User:BudjarnLambeth/12edo as a 2.3.5.17.19 tuning

From Xenharmonic Wiki
Jump to navigation Jump to search
This article or section contains multiple idiosyncratic terms. Such terms are used by only a few people and are not regularly used within the community.

This is a user page, not a real wiki page.

This page is only opinion, not fact.

Interpreting 12edo as a 2.3.5.17.19 system:

Intervals


0c (0 cents)

Behaves like: 1:1.


100c

Depending on context, behaves like: 20:19, 19:18, 18:17, 17:16 or 16:15.


200c

Depending on context, behaves like: 10:9, 19:17, 9:8 or 17:15.


300c

Depending on context, behaves like: 20:17, 32:27, 19:16 or 6:5.


400c

Depending on context, behaves like: 5:4, 34:27, 24:19 or 19:15.


500c

Depending on context, behaves like: 4:3 or 27:20.


600c

Depending on context, behaves like: 24:17, 17:12 or 27:19.


700c

Behaves like: 3:2.


800c

Depending on context, behaves like: 30:19, 19:12, 27:17 or 8:5.


900c

Depending on context, behaves like: 5:3, 32:19, 27:16 or 17:10.


1000c

Depending on context, behaves like: 30:17, 16:9 or 9:5.


1100c

Depending on context, behaves like: 15:8, 32:17, 17:9, 36:19 or 19:10.


1200c

Behaves like: 2:1.


Chords


Common chords

My interpretation of what the just harmonies are, hiding behind common practice chords.

Note names and common practice titles assume C is the tonic but of course you can transpose to any other key.

Harmonies from inversions of the chord are in italics.


Major chord

Just harmonies approximated:

  • 4:5:6
  • 2:3:5
  • 3:4:5

Note numbers: 0, 4, 7

Note names: C, E, G

Common practice title: C


Minor chord

Just harmonies:

  • 10:12:15
  • 16:19:24
  • 12:16:19

Note numbers: 0, 3, 7

Note names: C, Eb, G

Common practice title: Cm


Diminished chord

Just harmonies:

  • 17:20:24
  • 10:12:17
  • 12:17:20

Note numbers: 0, 3, 6

Note names: C, Eb, Gb

Common practice title: Cdim


Major seventh chord

Just harmonies:

  • 8:10:12:15
  • 20:25:30:38
  • 15:19:20:25

Note numbers: 0, 4, 7, 11

Note names: C, E, G, B

Common practice title: Cmaj7


Minor seventh chord

Just harmonies:

  • 10:12:15:18
  • 9:10:12:15

Note numbers: 0, 3, 7, 10

Note names: C, Eb, G, Bb

Common practice title: Cmin7


Dominant seventh chord

Just harmonies:

  • 20:25:30:36
  • 15:18:20:25

Note numbers: 0, 4, 7, 10

Note names: C, E, G, Bb

Common practice title: C7


Sus2 chord

Just harmonies:

  • 8:9:12
  • 18:20:27
  • 6:8:9

Note numbers: 0, 2, 7

Note names: C, D, G

Common practice title: Csus2


Sus4 chord

Just harmonies:

  • 6:8:9
  • 20:25:27

Note numbers: 0, 5, 7

Note names: C, F, G

Common practice title: Csus4


Augmented chord

Just harmonies:

  • 12:15:19
  • 15:18:20
  • 9:10:15

Note numbers: 0, 4, 8

Note names: C, E, G#

Common practice title: Caug


Dominant seventh chord

Just harmonies:

  • 20:25:30:36
  • 15:18:20:25

Note numbers: 0, 4, 7, 10

Note names: C, E, G, Bb

Common practice title: C7


Major ninth chord

Just harmonies:

  • 8:10:12:15:18
  • 8:9:10:12:15

Note numbers: 0, 4, 7, 11, 14

Note names: C, E, G, B, D

Common practice title: Cmaj9


Minor ninth chord

Just harmonies:

  • 40:48:60:72:85

Note numbers: 0, 3, 7, 10, 14

Note names: C, Eb, G, Bb, D

Common practice title: Cmin9


Dominant ninth chord

Just harmonies:

  • 40:50:60:72:85

Note numbers: 0, 4, 7, 10, 14

Note names: C, E, G, Bb, D

Common practice title: C9


Major eleventh chord

Just harmonies:

  • 24:30:36:45:54:64
  • 24:28:30:32:36:45

Note numbers: 0, 4, 7, 11, 14, 17

Note names: C, E, G, B, D, F

Common practice title: Cmaj11


Minor eleventh chord

Just harmonies:

  • 40:48:60:72:85:108
  • 40:48:54:60:72:85

Note numbers: 0, 3, 7, 10, 14, 17

Note names: C, Eb, G, Bb, D, F

Common practice title: Cmin11


Dominant eleventh chord

Just harmonies:

  • 40:50:60:72:85:108
  • 40:50:54:60:72:85

Note numbers: 0, 4, 7, 10, 14, 17

Note names: C, E, G, Bb, D, F

Common practice title: C11


Parent chords

My list of in my opinion the most harmonious 'parent chords' in 12edo, which you can use as palettes to build novel and pretty smaller chords. Choose one of these chords, take any subset of 2 or more notes from it, and you will make another, also harmonious chord.

These chords work particularly well if you drop the root note down an octave, better mimicking the shape of the harmonic series. (For example you can play "chord 0-12-15-19-20-21-22-23" instead of "chord 0-3-7-8-9-10-11").

Note names and common practice titles assume C is the tonic but of course you can transpose to any other key.


The over-9 parent chord of 12edo

Approximated just harmony: 9:10:12:16:17

Note numbers: 0, 2, 5, 10, 11

(With octave): 0, 12, 15, 17, 22, 23

Note names: C, D, F, A#/Bb, B

Common practice title: Dm7#5/C add(b6)


The over-10 parent chord of 12edo

Just harmony: 10:12:15:16:17:18:19

Note numbers: 0, 3, 7, 8, 9, 10, 11

(With octave): 0, 12, 15, 19, 20, 21, 22, 23

Note names: C, D#/Eb, G, G#/Ab, A, A#/Bb, B


The over-12 parent chord of 12edo

Just harmony: 12:15:16:17:18:19:20

Note numbers: 0, 4, 5, 6, 7, 8, 9

(With octave): 0, 12, 16, 17, 18, 19, 20, 21

Note names: C, E, F, F#/Gb, G, G#/Ab, A


The over-15 parent chord of 12edo

Just harmony: 15:16:17:18:19:20:24:27

Note numbers: 1, 2, 3, 4, 5, 8, 10

(With octave): 0, 12, 13, 14, 15, 16, 17, 20, 22

Note names: C, C#/Db, D, D#/Eb, E, F, G#/Ab, A#/Bb


The over-16 parent chord of 12edo

Just harmony: 16:17:18:19:20:24:30

Note numbers: 0, 1, 2, 3, 4, 7, 11

(With octave): 0, 12, 13, 14, 15, 16, 19, 23

Note names: C, C#/Db, D, D#/Eb, E, G, B

Common practice title: Cmaj9 add(m3,m9)


The over-17 parent chord of 12edo

Just harmony: 17:18:19:20:24:27:30:32

Note numbers: 0, 1, 2, 3, 6, 8, 10, 11

(With octave): 0, 12, 13, 14, 15, 18, 20, 22, 23

Note names: C, C#/Db, D, D#/Eb, F#/Gb, G#/Ab, A#/Bb, B


The over-18 parent chord of 12edo

Just harmony: 18:19:20:24:27:30:32:34

Note numbers: 0, 1, 2, 5, 7, 9, 10, 11

(With octave): 0, 12, 13, 14, 17, 19, 21, 22, 23

Note names: C, C#/Db, D, F, G, A, A#/Bb, B


The over-19 parent chord of 12edo

Just harmony: 19:20:24:27:30:32:36

Note numbers: 0, 1, 4, 6, 8, 9, 11

(With octave): 0, 12, 13, 16, 18, 20, 21, 23

Note names: C, C#/Db, E, F#/Gb, G#/Ab, A, B


The over-20 parent chord of 12edo

Just harmony: 20:24:25:27:30:32:34:36:38

Note numbers: 0, 3, 4, 5, 7, 8, 9, 10, 11

(With octave): 0, 12, 15, 16, 17, 18, 19, 20, 21, 22, 23

Note names: C, D#/Eb, E, F, G, G#/Ab, A, A#/Bb, B


The over-24 parent chord of 12edo

Just harmony: 24:27:30:32:34:36:38:40

Note numbers: 0, 2, 4, 5, 6, 7, 8, 9

(With octave): 0, 12, 14, 16, 17, 18, 19, 20, 21

Note names: C, D, E, F, F#/Gb, G, G#/Ab, A

Retrieved from "https://en.xen.wiki/index.php?title=User:BudjarnLambeth/12edo_as_a_2.3.5.17.19_tuning&oldid=193625"