19edo modes

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Some scales and modes available in 19edo. Please add more, discovered or newly-composed!

Note names in 19edo

The charts below primarily use the following note names (based on standard meantone/Pythagorean notation):

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18
C Ç

C# (Δb)

ΔÇ# (Db) D Þ

D# (εb, Sb)

ε, S

Þ# (Eb)

E E# (Fb) F ϕ

F# (Γb)

Γϕ# (Gb) G Z

G# (αb)

αZ# (Ab) A Æ

A# (βb, Bb)

Æ#β ,B(b) B, H B#, H# (Cb)

Note that E#=Fb and B#=Cb, but other notes are not enharmonic (for example, C# and Db are different; and E# is not the same as F). Double flats and sharps may be used as in "standard" notation; for example; Fx=F##=Gb and Bbb=A#.

Other systems of notation are of course possible, and may be preferred depending on the scales you are working with!

Meantone

meantone[5] (2L+3s / chroma-positive generator = 8\19 ~= 4/3)

UDP steps degrees note names comments audio
4|0 5 3 5 3 3 0 5 8 13 16 C Eb F Ab Bb minor pentatonic (2)
3|1 5 3 3 5 3 0 5 8 11 16 C Eb F G Bb minor pentatonic
2|2 3 5 3 5 3 0 3 8 11 16 C D F G Bb "mixolydian" pentatonic
1|3 3 5 3 3 5 0 3 8 11 14 C D F G A "suspended" pentatonic
0|4 3 3 5 3 5 0 3 6 11 14 C D E G A major pentatonic

meantone[7] (5L+2s / CPG = 11\19 ~= 3/2)

UDP steps degrees note names mode name audio
6|0 3 3 3 2 3 3 2 0 3 6 9 11 14 17 C D E F# G A B Lydian
5|1 3 3 2 3 3 3 2 0 3 6 8 11 14 17 C D E F G A B Ionian
4|2 3 3 2 3 3 2 3 0 3 6 8 11 14 16 C D E F G A Bb Mixolydian
3|3 3 2 3 3 3 2 3 0 3 5 8 11 14 16 C D Eb F G A Bb Dorian
2|4 3 2 3 3 2 3 3 0 3 5 8 11 13 16 C D Eb F G Ab Bb Aeolian
1|5 2 3 3 3 2 3 3 0 2 5 8 11 13 16 C Db Eb F G Ab Bb Phrygian
0|6 2 3 3 2 3 3 3 0 2 5 8 10 13 16 C Db Eb F Gb Ab Bb Locrian

meantone[12] (7L+5s / CPG = 8\19)

UDP steps degrees note names comments
11|0 2 2 1 2 1 2 2 1 2 1 2 1 0 2 4 5 7 8 10 12 13 15 16 18 C Db D# Eb E# F Gb G# Ab A# Bb B#

C Δ Þ S E# F Γ Z α Æ β B#

10|1 2 2 1 2 1 2 1 2 2 1 2 1 0 2 4 5 7 8 10 11 13 15 16 18 C Db D# Eb E# F Gb G Ab A# Bb B#

C Δ Þ S E# F Γ G α Æ β B#

9|2 2 1 2 2 1 2 1 2 2 1 2 1 0 2 3 5 7 8 10 11 13 15 16 18 C Db D Eb E# F Gb G Ab A# Bb B#

C Δ D S E# F Γ G α Æ β B#

8|3 2 1 2 2 1 2 1 2 1 2 2 1 0 2 3 5 7 8 10 11 13 14 16 18 C Db D Eb E# F Gb G Ab A Bb B#

C Δ D S E# F Γ G α A β B#

7|4 2 1 2 1 2 2 1 2 1 2 2 1 0 2 3 5 6 8 10 11 13 14 16 18 C Db D Eb E F Gb G Ab A Bb B#

C Δ D S E F Γ G α A β B#

6|5 2 1 2 1 2 2 1 2 1 2 1 2 0 2 3 5 6 8 10 11 13 14 16 17 C Db D Eb E F Gb G Ab A Bb B

C Δ D S E F Γ G α A β B

Yasser's Supradiatonic

(twelfths of 12-5 chords form C Ionian mode, elevenths of 11-4 chords form C Aeolian mode)

5|6 2 1 2 1 2 1 2 2 1 2 1 2 0 2 3 5 6 8 9 11 13 14 16 17 C Db D Eb E F F# G Ab A Bb B

C Δ D S E F ϕ G α A β B

fifths of 12-5 chords form C Ionian mode
4|7 1 2 2 1 2 1 2 2 1 2 1 2 0 1 3 5 6 8 9 11 13 14 16 17 C C# D Eb E F F# G Ab A Bb B

C Ç D S E F ϕ G α A β B

octaves of 11-5 chords form C Mixolydian mode
3|8 1 2 2 1 2 1 2 1 2 2 1 2 0 1 3 5 6 8 9 11 12 14 16 17 C C# D Eb E F F# G G# A Bb B

C Ç D S E F ϕ G Z A β B

2|9 1 2 1 2 2 1 2 1 2 2 1 2 0 1 3 4 6 8 9 11 12 14 16 17 C C# D D# E F F# G G# A Bb B

C Ç D Þ E F ϕ G Z A β B

octaves of 12-5 chords form C Ionian mode
1|10 1 2 1 2 2 1 2 1 2 1 2 2 0 1 3 4 6 8 9 11 12 14 15 17 C C# D D# E F F# G G# A A# B

C Ç D Þ E F ϕ G Z A Æ B

roots of 12-5 chords form C Ionian mode
0|11 1 2 1 2 1 2 2 1 2 1 2 2 0 1 3 4 6 7 9 11 12 14 15 17 C C# D D# E E# F# G G# A A# B

C Ç D Þ E Fb ϕ G Z A Æ B

Miscellaneous scales

2 3 1 4 1 4 4 - E# F# G# Ab B Cb D - Cartunes

1 1 6 3 1 1 6 - E# F Gbb A# B# C Dbb E# - enharmonic approximation

5 3 1 2 4 1 3 - C Eb F F# G A# B - Hyperblue Dorian (approximated from 31edo)

MOS scales and modes of rank-2 temperaments

Negri

negri[9] (1L+8s / chroma-positive generator = 17\19)

UDP steps degrees note names comments
8|0 3 2 2 2 2 2 2 2 2 0 3 5 7 9 11 13 15 17 C D Eb E# F# G Ab A# B
7|1 2 3 2 2 2 2 2 2 2 0 2 5 7 9 11 13 15 17 C Db Eb E# F# G Ab A# B
6|2 2 2 3 2 2 2 2 2 2 0 2 4 7 9 11 13 15 17 C Db D# E# F# G Ab A# B
5|3 2 2 2 3 2 2 2 2 2 0 2 4 6 9 11 13 15 17 C Db D# E F# G Ab A# B
4|4 2 2 2 2 3 2 2 2 2 0 2 4 6 8 11 13 15 17 C Db D# E F G Ab A# B symmetrical, has both 4/3 and 3/2
3|5 2 2 2 2 2 3 2 2 2 0 2 4 6 8 10 13 15 17 C Db D# E F Gb Ab A# B
2|6 2 2 2 2 2 2 3 2 2 0 2 4 6 8 10 12 15 17 C Db D# E F Gb G# A# B
1|7 2 2 2 2 2 2 2 3 2 0 2 4 6 8 10 12 14 17 C Db D# E F Gb G# A B
0|8 2 2 2 2 2 2 2 2 3 0 2 4 6 8 10 12 14 16 C Db D# E F Gb G# A Bb

negri[10] (9L+1s / CPG = 2\19)

UDP steps degrees note names
9|0 2 2 2 2 2 2 2 2 2 1 0 2 4 6 8 10 12 14 16 18 C Db D# E F Gb G# A Bb B#
8|1 2 2 2 2 2 2 2 2 1 2 0 2 4 6 8 10 12 14 16 17 C Db D# E F Gb G# A Bb B
7|2 2 2 2 2 2 2 2 1 2 2 0 2 4 6 8 10 12 14 15 17 C Db D# E F Gb G# A A# B
6|3 2 2 2 2 2 2 1 2 2 2 0 2 4 6 8 10 12 13 15 17 C Db D# E F Gb G# Ab A# B
5|4 2 2 2 2 2 1 2 2 2 2 0 2 4 6 8 10 11 13 15 17 C Db D# E F Gb G Ab A# B
4|5 2 2 2 2 1 2 2 2 2 2 0 2 4 6 8 9 11 13 15 17 C Db D# E F F# G Ab A# B
3|6 2 2 2 1 2 2 2 2 2 2 0 2 4 6 7 9 11 13 15 17 C Db D# E E# F# G Ab A# B
2|7 2 2 1 2 2 2 2 2 2 2 0 2 4 5 7 9 11 13 15 17 C Db D# Eb E# F# G Ab A# B
1|8 2 1 2 2 2 2 2 2 2 2 0 2 3 5 7 9 11 13 15 17 C Db D Eb E# F# G Ab A# B
0|9 1 2 2 2 2 2 2 2 2 2 0 1 3 5 7 9 11 13 15 17 C C# D Eb E# F# G Ab A# B

Deutone

deutone[6] (1L+5s / chroma-positive generator = 16\19)

UDP steps degrees note names
5|0 4 3 3 3 3 3 0 4 7 10 13 16 C D# E# Gb Ab Bb
4|1 3 4 3 3 3 3 0 3 7 10 13 16 C D E# Gb Ab Bb
3|2 3 3 4 3 3 3 0 3 6 10 13 16 C D E Gb Ab Bb
2|3 3 3 3 4 3 3 0 3 6 9 13 16 C D E F# Ab Bb
1|4 3 3 3 3 4 3 0 3 6 9 12 16 C D E F# G# Bb
0|5 3 3 3 3 3 4 0 3 6 9 12 15 C D E F# G# A#

deutone[7] (6L+1s / CPG = 3\19)

UDP steps degrees note names
6|0 3 3 3 3 3 3 1 0 3 6 9 12 15 18 C D E F# G# A# B#
5|1 3 3 3 3 3 1 3 0 3 6 9 12 15 16 C D E F# G# A# Bb
4|2 3 3 3 3 1 3 3 0 3 6 9 12 13 16 C D E F# G# Ab Bb
3|3 3 3 3 1 3 3 3 0 3 6 9 10 13 16 C D E F# Gb Ab Bb
2|4 3 3 1 3 3 3 3 0 3 6 7 10 13 16 C D E E# Gb Ab Bb
1|5 3 1 3 3 3 3 3 0 3 4 7 10 13 16 C D D# E# Gb Ab Bb
0|6 1 3 3 3 3 3 3 0 1 4 7 10 13 16 C C# D# E# Gb Ab Bb

deutone[13] (6L+7s / CPG = 3\19)

UDP steps degrees note names
12|0 2 1 2 1 2 1 2 1 2 1 2 1 1 0 2 3 5 6 8 9 11 12 14 15 17 18 C Db D Eb E F F# G G# A A# B B#
11|1 2 1 2 1 2 1 2 1 2 1 1 2 1 0 2 3 5 6 8 9 11 12 14 15 16 18 C Db D Eb E F F# G G# A A# Bb B#
10|2 2 1 2 1 2 1 2 1 1 2 1 2 1 0 2 3 5 6 8 9 11 12 13 15 16 18 C Db D Eb E F F# G G# Ab A# Bb B#
9|3 2 1 2 1 2 1 1 2 1 2 1 2 1 0 2 3 5 6 8 9 10 12 13 15 16 18 C Db D Eb E F F# Gb G# Ab A# Bb B#
8|4 2 1 2 1 1 2 1 2 1 2 1 2 1 0 2 3 5 6 7 9 10 12 13 15 16 18 C Db D Eb E E# F# Gb G# Ab A# Bb B#
7|5 2 1 1 2 1 2 1 2 1 2 1 2 1 0 2 3 4 6 7 9 10 12 13 15 16 18 C Db D D# E E# F# Gb G# Ab A# Bb B#
6|6 1 2 1 2 1 2 1 2 1 2 1 2 1 0 1 3 4 6 7 9 10 12 13 15 16 18 C C# D D# E E# F# Gb G# Ab A# Bb B#
5|7 1 2 1 2 1 2 1 2 1 2 1 1 2 0 1 3 4 6 7 9 10 12 13 15 16 17 C C# D D# E E# F# Gb G# Ab A# Bb B
4|8 1 2 1 2 1 2 1 2 1 1 2 1 2 0 1 3 4 6 7 9 10 12 13 14 16 17 C C# D D# E E# F# Gb G# Ab A Bb B
3|9 1 2 1 2 1 2 1 1 2 1 2 1 2 0 1 3 4 6 7 9 10 11 13 14 16 17 C C# D D# E E# F# Gb G Ab A Bb B
2|10 1 2 1 2 1 1 2 1 2 1 2 1 2 0 1 3 4 6 7 8 10 11 13 14 16 17 C C# D D# E E# F Gb G Ab A Bb B
1|11 1 2 1 1 2 1 2 1 2 1 2 1 2 0 1 3 4 5 7 8 10 11 13 14 16 17 C C# D D# Eb E# F Gb G Ab A Bb B
0|12 1 1 2 1 2 1 2 1 2 1 2 1 2 0 1 2 4 5 7 8 10 11 13 14 16 17 C C# Db D# Eb E# F Gb G Ab A Bb B

Godzilla / Semaphore

godzilla[5] (4L+1s / chroma-positive generator = 4\19 ~= 8/7 ~= 7/6)

UDP mode steps mode degrees note names
4|0 4 4 4 4 3 0 4 8 12 16 C D# F G# Bb
3|1 4 4 4 3 4 0 4 8 12 15 C D# F G# A#
2|2 4 4 3 4 4 0 4 8 11 15 C D# F G A#
1|3 4 3 4 4 4 0 4 7 11 15 C D# E# G A#
0|4 3 4 4 4 4 0 3 7 11 15 C D E# G A#

godzilla[9] (5L+4s / CPG = 15\19 ~= 7/4 ~= 12/7)

UDP mode steps mode degrees note names
8|0 3 3 1 3 1 3 1 3 1 0 3 6 7 10 11 14 15 18 C D E E# Gb G A A# B#
7|1 3 1 3 3 1 3 1 3 1 0 3 4 7 10 11 14 15 18 C D D# E# Gb G A A# B#
6|2 3 1 3 1 3 3 1 3 1 0 3 4 7 8 11 14 15 18 C D D# E# F G A A# B#
5|3 3 1 3 1 3 1 3 3 1 0 3 4 7 8 11 12 15 18 C D D# E# F G G# A# B#
4|4 3 1 3 1 3 1 3 1 3 0 3 4 7 8 11 12 15 16 C D D# E# F G G# A# Bb
3|5 1 3 3 1 3 1 3 1 3 0 1 4 7 8 11 12 15 16 C C# D# E# F G G# A# Bb
2|6 1 3 1 3 3 1 3 1 3 0 1 4 5 8 11 12 15 16 C C# D# Eb F G G# A# Bb
1|7 1 3 1 3 1 3 3 1 3 0 1 4 5 8 9 12 15 16 C C# D# Eb F F# G# A# Bb
0|8 1 3 1 3 1 3 1 3 3 0 1 4 5 8 9 12 13 16 C C# D# Eb F F# G# Ab Bb

godzilla[14] (5L+9s / CPG = 4\19)

UDP steps degrees note names
13|0 2 1 2 1 1 2 1 1 2 1 1 2 1 1 0 2 3 5 6 7 9 10 11 13 14 15 17 18 C Db D Eb E E# F# Gb G Ab A A# B B#
12|1 2 1 1 2 1 2 1 1 2 1 1 2 1 1 0 2 3 4 6 7 9 10 11 13 14 15 17 18 C Db D D# E E# F# Gb G Ab A A# B B#
11|2 2 1 1 2 1 1 2 1 2 1 1 2 1 1 0 2 3 4 6 7 8 10 11 13 14 15 17 18 C Db D D# E E# F Gb G Ab A A# B B#
10|3 2 1 1 2 1 1 2 1 1 2 1 2 1 1 0 2 3 4 6 7 8 10 11 12 14 15 17 18 C Db D D# E E# F Gb G G# A A# B B#
9|4 2 1 1 2 1 1 2 1 1 2 1 1 2 1 0 2 3 4 6 7 8 10 11 12 14 15 16 18 C Db D D# E E# F Gb G G# A A# Bb B#
8|5 1 2 1 2 1 1 2 1 1 2 1 1 2 1 0 1 3 4 6 7 8 10 11 12 14 15 16 18 C C# D D# E E# F Gb G G# A A# Bb B#
7|6 1 2 1 1 2 1 2 1 1 2 1 1 2 1 0 1 3 4 5 7 8 10 11 12 14 15 16 18 C C# D D# Eb E# F Gb G G# A A# Bb B#
6|7 1 2 1 1 2 1 1 2 1 2 1 1 2 1 0 1 3 4 5 7 8 9 11 12 14 15 16 18 C C# D D# Eb E# F F# G G# A A# Bb B#
5|8 1 2 1 1 2 1 1 2 1 1 2 1 2 1 0 1 3 4 5 7 8 9 11 12 13 15 16 18 C C# D D# Eb E# F F# G G# Ab A# Bb B#
4|9 1 2 1 1 2 1 1 2 1 1 2 1 1 2 0 1 3 4 5 7 8 9 11 12 13 15 16 17 C C# D D# Eb E# F F# G G# Ab A# Bb B
3|10 1 1 2 1 2 1 1 2 1 1 2 1 1 2 0 1 2 4 5 7 8 9 11 12 13 15 16 17 C C# Db D# Eb E# F F# G G# Ab A# Bb B
2|11 1 1 2 1 1 2 1 2 1 1 2 1 1 2 0 1 2 4 5 6 8 9 11 12 13 15 16 17 C C# Db D# Eb E F F# G G# Ab A# Bb B
1|12 1 1 2 1 1 2 1 1 2 1 2 1 1 2 0 1 2 4 5 6 8 9 10 12 13 15 16 17 C C# Db D# Eb E F F# Gb G# Ab A# Bb B
0|13 1 1 2 1 1 2 1 1 2 1 1 2 1 2 0 1 2 4 5 6 8 9 10 12 13 14 16 17 C C# Db D# Eb E F F# Gb G# Ab A Bb B

Kleismic / Hanson

kleismic[7] (4L+3s / chroma-positive generator = 14\19 ~= 5/3)

UDP steps degrees note names comments
6|0 4 4 1 4 1 4 1 0 4 8 9 13 14 18 C D# F F# Ab A B# has 4/3
5|1 4 1 4 4 1 4 1 0 4 5 9 13 14 18 C D# Eb F# Ab A B#
4|2 4 1 4 1 4 4 1 0 4 5 9 10 14 18 C D# Eb F# Gb A B#
3|3 4 1 4 1 4 1 4 0 4 5 9 10 14 15 C D# Eb F# Gb A A# symmetrical
2|4 1 4 4 1 4 1 4 0 1 5 9 10 14 15 C C# Eb F# Gb A A#
1|5 1 4 1 4 4 1 4 0 1 5 6 10 14 15 C C# Eb E Gb A A#
0|6 1 4 1 4 1 4 4 0 1 5 6 10 11 15 C C# Eb E Gb G A# has 3/2

kleismic[11] (4L+7s / CPG = 14\19)

UDP steps degrees note names comments
10|0 3 1 3 1 1 3 1 1 3 1 1 0 3 4 7 8 9 12 13 14 17 18 C D D# E# F F# G# Ab A B B#
9|1 3 1 1 3 1 3 1 1 3 1 1 0 3 4 5 8 9 12 13 14 17 18 C D D# Eb F F# G# Ab A B B#
8|2 3 1 1 3 1 1 3 1 3 1 1 0 3 4 5 8 9 10 13 14 17 18 C D D# Eb F F# Gb Ab A B B#
7|3 3 1 1 3 1 1 3 1 1 3 1 0 3 4 5 8 9 10 13 14 15 18 C D D# Eb F F# Gb Ab A A# B#
6|4 1 3 1 3 1 1 3 1 1 3 1 0 1 4 5 8 9 10 13 14 15 18 C C# D# Eb F F# Gb Ab A A# B#
5|5 1 3 1 1 3 1 3 1 1 3 1 0 1 4 5 6 9 10 13 14 15 18 C C# D# Eb E F# Gb Ab A A# B# symmetrical, has neither 4/3 nor 3/2
4|6 1 3 1 1 3 1 1 3 1 3 1 0 1 4 5 6 9 10 11 14 15 18 C C# D# Eb E F# Gb G A A# B#
3|7 1 3 1 1 3 1 1 3 1 1 3 0 1 4 5 6 9 10 11 14 15 16 C C# D# Eb E F# Gb G A A# Bb
2|8 1 1 3 1 3 1 1 3 1 1 3 0 1 2 5 6 9 10 11 14 15 16 C C# Db Eb E F# Gb G A A# Bb
1|9 1 1 3 1 1 3 1 3 1 1 3 0 1 2 5 6 7 10 11 14 15 16 C C# Db Eb E E# Gb G A A# Bb
0|10 1 1 3 1 1 3 1 1 3 1 3 0 1 2 5 6 7 10 11 12 15 16 C C# Db Eb E E# Gb G G# A# Bb

kleismic[15] (4L+11s / CPG = 14\19)

UDP steps degrees note names
14|0 2 1 1 2 1 1 1 2 1 1 1 2 1 1 1 0 2 3 4 6 7 8 9 11 12 13 14 16 17 18 C Db D D# E E# F F# G G# Ab A Bb B B#
13|1 2 1 1 1 2 1 1 2 1 1 1 2 1 1 1 0 2 3 4 5 7 8 9 11 12 13 14 16 17 18 C Db D D# Eb E# F F# G G# Ab A Bb B B#
12|2 2 1 1 1 2 1 1 1 2 1 1 2 1 1 1 0 2 3 4 5 7 8 9 10 12 13 14 16 17 18 C Db D D# Eb E# F F# Gb G# Ab A Bb B B#
11|3 2 1 1 1 2 1 1 1 2 1 1 1 2 1 1 0 2 3 4 5 7 8 9 10 12 13 14 15 17 18 C Db D D# Eb E# F F# Gb G# Ab A A# B B#
10|4 1 2 1 1 2 1 1 1 2 1 1 1 2 1 1 0 1 3 4 5 7 8 9 10 12 13 14 15 17 18 C C# D D# Eb E# F F# Gb G# Ab A A# B B#
9|5 1 2 1 1 1 2 1 1 2 1 1 1 2 1 1 0 1 3 4 5 6 8 9 10 12 13 14 15 17 18 C C# D D# Eb E F F# Gb G# Ab A A# B B#
8|6 1 2 1 1 1 2 1 1 1 2 1 1 2 1 1 0 1 3 4 5 6 8 9 10 11 13 14 15 17 18 C C# D D# Eb E F F# Gb G Ab A A# B B#
7|7 1 2 1 1 1 2 1 1 1 2 1 1 1 2 1 0 1 3 4 5 6 8 9 10 11 13 14 15 16 18 C C# D D# Eb E F F# Gb G Ab A A# Bb B#
6|8 1 1 2 1 1 2 1 1 1 2 1 1 1 2 1 0 1 2 4 5 6 8 9 10 11 13 14 15 16 18 C C# Db D# Eb E F F# Gb G Ab A A# Bb B#
5|9 1 1 2 1 1 1 2 1 1 2 1 1 1 2 1 0 1 2 4 5 6 7 9 10 11 13 14 15 16 18 C C# Db D# Eb E E# F# Gb G Ab A A# Bb B#
4|10 1 1 2 1 1 1 2 1 1 1 2 1 1 2 1 0 1 2 4 5 6 7 9 10 11 12 14 15 16 18 C C# Db D# Eb E E# F# Gb G G# A A# Bb B#
3|11 1 1 2 1 1 1 2 1 1 1 2 1 1 1 2 0 1 2 4 5 6 7 9 10 11 12 14 15 16 17 C C# Db D# Eb E E# F# Gb G G# A A# Bb B
2|12 1 1 1 2 1 1 2 1 1 1 2 1 1 1 2 0 1 2 3 5 6 7 9 10 11 12 14 15 16 17 C C# Db D Eb E E# F# Gb G G# A A# Bb B
1|13 1 1 1 2 1 1 1 2 1 1 2 1 1 1 2 0 1 2 3 5 6 7 8 10 11 12 14 15 16 17 C C# Db D Eb E E# F Gb G G# A A# Bb B
0|14 1 1 1 2 1 1 1 2 1 1 1 2 1 1 2 0 1 2 3 5 6 7 8 10 11 12 13 15 16 17 C C# Db D Eb E E# F Gb G G# Ab A# Bb B

Magic

magic[7] (3L+4s / chroma-positive generator = 6\19 ~=5/4)

UDP steps degrees note names
6|0 5 1 5 1 5 1 1 0 5 6 11 12 17 18 C Eb E G G# B B#
5|1 5 1 5 1 1 5 1 0 5 6 11 12 13 18 C Eb E G G# Ab B#
4|2 5 1 1 5 1 5 1 0 5 6 7 12 13 18 C Eb E E# G# Ab B#
3|3 1 5 1 5 1 5 1 0 1 6 7 12 13 18 C C# E E# G# Ab B#
2|4 1 5 1 5 1 1 5 0 1 6 7 12 13 14 C C# E E# G# Ab A
1|5 1 5 1 1 5 1 5 0 1 6 7 8 13 14 C C# E E# F Ab A
0|6 1 1 5 1 5 1 5 0 1 2 7 8 13 14 C C# Db E# F Ab A

magic[10] (3L+7s / CPG = 6\19)

UDP steps degrees note names
9|0 4 1 1 4 1 1 4 1 1 1 0 4 5 6 10 11 12 16 17 18 C D# Eb E Gb G G# Bb B B#
8|1 4 1 1 4 1 1 1 4 1 1 0 4 5 6 10 11 12 13 17 18 C D# Eb E Gb G G# Ab B B#
7|2 4 1 1 1 4 1 1 4 1 1 0 4 5 6 7 11 12 13 17 18 C D# Eb E E# G G# Ab B B#
6|3 1 4 1 1 4 1 1 4 1 1 0 1 5 6 7 11 12 13 17 18 C C# Eb E E# G G# Ab B B#
5|4 1 4 1 1 4 1 1 1 4 1 0 1 5 6 7 11 12 13 14 18 C C# Eb E E# G G# Ab A B#
4|5 1 4 1 1 1 4 1 1 4 1 0 1 5 6 7 8 12 13 14 18 C C# Eb E E# F G# Ab A B#
3|6 1 1 4 1 1 4 1 1 4 1 0 1 2 6 7 8 12 13 14 18 C C# Db E E# F G# Ab A B#
2|7 1 1 4 1 1 4 1 1 1 4 0 1 2 6 7 8 12 13 14 15 C C# Db E E# F G# Ab A A#
1|8 1 1 4 1 1 1 4 1 1 4 0 1 2 6 7 8 9 13 14 15 C C# Db E E# F F# Ab A A#
0|9 1 1 1 4 1 1 4 1 1 4 0 1 2 3 7 8 9 13 14 15 C C# Db D E# F F# Ab A A#

magic[13] (3L+10s / CPG = 6\19 ~=5/4)

UDP steps degrees note names
12|0 3 1 1 1 3 1 1 1 3 1 1 1 1 0 3 4 5 6 9 10 11 12 15 16 17 18 C D D# Eb E F# Gb G G# A# Bb B B#
11|1 3 1 1 1 3 1 1 1 1 3 1 1 1 0 3 4 5 6 9 10 11 12 13 16 17 18 C D D# Eb E F# Gb G G# Ab Bb B B#
10|2 3 1 1 1 1 3 1 1 1 3 1 1 1 0 3 4 5 6 7 10 11 12 13 16 17 18 C D D# Eb E E# Gb G G# Ab Bb B B#
9|3 1 3 1 1 1 3 1 1 1 3 1 1 1 0 1 4 5 6 7 10 11 12 13 16 17 18 C C# D# Eb E E# Gb G G# Ab Bb B B#
8|4 1 3 1 1 1 3 1 1 1 1 3 1 1 0 1 4 5 6 7 10 11 12 13 14 17 18 C C# D# Eb E E# Gb G G# Ab A B B#
7|5 1 3 1 1 1 1 3 1 1 1 3 1 1 0 1 4 5 6 7 8 11 12 13 14 17 18 C C# D# Eb E E# F G G# Ab A B B#
6|6 1 1 3 1 1 1 3 1 1 1 3 1 1 0 1 2 5 6 7 8 11 12 13 14 17 18 C C# Db Eb E E# F G G# Ab A B B#
5|7 1 1 3 1 1 1 3 1 1 1 1 3 1 0 1 2 5 6 7 8 11 12 13 14 15 18 C C# Db Eb E E# F G G# Ab A A# B#
4|8 1 1 3 1 1 1 1 3 1 1 1 3 1 0 1 2 5 6 7 8 9 12 13 14 15 18 C C# Db Eb E E# F F# G# Ab A A# B#
3|9 1 1 1 3 1 1 1 3 1 1 1 3 1 0 1 2 3 6 7 8 9 12 13 14 15 18 C C# Db D E E# F F# G# Ab A A# B#
2|10 1 1 1 3 1 1 1 3 1 1 1 1 3 0 1 2 3 6 7 8 9 12 13 14 15 16 C C# Db D E E# F F# G# Ab A A# Bb
1|11 1 1 1 3 1 1 1 1 3 1 1 1 3 0 1 2 3 6 7 8 9 10 13 14 15 16 C C# Db D E E# F F# Gb Ab A A# Bb
0|12 1 1 1 1 3 1 1 1 3 1 1 1 3 0 1 2 3 4 7 8 9 10 13 14 15 16 C C# Db D D# E# F F# Gb Ab A A# Bb

magic[16] (3L+13s / CPG = 6\19)

UDP steps degrees note names
15|0 2 1 1 1 1 2 1 1 1 1 2 1 1 1 1 1 0 2 3 4 5 6 8 9 10 11 12 14 15 16 17 18 C Db D D# Eb E F F# Gb G G# A A# Bb B B#
14|1 2 1 1 1 1 2 1 1 1 1 1 2 1 1 1 1 0 2 3 4 5 6 8 9 10 11 12 13 15 16 17 18 C Db D D# Eb E F F# Gb G G# Ab A# Bb B B#
13|2 2 1 1 1 1 1 2 1 1 1 1 2 1 1 1 1 0 2 3 4 5 6 7 9 10 11 12 13 15 16 17 18 C Db D D# Eb E E# F# Gb G G# Ab A# Bb B B#
12|3 1 2 1 1 1 1 2 1 1 1 1 2 1 1 1 1 0 1 3 4 5 6 7 9 10 11 12 13 15 16 17 18 C C# D D# Eb E E# F# Gb G G# Ab A# Bb B B#
11|4 1 2 1 1 1 1 2 1 1 1 1 1 2 1 1 1 0 1 3 4 5 6 7 9 10 11 12 13 14 16 17 18 C C# D D# Eb E E# F# Gb G G# Ab A Bb B B#
10|5 1 2 1 1 1 1 1 2 1 1 1 1 2 1 1 1 0 1 3 4 5 6 7 8 10 11 12 13 14 16 17 18 C C# D D# Eb E E# F Gb G G# Ab A Bb B B#
9|6 1 1 2 1 1 1 1 2 1 1 1 1 2 1 1 1 0 1 2 4 5 6 7 8 10 11 12 13 14 16 17 18 C C# Db D# Eb E E# F Gb G G# Ab A Bb B B#
8|7 1 1 2 1 1 1 1 2 1 1 1 1 1 2 1 1 0 1 2 4 5 6 7 8 10 11 12 13 14 15 17 18 C C# Db D# Eb E E# F Gb G G# Ab A A# B B#
7|8 1 1 2 1 1 1 1 1 2 1 1 1 1 2 1 1 0 1 2 4 5 6 7 8 9 11 12 13 14 15 17 18 C C# Db D# Eb E E# F F# G G# Ab A A# B B#
6|9 1 1 1 2 1 1 1 1 2 1 1 1 1 2 1 1 0 1 2 3 5 6 7 8 9 11 12 13 14 15 17 18 C C# Db D Eb E E# F F# G G# Ab A A# B B#
5|10 1 1 1 2 1 1 1 1 2 1 1 1 1 1 2 1 0 1 2 3 5 6 7 8 9 11 12 13 14 15 16 18 C C# Db D Eb E E# F F# G G# Ab A A# Bb B#
4|11 1 1 1 2 1 1 1 1 1 2 1 1 1 1 2 1 0 1 2 3 5 6 7 8 9 10 12 13 14 15 16 18 C C# Db D Eb E E# F F# Gb G# Ab A A# Bb B#
3|12 1 1 1 1 2 1 1 1 1 2 1 1 1 1 2 1 0 1 2 3 4 6 7 8 9 10 12 13 14 15 16 18 C C# Db D D# E E# F F# Gb G# Ab A A# Bb B#
2|13 1 1 1 1 2 1 1 1 1 2 1 1 1 1 1 2 0 1 2 3 4 6 7 8 9 10 12 13 14 15 16 17 C C# Db D D# E E# F F# Gb G# Ab A A# Bb B
1|14 1 1 1 1 2 1 1 1 1 1 2 1 1 1 1 2 0 1 2 3 4 6 7 8 9 10 11 13 14 15 16 17 C C# Db D D# E E# F F# Gb G Ab A A# Bb B
0|15 1 1 1 1 1 2 1 1 1 1 2 1 1 1 1 2 0 1 2 3 4 5 7 8 9 10 11 13 14 15 16 17 C C# Db D D# Eb E# F F# Gb G Ab A A# Bb B

Sensi

sensi[5] (3L+2s / chroma-positive generator = 12\19)

UDP mode steps mode degrees note names
4|0 5 5 2 5 2 0 5 10 12 17 C Eb Gb G# B
3|1 5 2 5 5 2 0 5 7 12 17 C Eb E# G# B
2|2 5 2 5 2 5 0 5 7 12 14 C Eb E# G# A
1|3 2 5 5 2 5 0 2 7 12 14 C Db E# G# A
0|4 2 5 2 5 5 0 2 7 9 14 C Db E# F# A

sensi[8] (3L+5s / CPG = 12\19)

UDP mode steps mode degrees note names
7|0 3 2 3 2 2 3 2 2 0 3 5 8 10 12 15 17 C D Eb F Gb G# A# B
6|1 3 2 2 3 2 3 2 2 0 3 5 7 10 12 15 17 C D Eb E# Gb G# A# B
5|2 3 2 2 3 2 2 3 2 0 3 5 7 10 12 14 17 C D Eb E# Gb G# A B
4|3 2 3 2 3 2 2 3 2 0 2 5 7 10 12 14 17 C Db Eb E# Gb G# A B
3|4 2 3 2 2 3 2 3 2 0 2 5 7 9 12 14 17 C Db Eb E# F# G# A B
2|5 2 3 2 2 3 2 2 3 0 2 5 7 9 12 14 16 C Db Eb E# F# G# A Bb
1|6 2 2 3 2 3 2 2 3 0 2 4 7 9 12 14 16 C Db D# E# F# G# A Bb
0|7 2 2 3 2 2 3 2 3 0 2 4 7 9 11 14 16 C Db D# E# F# G A Bb

sensi[11] (8L+3s / CPG = 7\19)

UDP mode steps mode degrees note names
10|0 2 2 2 1 2 2 2 1 2 2 1 0 2 4 6 7 9 11 13 14 16 18 C Db D# E E# F# G Ab A Bb B#
9|1 2 2 2 1 2 2 1 2 2 2 1 0 2 4 6 7 9 11 12 14 16 18 C Db D# E E# F# G G# A Bb B#
8|2 2 2 1 2 2 2 1 2 2 2 1 0 2 4 5 7 9 11 12 14 16 18 C Db D# Eb E# F# G G# A Bb B#
7|3 2 2 1 2 2 2 1 2 2 1 2 0 2 4 5 7 9 11 12 14 16 17 C Db D# Eb E# F# G G# A Bb B
6|4 2 2 1 2 2 1 2 2 2 1 2 0 2 4 5 7 9 10 12 14 16 17 C Db D# Eb E# F# Gb G# A Bb B
5|5 2 1 2 2 2 1 2 2 2 1 2 0 2 3 5 7 9 10 12 14 16 17 C Db D Eb E# F# Gb G# A Bb B
4|6 2 1 2 2 2 1 2 2 1 2 2 0 2 3 5 7 9 10 12 14 15 17 C Db D Eb E# F# Gb G# A A# B
3|7 2 1 2 2 1 2 2 2 1 2 2 0 2 3 5 7 8 10 12 14 15 17 C Db D Eb E# F Gb G# A A# B
2|8 1 2 2 2 1 2 2 2 1 2 2 0 1 3 5 7 8 10 12 14 15 17 C C# D Eb E# F Gb G# A A# B
1|9 1 2 2 2 1 2 2 1 2 2 2 0 1 3 5 7 8 10 12 13 15 17 C C# D Eb E# F Gb G# Ab A# B
0|10 1 2 2 1 2 2 2 1 2 2 2 0 1 3 5 6 8 10 12 13 15 17 C C# D Eb E F Gb G# Ab A# B

Liese / Triton

liese[5] (2L+3s / chroma-positive generator = 9\19 ~= 7/5)

UDP steps degrees note names
4|0 8 1 8 1 1 0 8 9 17 18 C F F# B B#
3|1 8 1 1 8 1 0 8 9 10 18 C F F# Gb B#
2|2 1 8 1 8 1 0 1 9 10 18 C C# F# Gb B#
1|3 1 8 1 1 8 0 1 9 10 11 C C# F# Gb G
0|4 1 1 8 1 8 0 1 2 10 11 C C# Db Gb G

liese[7] (2L+5s / CPG = 9\19)

UDP steps degrees note names
6|0 7 1 1 7 1 1 1 0 7 8 9 16 17 18 C E# F F# Bb B B#
5|1 7 1 1 1 7 1 1 0 7 8 9 10 17 18 C E# F F# Gb B B#
4|2 1 7 1 1 7 1 1 0 1 8 9 10 17 18 C C# F F# Gb B B#
3|3 1 7 1 1 1 7 1 0 1 8 9 10 11 18 C C# F F# Gb G B#
2|4 1 1 7 1 1 7 1 0 1 2 9 10 11 18 C C# Db F# Gb G B#
1|5 1 1 7 1 1 1 7 0 1 2 9 10 11 12 C C# Db F# Gb G G#
0|6 1 1 1 7 1 1 7 0 1 2 3 10 11 12 C C# Db D Gb G G#

liese[9] (2L+7s / CPG = 9\19)

UDP steps degrees note names
8|0 6 1 1 1 6 1 1 1 1 0 6 7 8 9 15 16 17 18 C E E# F F# A# Bb B B#
7|1 6 1 1 1 1 6 1 1 1 0 6 7 8 9 10 16 17 18 C E E# F F# Gb Bb B B#
6|2 1 6 1 1 1 6 1 1 1 0 1 7 8 9 10 16 17 18 C C# E# F F# Gb Bb B B#
5|3 1 6 1 1 1 1 6 1 1 0 1 7 8 9 10 11 17 18 C C# E# F F# Gb G B B#
4|4 1 1 6 1 1 1 6 1 1 0 1 2 8 9 10 11 17 18 C C# Db F F# Gb G B B#
3|5 1 1 6 1 1 1 1 6 1 0 1 2 8 9 10 11 12 18 C C# Db F F# Gb G G# B#
2|6 1 1 1 6 1 1 1 6 1 0 1 2 3 9 10 11 12 18 C C# Db D F# Gb G G# B#
1|7 1 1 1 6 1 1 1 1 6 0 1 2 3 9 10 11 12 13 C C# Db D F# Gb G G# Ab
0|8 1 1 1 1 6 1 1 1 6 0 1 2 3 4 10 11 12 13 C C# Db D D# Gb G G# Ab

liese[11] (2L+9s / CPG = 9\19)

UDP steps degrees note names
10|0 5 1 1 1 1 5 1 1 1 1 1 0 5 6 7 8 9 14 15 16 17 18 C Eb E E# F F# A A# Bb B B#
9|1 5 1 1 1 1 1 5 1 1 1 1 0 5 6 7 8 9 10 15 16 17 18 C Eb E E# F F# Gb A# Bb B B#
8|2 1 5 1 1 1 1 5 1 1 1 1 0 1 6 7 8 9 10 15 16 17 18 C C# E E# F F# Gb A# Bb B B#
7|3 1 5 1 1 1 1 1 5 1 1 1 0 1 6 7 8 9 10 11 16 17 18 C C# E E# F F# Gb G Bb B B#
6|4 1 1 5 1 1 1 1 5 1 1 1 0 1 2 7 8 9 10 11 16 17 18 C C# Db E# F F# Gb G Bb B B#
5|5 1 1 5 1 1 1 1 1 5 1 1 0 1 2 7 8 9 10 11 12 17 18 C C# Db E# F F# Gb G G# B B#
4|6 1 1 1 5 1 1 1 1 5 1 1 0 1 2 3 8 9 10 11 12 17 18 C C# Db D F F# Gb G G# B B#
3|7 1 1 1 5 1 1 1 1 1 5 1 0 1 2 3 8 9 10 11 12 13 18 C C# Db D F F# Gb G G# Ab B#
2|8 1 1 1 1 5 1 1 1 1 5 1 0 1 2 3 4 9 10 11 12 13 18 C C# Db D D# F# Gb G G# Ab B#
1|9 1 1 1 1 5 1 1 1 1 1 5 0 1 2 3 4 9 10 11 12 13 14 C C# Db D D# F# Gb G G# Ab A
0|10 1 1 1 1 1 5 1 1 1 1 5 0 1 2 3 4 5 10 11 12 13 14 C C# Db D D# Eb Gb G G# Ab A

MOS scales of sizes 13, 15, and 17 also exist, and follow a similar pattern:

liese[13] 4111114111111 etc.

liese[15] 311111131111111 etc.

liese[17] 21111111211111111 etc.

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