb F G Cb
|}


{| class="wikitable center-all"
{| class="wikitable center-all"
Line 562: Line 533:
!Ion b2 b6
!Ion b2 b6
!Ion b2 b3 b6
!Ion b2 b3 b6
|-
|Db Eb F Gb Ab Bb C
|Db Eb Fb Gb Ab Bb C
|C# D# E F# G# A# B#
|C# D# E F# G# A B#
|C# D E# F# G# A# B#
|C# D E F# G# A# B#
|C# D E# F# G# A B#
|C# D E F# G# A B#
|-
|-
|F# G# A# B C# D# E#
|F# G# A# B C# D# E#
Line 656: Line 636:
|Ab Bb Cb Db Eb F G
|Ab Bb Cb Db Eb F G
|Ab Bb C Db Eb Fb G
|Ab Bb C Db Eb Fb G
|Ab Bb Cb Db Eb Fb G
|G# A# B C# D# E Fx
|Ab Bbb C Db Eb F G
|Ab Bbb C Db Eb F G
|Ab Bbb Cb Db Eb F G
|Ab Bbb Cb Db Eb F G
|Ab Bbb C Db Eb Fb G
|Ab Bbb C Db Eb Fb G
|Ab Bbb Cb Db Eb Fb G
|G# A B C# D# E Fx
|}
 
{| class="wikitable center-all"
|+style=white-space:nowrap|
Pentatonic modes & diatonic extended
|+
!Penta MOS
!Penta dom
!Penta app
!2 2 1 1 1 2 1 1 1
!2 2 1 2 1 1 2 1
|-
|-
|Db Eb F Gb Ab Bb C
|F# G# A# C# D#
|Db Eb Fb Gb Ab Bb C
|E# G# B C# D#
|C# D# E# F# G# A B#
|F# G# A# B# E
|C# D# E F# G# A B#
|F# G# A# B B# C# D# E E#
|C# D E# F# G# A# B#
|F# G# A# B C# D D# E#
|C# D E F# G# A# B#
|-
|C# D E# F# G# A B#
|B C# D# F# G#
|C# D E F# G# A B#
|A# C# E F# G#
|B C# D# E# A
|B C# D# E E# F# G# A A#
|B C# D# E F# G G# A#
|-
|E F# G# B C#
|D# F# A B C#
|E F# G# A# D
|E F# G# A A# B C# D D#
|E F# G# A B C C# D#
|-
|A B C# E F#
|G# B D E F#
|A B C# D# G
|A B C# D D# E F# G G#
|A B C# D E F F# G#
|-
|D E F# A B
|C# E G A B
|D E F# G# C
|D E F# G G# A B C C#
|D E F# G A Bb B C#
|-
|G A B D E
|F# A C D E
|G A B C# F
|G A B C C# D E F F#
|G A B C D Eb E F#
|-
|C D E G A
|B D F G A
|C D E F# Bb
|C D E F F# G A Bb B
|C D E F G Ab A B
|-
|F G A C D
|E G Bb C D
|F G A B Eb
|F G A Bb B C D Eb E
|F G A Bb C Db D E
|-
|Bb C D F G
|A C Eb F G
|Bb C D E Ab
|Bb C D Eb E F G Ab A
|Bb C D Eb F Gb G A
|-
|Eb F G Bb C
|D F Ab Bb C
|Eb F G A Db
|Eb F G Ab A Bb C Db D
|Eb F G Ab Bb Cb C D
|-
|Ab Bb C Eb F
|G Bb Db Eb F
|Ab Bb C D Gb
|Ab Bb C Db D Eb F Gb G
|Ab Bb C Db Eb Fb F G
|-
|Db Eb F Ab Bb
|C Eb Gb Ab Bb
|Db Eb F G Cb
|Db Eb F Gb G Ab Bb Cb C
|C# D# E# F# G# A A# B#
|}
|}


Line 683: Line 737:
!1 1 2 1 1 1 1 2 1 1
!1 1 2 1 1 1 1 2 1 1
!1 3 1 1 1 3 1 1
!1 3 1 1 1 3 1 1
!1 2 2 1 1 2 2 1
!1 1 2 2 1 1 2 2
!1 4 1 1 4 1
!1 4 1 1 4 1
!1 1 1 1 1 1 1 1 1 1 1 1
!1 1 1 1 1 1 1 1 1 1 1 1
Line 695: Line 749:
|C Db D E F F# G Ab Bb B
|C Db D E F F# G Ab Bb B
|C Db E F F# G Bb B
|C Db E F F# G Bb B
|C Db Eb F F# G A B
|C Db D E F# G Ab Bb
|C Db F F# G B
|C Db F F# G B
|C Db D Eb E F F# G Ab A Bb B
|C Db D Eb E F F# G Ab A Bb B
Line 707: Line 761:
|C# D Eb F F# G Ab A B C
|C# D Eb F F# G Ab A B C
|C# D F F# G Ab B C
|C# D F F# G Ab B C
|C# D E F# G Ab Bb C
|C# D Eb F G Ab A B
|C# D F# G Ab C
|C# D F# G Ab C
|
|
Line 719: Line 773:
|D Eb E F# G G# A Bb C C#
|D Eb E F# G G# A Bb C C#
|D Eb F# G G# A C C#
|D Eb F# G G# A C C#
|D Eb F G G# A B C#
|D Eb E F# G# A Bb C
|D Eb G G# A C#
|D Eb G G# A C#
|
|
Line 731: Line 785:
|D# E F G G# A Bb B C# D
|D# E F G G# A Bb B C# D
|D# E G G# A Bb C# D
|D# E G G# A Bb C# D
|D# E F# G# A Bb C D
|D# E F G A Bb B C#
|D# E G# A Bb D
|D# E G# A Bb D
|
|
Line 743: Line 797:
|E F F# G# A A# B C D D#
|E F F# G# A A# B C D D#
|E F G# A A# B D D#
|E F G# A A# B D D#
|E F G A A# B C# D#
|E F F# G# A# B C D
|E F A A# B D#
|E F A A# B D#
|
|
Line 755: Line 809:
|F Gb G A Bb B C Db Eb E
|F Gb G A Bb B C Db Eb E
|F Gb A Bb B C Eb E
|F Gb A Bb B C Eb E
|F Gb Ab Bb B C D E
|F Gb G A B C Db Eb
|F Gb Bb B C E
|F Gb Bb B C E
|
|
Line 761: Line 815:


{| class="wikitable center-all"
{| class="wikitable center-all"
|+style=white-space:nowrap|Alterations of modes of limited transposition
|+style=white-space:nowrap|Pajara modes
|+
|+
!2 2 1 2 1 1 2 1
!2 2 1 1 1 2 1 1 1
!1 1 1 1 1 2 1 1 1 2
!1 1 1 1 1 2 1 1 1 2
!1 1 1 1 3 1 1 3
!1 1 1 1 3 1 1 3
Line 770: Line 822:
!1 1 1 4 1 4
!1 1 1 4 1 4
|-
|-
|F# G# A# B C# D D# E#
|F# G# A# B B# C# D# E E#
|F# G G# A A# B C# D D# E
|F# G G# A A# B C# D D# E
|F# G G# A A# C# D D#
|F# G G# A A# C# D D#
Line 777: Line 827:
|F# G G# A C# D
|F# G G# A C# D
|-
|-
|B C# D# E F# G G# A#
|B C# D# E E# F# G# A A#
|B C C# D D# E F# G G# A
|B C C# D D# E F# G G# A
|B C C# D D# F# G G#
|B C C# D D# F# G G#
Line 784: Line 832:
|B C C# D F# G
|B C C# D F# G
|-
|-
|E F# G# A B C C# D#
|E F# G# A A# B C# D D#
|E F F# G G# A B C C# D
|E F F# G G# A B C C# D
|E F F# G G# B C C#
|E F F# G G# B C C#
Line 791: Line 837:
|E F F# G B C
|E F F# G B C
|-
|-
|A B C# D E F F# G#
|A B C# D D# E F# G G#
|A Bb B C C# D E F F# G
|A Bb B C C# D E F F# G
|A Bb B C C# E F F#
|A Bb B C C# E F F#
Line 798: Line 842:
|A Bb B C E F
|A Bb B C E F
|-
|-
|D E F# G A Bb B C#
|D E F# G G# A B C C#
|D Eb E F F# G A Bb B C
|D Eb E F F# G A Bb B C
|D Eb E F F# A Bb B
|D Eb E F F# A Bb B
Line 805: Line 847:
|D Eb E F A Bb
|D Eb E F A Bb
|-
|-
|G A B C D Eb E F#
|G A B C C# D E F F#
|G Ab A Bb B C D Eb E F
|G Ab A Bb B C D Eb E F
|G Ab A Bb B D Eb E
|G Ab A Bb B D Eb E
Line 812: Line 852:
|G Ab A Bb D Eb
|G Ab A Bb D Eb
|-
|-
|C D E F G Ab A B
|C D E F F# G A Bb B
|C Db D Eb E F G Ab A Bb
|C Db D Eb E F G Ab A Bb
|C Db D Eb E G Ab A
|C Db D Eb E G Ab A
Line 819: Line 857:
|C Db D Eb G Ab
|C Db D Eb G Ab
|-
|-
|F G A Bb C Db D E
|F G A Bb B C D Eb E
|F Gb G Ab A Bb C Db D Eb
|F Gb G Ab A Bb C Db D Eb
|F Gb G Ab A C Db D
|F Gb G Ab A C Db D
Line 826: Line 862:
|F Gb G Ab C Db
|F Gb G Ab C Db
|-
|-
|Bb C D Eb F Gb G A
|Bb C D Eb E F G Ab A
|Bb Cb C Db D Eb F Gb G Ab
|Bb Cb C Db D Eb F Gb G Ab
|Bb Cb C Db D F Gb G
|Bb Cb C Db D F Gb G
Line 833: Line 867:
|Bb Cb C Db F Gb
|Bb Cb C Db F Gb
|-
|-
|Eb F G Ab Bb Cb C D
|Eb F G Ab A Bb C Db D
|Eb Fb F Gb G Ab Bb Cb C Db
|Eb Fb F Gb G Ab Bb Cb C Db
|Eb Fb F Gb G Bb Cb C
|Eb Fb F Gb G Bb Cb C
Line 840: Line 872:
|Eb Fb F Gb Bb Cb
|Eb Fb F Gb Bb Cb
|-
|-
|Ab Bb C Db Eb Fb F G
|Ab Bb C Db D Eb F Gb G
|G# A A# B B# C# D# E E# F#
|G# A A# B B# C# D# E E# F#
|G# A A# B B# D# E E#
|G# A A# B B# D# E E#
Line 847: Line 877:
|G# A A# B D# E
|G# A A# B D# E
|-
|-
|C# D# E# F# G# A A# B#
|Db Eb F Gb G Ab Bb Cb C
|C# D D# E E# F# G# A A# B
|C# D D# E E# F# G# A A# B
|C# D D# E E# G# A A#
|C# D D# E E# G# A A#
Line 855: Line 883:
|}
|}


{| class="wikitable center-all"
[[File:12edo modes.pdf|12 edo modes]]
|+style=white-space:nowrap|Alterations of modes of limited transposition
|+
!2 2 1 2 1 1 2 1
!2 2 1 1 1 2 1 1 1
!1 1 1 1 1 2 1 1 1 2
!1 1 1 1 3 1 1 3
!1 1 1 2 2 1 2 2
!1 1 1 4 1 4
|-
|F# G# A# B C# D D# E#
|F# G# A# B B# C# D# E E#
|F# G G# A A# B C# D D# E
|F# G G# A A# C# D D#
|F# G G# A B C# D E
|F# G G# A C# D
|-
|B C# D# E F# G G# A#
|B C# D# E E# F# G# A A#
|B C C# D D# E F# G G# A
|B C C# D D# F# G G#
|B C C# D E F# G A
|B C C# D F# G
|-
|E F# G# A B C C# D#
|E F# G# A A# B C# D D#
|E F F# G G# A B C C# D
|E F F# G G# B C C#
|E F F# G A B C D
|E F F# G B C
|-
|A B C# D E F F# G#
|A B C# D D# E F# G G#
|A Bb B C C# D E F F# G
|A Bb B C C# E F F#
|A Bb B C D E F G
|A Bb B C E F
|-
|D E F# G A Bb B C#
|D E F# G G# A B C C#
|D Eb E F F# G A Bb B C
|D Eb E F F# A Bb B
|D Eb E F G A Bb C
|D Eb E F A Bb
|-
|G A B C D Eb E F#
|G A B C C# D E F F#
|G Ab A Bb B C D Eb E F
|G Ab A Bb B D Eb E
|G Ab A Bb C D Eb F
|G Ab A Bb D Eb
|-
|C D E F G Ab A B
|C D E F F# G A Bb B
|C Db D Eb E F G Ab A Bb
|C Db D Eb E G Ab A
|C Db D Eb F G Ab Bb
|C Db D Eb G Ab
|-
|F G A Bb C Db D E
|F G A Bb B C D Eb E
|F Gb G Ab A Bb C Db D Eb
|F Gb G Ab A C Db D
|F Gb G Ab Bb C Db Eb
|F Gb G Ab C Db
|-
|Bb C D Eb F Gb G A
|Bb C D Eb E F G Ab A
|Bb Cb C Db D Eb F Gb G Ab
|Bb Cb C Db D F Gb G
|Bb Cb C Db Eb F Gb Ab
|Bb Cb C Db F Gb
|-
|Eb F G Ab Bb Cb C D
|Eb F G Ab A Bb C Db D
|Eb Fb F Gb G Ab Bb Cb C Db
|Eb Fb F Gb G Bb Cb C
|Eb Fb F Gb Ab Bb Cb Db
|Eb Fb F Gb Bb Cb
|-
|Ab Bb C Db Eb Fb F G
|Ab Bb C Db D Eb F Gb G
|G# A A# B B# C# D# E E# F#
|G# A A# B B# D# E E#
|G# A A# B C# D# E F#
|G# A A# B D# E
|-
|C# D# E# F# G# A A# B#
|Db Eb F Gb G Ab Bb Cb C
|C# D D# E E# F# G# A A# B
|C# D D# E E# G# A A#
|C# D D# E F# G# A B
|C# D D# E G# A
|}


== Modes series ==
== Modes series ==
Line 1,100: Line 1,035:
|7 7 9 7 7 4 3 4
|7 7 9 7 7 4 3 4
|-
|-
| rowspan="6" |1 2 2 1
| rowspan="6" |1 1 2 2
| rowspan="2" |3<sup>-4</sup> • 5<sup>1</sup>
| rowspan="2" |3<sup>-4</sup> • 5<sup>1</sup>
|5 8 8 9 5 4 4 5
|5 8 8 9 5 4 4 5
Line 1,150: Line 1,085:
|7 3 4 3 7
|7 3 4 3 7
|-
|-
|2 2 3 3 2
| colspan="2" |2 2 3 3 2 ;  2 2 2 4 2
| colspan="5" |None
| colspan="4" |None
|-
|2 2 2 4 2
| colspan="5" |None
|-
|-
| rowspan="9" |2 2 1 2 2 2 1
| rowspan="9" |2 2 1 2 2 2 1
Line 1,348: Line 1,280:
|8 9 5 8 7 3 8
|8 9 5 8 7 3 8
|4 9 5 4 7 3 4
|4 9 5 4 7 3 4
|-
| colspan="2" |2 2 1 2 1 1 2 1
| colspan="4" |Too many (41 perfect circles, 41 plagal circles)
|-
|-
| colspan="2" |2 2 1 1 1 2 1 1 1
| colspan="2" |2 2 1 1 1 2 1 1 1
Line 1,353: Line 1,288:
|}
|}


=== Blues scales ===
=== Pajara and Blues scales ===
{| class="wikitable"
{| class="wikitable"
|+
|+
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