19edo modes: Difference between revisions

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


=Note names in 19edo=
== Note names in 19edo ==
The charts below primarily use the following note names (based on standard meantone/Pythagorean notation):
The charts below primarily use the following note names (based on standard meantone/Pythagorean notation):


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


==[[Meantone|Meantone]]==
== MOS scales and modes of rank-2 temperaments ==
 
=== [[Meantone|Meantone]] ===


'''meantone[5]''' ([[2L_3s|2L+3s]] / [[Modal_UDP_Notation|chroma-positive generator]] = 8\19 ~= 4/3)
'''meantone[5]''' ([[2L_3s|2L+3s]] / [[Modal_UDP_Notation|chroma-positive generator]] = 8\19 ~= 4/3)
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=MOS scales and modes of rank-2 temperaments=
=== [[Negri|Negri]] ===
 
==[[Negri|Negri]]==


'''negri[9]''' ([[1L_8s|1L+8s]] / [[Modal_UDP_Notation|chroma-positive generator]] = 17\19)
'''negri[9]''' ([[1L_8s|1L+8s]] / [[Modal_UDP_Notation|chroma-positive generator]] = 17\19)
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|}


==[[deutone|Deutone]]==
=== [[deutone|Deutone]] ===


'''deutone[6]''' ([[1L_5s|1L+5s ]]/ [[Modal_UDP_Notation|chroma-positive generator]] = 16\19)
'''deutone[6]''' ([[1L_5s|1L+5s ]]/ [[Modal_UDP_Notation|chroma-positive generator]] = 16\19)
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==[[Semaphore_and_Godzilla|Godzilla / Semaphore]]==
=== [[Semaphore_and_Godzilla|Godzilla / Semaphore]] ===


'''godzilla[5]''' ([[4L_1s|4L+1s ]]/ [[Modal_UDP_Notation|chroma-positive generator]] = 4\19 ~= 8/7 ~= 7/6)
'''godzilla[5]''' ([[4L_1s|4L+1s ]]/ [[Modal_UDP_Notation|chroma-positive generator]] = 4\19 ~= 8/7 ~= 7/6)
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==[[Kleismic_family|Kleismic / Hanson]]==
=== [[Kleismic_family|Kleismic / Hanson]] ===


'''kleismic[7]''' ([[4L_3s|4L+3s ]]/ [[Modal_UDP_Notation|chroma-positive generator]] = 14\19 ~= 5/3)
'''kleismic[7]''' ([[4L_3s|4L+3s ]]/ [[Modal_UDP_Notation|chroma-positive generator]] = 14\19 ~= 5/3)
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==[[Magic|Magic]]==
=== [[Magic|Magic]] ===


'''magic[7]''' ([[3L_4s|3L+4s]] / [[Modal_UDP_Notation|chroma-positive generator]] = 6\19 ~=5/4)
'''magic[7]''' ([[3L_4s|3L+4s]] / [[Modal_UDP_Notation|chroma-positive generator]] = 6\19 ~=5/4)
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==[[Sensi|Sensi]]==
=== [[Sensi|Sensi]] ===


'''sensi[5]''' ([[3L_2s|3L+2s]] / [[Modal_UDP_Notation|chroma-positive generator]] = 12\19)
'''sensi[5]''' ([[3L_2s|3L+2s]] / [[Modal_UDP_Notation|chroma-positive generator]] = 12\19)
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==[[Meantone_family#Liese|Liese]] / [[Marvel_temperaments#Triton|Triton]]==
=== [[Meantone_family#Liese|Liese]] / [[Marvel_temperaments#Triton|Triton]] ===


'''liese[5]''' ([[2L_3s|2L+3s]] / [[Modal_UDP_Notation|chroma-positive generator]] = 9\19 ~= 7/5)
'''liese[5]''' ([[2L_3s|2L+3s]] / [[Modal_UDP_Notation|chroma-positive generator]] = 9\19 ~= 7/5)
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'''liese[17]''' 21111111211111111 etc.
'''liese[17]''' 21111111211111111 etc.


= Strictly proper scales =
== Strictly proper scales ==
''See [[Strictly proper 19edo scales]]''
''See [[Strictly proper 19edo scales]]''


=Miscellaneous scales=
== Miscellaneous scales ==


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

Revision as of 09:54, 2 December 2024

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!

MOS scales and modes of rank-2 temperaments

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

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.

Strictly proper scales

See Strictly proper 19edo scales

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)


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