View source for User:BudjarnLambeth/12edo as a 2.3.5.17.19 tuning

{{Idiosyncratic terms}}

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Interpreting 12edo as a 2.3.5.17.19 system:

== Intervals ==
<br>

; 0c (0 [[cents]])

Behaves like: [[1/1|1:1]].


; 100c

Depending on context, behaves like: [[20/19|20:19]], [[19/18|19:18]], [[18/17|18:17]], [[17/16|17:16]] or [[16/15|16:15]].


; 200c

Depending on context, behaves like: [[10/9|10:9]], [[19/17|19:17]], [[9/8|9:8]] or [[17/15|17:15]].


; 300c

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


; 400c

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


; 500c

Depending on context, behaves like: [[4/3|4:3]] or [[27/20|27:20]].


; 600c

Depending on context, behaves like: [[24/17|24:17]], [[17/12|17:12]] or [[27/19|27:19]].


; 700c

Behaves like: [[3/2|3:2]].


; 800c

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


; 900c

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


; 1000c

Depending on context, behaves like: [[30/17|30:17]], [[16/9|16:9]] or [[9/5|9:5]].


; 1100c

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


; 1200c

Behaves like: [[2/1|2:1]].
<br>


== Chords ==
<br>

=== 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
<br>


=== 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