19edo modes: Difference between revisions

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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):


{| class="wikitable"
{| class="wikitable" style="text-align: center;"
|-
|-
| style="text-align:center;" | 0
| 0
| style="text-align:center;" | 1
| 1
| style="text-align:center;" | 2
| 2
| style="text-align:center;" | 3
| 3
| style="text-align:center;" | 4
| 4
| style="text-align:center;" | 5
| 5
| style="text-align:center;" | 6
| 6
| style="text-align:center;" | 7
| 7
| style="text-align:center;" | 8
| 8
| style="text-align:center;" | 9
| 9
| style="text-align:center;" | 10
| 10
| style="text-align:center;" | 11
| 11
| style="text-align:center;" | 12
| 12
| style="text-align:center;" | 13
| 13
| style="text-align:center;" | 14
| 14
| style="text-align:center;" | 15
| 15
| style="text-align:center;" | 16
| 16
| style="text-align:center;" | 17
| 17
| style="text-align:center;" | 18
| 18
|-
|-
| style="text-align:center;" | C
| C
| style="text-align:center;" | Ç
| Ç


C# (<span style="font-size: 13.3333339691162px;">Δb)</span>
C# (<span style="font-size: 13.3333339691162px;">Δb)</span>
| style="text-align:center;" | <span style="display: block; text-align: center;"><span style="font-size: 13.3333339691162px;">Δ</span></span><span style="display: block; text-align: center;">Ç# (Db)</span>
| <span style="display: block; text-align: center;"><span style="font-size: 13.3333339691162px;">Δ</span></span><span style="display: block; text-align: center;">Ç# (Db)</span>
| style="text-align:center;" | D
| D
| style="text-align:center;" | Þ
| Þ


D# (<span style="font-size: 13.3333339691162px;">εb, Sb)</span>
D# (<span style="font-size: 13.3333339691162px;">εb, Sb)</span>
| style="text-align:center;" | <span style="font-size: 13.3333339691162px;">ε, S</span>
| <span style="font-size: 13.3333339691162px;">ε, S</span>


<span style="display: block; text-align: center;">Þ# (Eb)</span>
<span style="display: block; text-align: center;">Þ# (Eb)</span>
| style="text-align:center;" | E
| E
| style="text-align:center;" | E# (Fb)
| E# (Fb)
| style="text-align:center;" | F
| F
| style="text-align:center;" | ϕ
| ϕ


F# (Γb)
F# (Γb)
| style="text-align:center;" | <span style="display: block; text-align: center;">Γ</span>ϕ# (Gb)
| <span style="display: block; text-align: center;">Γ</span>ϕ# (Gb)
| style="text-align:center;" | G
| G
| style="text-align:center;" | Z
| Z


G# (<span style="font-size: 13.3333339691162px;">αb)</span>
G# (<span style="font-size: 13.3333339691162px;">αb)</span>
| style="text-align:center;" | <span style="display: block; font-size: 13.3333339691162px; text-align: center;">α</span><span style="line-height: 1.5;">Z# (</span>Ab)
| <span style="display: block; font-size: 13.3333339691162px; text-align: center;">α</span><span style="line-height: 1.5;">Z# (</span>Ab)
| style="text-align:center;" | A
| A
| style="text-align:center;" | Æ
| Æ


A# (βb, Bb)
A# (βb, Bb)
| style="text-align:center;" | <span style="display: block; text-align: center;">Æ#</span><span style="display: block; text-align: center;">β ,B(b)</span>
| <span style="display: block; text-align: center;">Æ#</span><span style="display: block; text-align: center;">β ,B(b)</span>
| style="text-align:center;" | B, H
| B, H
| style="text-align:center;" | B#, H# (Cb)
| 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#.
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#.
Line 64: Line 64:


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


{| class="wikitable"
{| class="wikitable"
|-
|-
! | UDP
! UDP
! | steps
! Steps
! | degrees
! Degrees
! | note names
! Note names
! | comments
! Comments
!audio
! Audio
|-
|-
| | 4|0
| 4{{pipe}}0
| | 5 3 5 3 3
| 5 3 5 3 3
| | 0 5 8 13 16
| 0 5 8 13 16
| | C Eb F Ab Bb
| C Eb F Ab Bb
| | minor pentatonic (2)
| minor pentatonic (2)
|[[File:Minor 2 Pentatonic (19-EDO).mp3|frameless]]
| [[File:Minor 2 Pentatonic (19-EDO).mp3|frameless]]
|-
|-
| | 3|1
| 3{{pipe}}1
| | 5 3 3 5 3
| 5 3 3 5 3
| | 0 5 8 11 16
| 0 5 8 11 16
| | C Eb F G Bb
| C Eb F G Bb
| | minor pentatonic
| minor pentatonic
|[[File:Minor Pentatonic (19-EDO).mp3|frameless]]
| [[File:Minor Pentatonic (19-EDO).mp3|frameless]]
|-
|-
| | 2|2
| 2{{pipe}}2
| | 3 5 3 5 3
| 3 5 3 5 3
| | 0 3 8 11 16
| 0 3 8 11 16
| | C D F G Bb
| C D F G Bb
| | "mixolydian" pentatonic
| "mixolydian" pentatonic
|[[File:Mixolydian Pentatonic (19-EDO).mp3|frameless]]
| [[File:Mixolydian Pentatonic (19-EDO).mp3|frameless]]
|-
|-
| | 1|3
| 1{{pipe}}3
| | 3 5 3 3 5
| 3 5 3 3 5
| | 0 3 8 11 14
| 0 3 8 11 14
| | C D F G A
| C D F G A
| | "suspended" pentatonic
| "suspended" pentatonic
|[[File:Suspended Pentatonic (19-EDO).mp3|frameless]]
| [[File:Suspended Pentatonic (19-EDO).mp3|frameless]]
|-
|-
| | 0|4
| 0{{pipe}}4
| | 3 3 5 3 5
| 3 3 5 3 5
| | 0 3 6 11 14
| 0 3 6 11 14
| | C D E G A
| C D E G A
| | major pentatonic
| major pentatonic
|[[File:Major Pentatonic (19-EDO).mp3|frameless]]
| [[File:Major Pentatonic (19-EDO).mp3|frameless]]
|}
|}


Line 118: Line 116:
{| class="wikitable"
{| class="wikitable"
|-
|-
! | UDP
! UDP
! | steps
! Steps
! | degrees
! Degrees
! | note names
! Note names
! | mode name
! Mode name
!audio
! Audio
|-
|-
| | 6|0
| 6{{pipe}}0
| | 3 3 3 2 3 3 2
| 3 3 3 2 3 3 2
| | 0 3 6 9 11 14 17
| 0 3 6 9 11 14 17
| | C D E F# G A B
| C D E F# G A B
| | Lydian
| Lydian
|[[File:Lydian (19-EDO).mp3|frameless]]
| [[File:Lydian (19-EDO).mp3|frameless]]
|-
|-
| | 5|1
| 5{{pipe}}1
| | 3 3 2 3 3 3 2
| 3 3 2 3 3 3 2
| | 0 3 6 8 11 14 17
| 0 3 6 8 11 14 17
| | C D E F G A B
| C D E F G A B
| | Ionian
| Ionian
|[[File:Ionian (19-EDO).mp3|frameless]]
| [[File:Ionian (19-EDO).mp3|frameless]]
|-
|-
| | 4|2
| 4{{pipe}}2
| | 3 3 2 3 3 2 3
| 3 3 2 3 3 2 3
| | 0 3 6 8 11 14 16
| 0 3 6 8 11 14 16
| | C D E F G A Bb
| C D E F G A Bb
| | Mixolydian
| Mixolydian
|[[File:Mixolydian (19-EDO).mp3|frameless]]
| [[File:Mixolydian (19-EDO).mp3|frameless]]
|-
|-
| | 3|3
| 3{{pipe}}3
| | 3 2 3 3 3 2 3
| 3 2 3 3 3 2 3
| | 0 3 5 8 11 14 16
| 0 3 5 8 11 14 16
| | C D Eb F G A Bb
| C D Eb F G A Bb
| | Dorian
| Dorian
|[[File:Dorian (19-EDO).mp3|frameless]]
| [[File:Dorian (19-EDO).mp3|frameless]]
|-
|-
| | 2|4
| 2{{pipe}}4
| | 3 2 3 3 2 3 3
| 3 2 3 3 2 3 3
| | 0 3 5 8 11 13 16
| 0 3 5 8 11 13 16
| | C D Eb F G Ab Bb
| C D Eb F G Ab Bb
| | Aeolian
| Aeolian
|[[File:Aeolian (19-EDO).mp3|frameless]]
| [[File:Aeolian (19-EDO).mp3|frameless]]
|-
|-
| | 1|5
| 1{{pipe}}5
| | 2 3 3 3 2 3 3
| 2 3 3 3 2 3 3
| | 0 2 5 8 11 13 16
| 0 2 5 8 11 13 16
| | C Db Eb F G Ab Bb
| C Db Eb F G Ab Bb
| | Phrygian
| Phrygian
|[[File:Phrygian (19-EDO).mp3|frameless]]
| [[File:Phrygian (19-EDO).mp3|frameless]]
|-
|-
| | 0|6
| 0{{pipe}}6
| | 2 3 3 2 3 3 3
| 2 3 3 2 3 3 3
| | 0 2 5 8 10 13 16
| 0 2 5 8 10 13 16
| | C Db Eb F Gb Ab Bb
| C Db Eb F Gb Ab Bb
| | Locrian
| Locrian
|[[File:Locrian (19-EDO).mp3|frameless]]
| [[File:Locrian (19-EDO).mp3|frameless]]
|}
|}


Line 179: Line 177:
{| class="wikitable"
{| class="wikitable"
|-
|-
! | UDP
! UDP
! | steps
! Steps
! | degrees
! Degrees
! | note names
! Note names
! | comments
! Comments
|-
|-
| | 11|0
| 11{{pipe}}0
| | 2 2 1 2 1 2 2 1 2 1 2 1
| 2 2 1 2 1 2 2 1 2 1 2 1
| | 0 2 4 5 7 8 10 12 13 15 16 18
| 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 Db D# Eb E# F Gb G# Ab A# Bb B#


C <span style="font-size: 13.3333339691162px;">Δ </span>Þ S E# F Γ Z <span style="font-size: 13.3333339691162px;">α Æ </span>β B#
C <span style="font-size: 13.3333339691162px;">Δ </span>Þ S E# F Γ Z <span style="font-size: 13.3333339691162px;">α Æ </span>β B#
| |  
|
|-
|-
| | 10|1
| 10{{pipe}}1
| | 2 2 1 2 1 2 1 2 2 1 2 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
| 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 Db D# Eb E# F Gb G Ab A# Bb B#


C <span style="font-size: 13.3333339691162px;">Δ </span>Þ S E# F Γ G <span style="font-size: 13.3333339691162px;">α Æ </span>β B#
C <span style="font-size: 13.3333339691162px;">Δ </span>Þ S E# F Γ G <span style="font-size: 13.3333339691162px;">α Æ </span>β B#
| |  
|
|-
|-
| | 9|2
| 9{{pipe}}2
| | 2 1 2 2 1 2 1 2 2 1 2 1
| 2 1 2 2 1 2 1 2 2 1 2 1
| | 0 2 3 5 7 8 10 11 13 15 16 18
| 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 Db D Eb E# F Gb G Ab A# Bb B#


C <span style="font-size: 13.3333339691162px;">Δ D</span> S E# F Γ G <span style="font-size: 13.3333339691162px;">α Æ </span>β B#
C <span style="font-size: 13.3333339691162px;">Δ D</span> S E# F Γ G <span style="font-size: 13.3333339691162px;">α Æ </span>β B#
| |  
|
|-
|-
| | 8|3
| 8{{pipe}}3
| | 2 1 2 2 1 2 1 2 1 2 2 1
| 2 1 2 2 1 2 1 2 1 2 2 1
| | 0 2 3 5 7 8 10 11 13 14 16 18
| 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 Db D Eb E# F Gb G Ab A Bb B#


C <span style="font-size: 13.3333339691162px;">Δ D</span> S E# F Γ G <span style="font-size: 13.3333339691162px;">α A </span>β B#
C <span style="font-size: 13.3333339691162px;">Δ D</span> S E# F Γ G <span style="font-size: 13.3333339691162px;">α A </span>β B#
| |  
|
|-
|-
| | 7|4
| 7{{pipe}}4
| | 2 1 2 1 2 2 1 2 1 2 2 1
| 2 1 2 1 2 2 1 2 1 2 2 1
| | 0 2 3 5 6 8 10 11 13 14 16 18
| 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 Db D Eb E F Gb G Ab A Bb B#


C <span style="font-size: 13.3333339691162px;">Δ D</span> S E F Γ G <span style="font-size: 13.3333339691162px;">α A </span>β B#
C <span style="font-size: 13.3333339691162px;">Δ D</span> S E F Γ G <span style="font-size: 13.3333339691162px;">α A </span>β B#
| |  
|
|-
|-
| | 6|5
| 6{{pipe}}5
| | 2 1 2 1 2 2 1 2 1 2 1 2
| 2 1 2 1 2 2 1 2 1 2 1 2
| | 0 2 3 5 6 8 10 11 13 14 16 17
| 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 Db D Eb E F Gb G Ab A Bb B


C <span style="font-size: 13.3333339691162px;">Δ D</span> S E F Γ G <span style="font-size: 13.3333339691162px;">α A </span>β B
C <span style="font-size: 13.3333339691162px;">Δ D</span> S E F Γ G <span style="font-size: 13.3333339691162px;">α A </span>β B
| | Yasser's Supradiatonic
| Yasser's Supradiatonic


(<span style="line-height: 1.5;">twelfths of 12-5 chords form C Ionian mode, </span>elevenths of 11-4 chords form C Aeolian mode<span style="line-height: 1.5;">)</span>
(<span style="line-height: 1.5;">twelfths of 12-5 chords form C Ionian mode, </span>elevenths of 11-4 chords form C Aeolian mode<span style="line-height: 1.5;">)</span>
|-
|-
| | 5|6
| 5{{pipe}}6
| | 2 1 2 1 2 1 2 2 1 2 1 2
| 2 1 2 1 2 1 2 2 1 2 1 2
| | 0 2 3 5 6 8 9 11 13 14 16 17
| 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 Db D Eb E F F# G Ab A Bb B


C <span style="font-size: 13.3333339691162px;">Δ D</span> S E F ϕ G <span style="font-size: 13.3333339691162px;">α A </span>β B
C <span style="font-size: 13.3333339691162px;">Δ D</span> S E F ϕ G <span style="font-size: 13.3333339691162px;">α A </span>β B
| | fifths of 12-5 chords form C Ionian mode
| fifths of 12-5 chords form C Ionian mode
|-
|-
| | 4|7
| 4{{pipe}}7
| | 1 2 2 1 2 1 2 2 1 2 1 2
| 1 2 2 1 2 1 2 2 1 2 1 2
| | 0 1 3 5 6 8 9 11 13 14 16 17
| 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 C# D Eb E F F# G Ab A Bb B


C Ç<span style="font-size: 13.3333339691162px; line-height: 1.5;"> D</span><span style="line-height: 1.5;"> S E F ϕ G </span><span style="font-size: 13.3333339691162px; line-height: 1.5;">α A </span><span style="line-height: 1.5;">β B</span>
C Ç<span style="font-size: 13.3333339691162px; line-height: 1.5;"> D</span><span style="line-height: 1.5;"> S E F ϕ G </span><span style="font-size: 13.3333339691162px; line-height: 1.5;">α A </span><span style="line-height: 1.5;">β B</span>
| | octaves of 11-5 chords form C Mixolydian mode
| octaves of 11-5 chords form C Mixolydian mode
|-
|-
| | 3|8
| 3{{pipe}}8
| | 1 2 2 1 2 1 2 1 2 2 1 2
| 1 2 2 1 2 1 2 1 2 2 1 2
| | 0 1 3 5 6 8 9 11 12 14 16 17
| 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 C# D Eb E F F# G G# A Bb B


C Ç<span style="font-size: 13.3333339691162px;"> D</span> S E F ϕ G Z<span style="font-size: 13.3333339691162px;"> A </span>β B
C Ç<span style="font-size: 13.3333339691162px;"> D</span> S E F ϕ G Z<span style="font-size: 13.3333339691162px;"> A </span>β B
| |  
|
|-
|-
| | 2|9
| 2{{pipe}}9
| | 1 2 1 2 2 1 2 1 2 2 1 2
| 1 2 1 2 2 1 2 1 2 2 1 2
| | 0 1 3 4 6 8 9 11 12 14 16 17
| 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 C# D D# E F F# G G# A Bb B


C Ç<span style="font-size: 13.3333339691162px;"> D</span> Þ E F ϕ G Z<span style="font-size: 13.3333339691162px;"> A </span>β B
C Ç<span style="font-size: 13.3333339691162px;"> D</span> Þ E F ϕ G Z<span style="font-size: 13.3333339691162px;"> A </span>β B
| | octaves of 12-5 chords form C Ionian mode
| octaves of 12-5 chords form C Ionian mode
|-
|-
| | 1|10
| 1{{pipe}}10
| | 1 2 1 2 2 1 2 1 2 1 2 2
| 1 2 1 2 2 1 2 1 2 1 2 2
| | 0 1 3 4 6 8 9 11 12 14 15 17
| 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 C# D D# E F F# G G# A A# B


C Ç<span style="font-size: 13.3333339691162px;"> D</span> Þ E F ϕ G Z A<span style="font-size: 13.3333339691162px;"> Æ B</span>
C Ç<span style="font-size: 13.3333339691162px;"> D</span> Þ E F ϕ G Z A<span style="font-size: 13.3333339691162px;"> Æ B</span>
| | roots of 12-5 chords form C Ionian mode
| roots of 12-5 chords form C Ionian mode
|-
|-
| | 0|11
| 0{{pipe}}11
| | 1 2 1 2 1 2 2 1 2 1 2 2
| 1 2 1 2 1 2 2 1 2 1 2 2
| | 0 1 3 4 6 7 9 11 12 14 15 17
| 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 C# D D# E E# F# G G# A A# B


C Ç<span style="font-size: 13.3333339691162px;"> D</span> Þ E Fb ϕ G Z A<span style="font-size: 13.3333339691162px;"> Æ B</span>
C Ç<span style="font-size: 13.3333339691162px;"> D</span> Þ E Fb ϕ G Z A<span style="font-size: 13.3333339691162px;"> Æ B</span>
| |  
|
|}
|}


=== [[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)


{| class="wikitable"
{| class="wikitable"
|-
|-
! | UDP
! UDP
! | steps
! Steps
! | degrees
! Degrees
! | note names
! Note names
! | comments
! Comments
|-
|-
| | 8|0
| 8{{pipe}}0
| | 3 2 2 2 2 2 2 2 2
| 3 2 2 2 2 2 2 2 2
| | 0 3 5 7 9 11 13 15 17
| 0 3 5 7 9 11 13 15 17
| | C D Eb E# F# G Ab A# B
| C D Eb E# F# G Ab A# B
| |  
|
|-
|-
| | 7|1
| 7{{pipe}}1
| | 2 3 2 2 2 2 2 2 2
| 2 3 2 2 2 2 2 2 2
| | 0 2 5 7 9 11 13 15 17
| 0 2 5 7 9 11 13 15 17
| | C Db Eb E# F# G Ab A# B
| C Db Eb E# F# G Ab A# B
| |  
|
|-
|-
| | 6|2
| 6{{pipe}}2
| | 2 2 3 2 2 2 2 2 2
| 2 2 3 2 2 2 2 2 2
| | 0 2 4 7 9 11 13 15 17
| 0 2 4 7 9 11 13 15 17
| | C Db D# E# F# G Ab A# B
| C Db D# E# F# G Ab A# B
| |  
|
|-
|-
| | 5|3
| 5{{pipe}}3
| | 2 2 2 3 2 2 2 2 2
| 2 2 2 3 2 2 2 2 2
| | 0 2 4 6 9 11 13 15 17
| 0 2 4 6 9 11 13 15 17
| | C Db D# E F# G Ab A# B
| C Db D# E F# G Ab A# B
| |  
|
|-
|-
| | 4|4
| 4{{pipe}}4
| | 2 2 2 2 3 2 2 2 2
| 2 2 2 2 3 2 2 2 2
| | 0 2 4 6 8 11 13 15 17
| 0 2 4 6 8 11 13 15 17
| | C Db D# E F G Ab A# B
| C Db D# E F G Ab A# B
| | symmetrical, has both 4/3 and 3/2
| symmetrical, has both 4/3 and 3/2
|-
|-
| | 3|5
| 3{{pipe}}5
| | 2 2 2 2 2 3 2 2 2
| 2 2 2 2 2 3 2 2 2
| | 0 2 4 6 8 10 13 15 17
| 0 2 4 6 8 10 13 15 17
| | C Db D# E F Gb Ab A# B
| C Db D# E F Gb Ab A# B
| |  
|
|-
|-
| | 2|6
| 2{{pipe}}6
| | 2 2 2 2 2 2 3 2 2
| 2 2 2 2 2 2 3 2 2
| | 0 2 4 6 8 10 12 15 17
| 0 2 4 6 8 10 12 15 17
| | C Db D# E F Gb G# A# B
| C Db D# E F Gb G# A# B
| |  
|
|-
|-
| | 1|7
| 1{{pipe}}7
| | 2 2 2 2 2 2 2 3 2
| 2 2 2 2 2 2 2 3 2
| | 0 2 4 6 8 10 12 14 17
| 0 2 4 6 8 10 12 14 17
| | C Db D# E F Gb G# A B
| C Db D# E F Gb G# A B
| |  
|
|-
|-
| | 0|8
| 0{{pipe}}8
| | 2 2 2 2 2 2 2 2 3
| 2 2 2 2 2 2 2 2 3
| | 0 2 4 6 8 10 12 14 16
| 0 2 4 6 8 10 12 14 16
| | C Db D# E F Gb G# A Bb
| C Db D# E F Gb G# A Bb
| |  
|
|}
|}


Line 355: Line 352:
{| class="wikitable"
{| class="wikitable"
|-
|-
! | UDP
! UDP
! | steps
! Steps
! | degrees
! Degrees
! | note names
! Note names
|-
|-
| | 9|0
| 9{{pipe}}0
| | 2 2 2 2 2 2 2 2 2 1
| 2 2 2 2 2 2 2 2 2 1
| | 0 2 4 6 8 10 12 14 16 18
| 0 2 4 6 8 10 12 14 16 18
| | C Db D# E F Gb G# A Bb B#
| C Db D# E F Gb G# A Bb B#
|-
|-
| | 8|1
| 8{{pipe}}1
| | 2 2 2 2 2 2 2 2 1 2
| 2 2 2 2 2 2 2 2 1 2
| | 0 2 4 6 8 10 12 14 16 17
| 0 2 4 6 8 10 12 14 16 17
| | C Db D# E F Gb G# A Bb B
| C Db D# E F Gb G# A Bb B
|-
|-
| | 7|2
| 7{{pipe}}2
| | 2 2 2 2 2 2 2 1 2 2
| 2 2 2 2 2 2 2 1 2 2
| | 0 2 4 6 8 10 12 14 15 17
| 0 2 4 6 8 10 12 14 15 17
| | C Db D# E F Gb G# A A# B
| C Db D# E F Gb G# A A# B
|-
|-
| | 6|3
| 6{{pipe}}3
| | 2 2 2 2 2 2 1 2 2 2
| 2 2 2 2 2 2 1 2 2 2
| | 0 2 4 6 8 10 12 13 15 17
| 0 2 4 6 8 10 12 13 15 17
| | C Db D# E F Gb G# Ab A# B
| C Db D# E F Gb G# Ab A# B
|-
|-
| | 5|4
| 5{{pipe}}4
| | 2 2 2 2 2 1 2 2 2 2
| 2 2 2 2 2 1 2 2 2 2
| | 0 2 4 6 8 10 11 13 15 17
| 0 2 4 6 8 10 11 13 15 17
| | C Db D# E F Gb G Ab A# B
| C Db D# E F Gb G Ab A# B
|-
|-
| | 4|5
| 4{{pipe}}5
| | 2 2 2 2 1 2 2 2 2 2
| 2 2 2 2 1 2 2 2 2 2
| | 0 2 4 6 8 9 11 13 15 17
| 0 2 4 6 8 9 11 13 15 17
| | C Db D# E F F# G Ab A# B
| C Db D# E F F# G Ab A# B
|-
|-
| | 3|6
| 3{{pipe}}6
| | 2 2 2 1 2 2 2 2 2 2
| 2 2 2 1 2 2 2 2 2 2
| | 0 2 4 6 7 9 11 13 15 17
| 0 2 4 6 7 9 11 13 15 17
| | C Db D# E E# F# G Ab A# B
| C Db D# E E# F# G Ab A# B
|-
|-
| | 2|7
| 2{{pipe}}7
| | 2 2 1 2 2 2 2 2 2 2
| 2 2 1 2 2 2 2 2 2 2
| | 0 2 4 5 7 9 11 13 15 17
| 0 2 4 5 7 9 11 13 15 17
| | C Db D# Eb E# F# G Ab A# B
| C Db D# Eb E# F# G Ab A# B
|-
|-
| | 1|8
| 1{{pipe}}8
| | 2 1 2 2 2 2 2 2 2 2
| 2 1 2 2 2 2 2 2 2 2
| | 0 2 3 5 7 9 11 13 15 17
| 0 2 3 5 7 9 11 13 15 17
| | C Db D Eb E# F# G Ab A# B
| C Db D Eb E# F# G Ab A# B
|-
|-
| | 0|9
| 0{{pipe}}9
| | 1 2 2 2 2 2 2 2 2 2
| 1 2 2 2 2 2 2 2 2 2
| | 0 1 3 5 7 9 11 13 15 17
| 0 1 3 5 7 9 11 13 15 17
| | C C# D Eb E# F# G Ab A# B
| C C# D Eb E# F# G Ab A# B
|}
|}


=== [[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)


{| class="wikitable"
{| class="wikitable"
|-
|-
! | UDP
! UDP
! | steps
! Steps
! | degrees
! Degrees
! | note names
! Note names
|-
|-
| | 5|0
| 5{{pipe}}0
| | 4 3 3 3 3 3
| 4 3 3 3 3 3
| | 0 4 7 10 13 16
| 0 4 7 10 13 16
| | C D# E# Gb Ab Bb
| C D# E# Gb Ab Bb
|-
|-
| | 4|1
| 4{{pipe}}1
| | 3 4 3 3 3 3
| 3 4 3 3 3 3
| | 0 3 7 10 13 16
| 0 3 7 10 13 16
| | C D E# Gb Ab Bb
| C D E# Gb Ab Bb
|-
|-
| | 3|2
| 3{{pipe}}2
| | 3 3 4 3 3 3
| 3 3 4 3 3 3
| | 0 3 6 10 13 16
| 0 3 6 10 13 16
| | C D E Gb Ab Bb
| C D E Gb Ab Bb
|-
|-
| | 2|3
| 2{{pipe}}3
| | 3 3 3 4 3 3
| 3 3 3 4 3 3
| | 0 3 6 9 13 16
| 0 3 6 9 13 16
| | C D E F# Ab Bb
| C D E F# Ab Bb
|-
|-
| | 1|4
| 1{{pipe}}4
| | 3 3 3 3 4 3
| 3 3 3 3 4 3
| | 0 3 6 9 12 16
| 0 3 6 9 12 16
| | C D E F# G# Bb
| C D E F# G# Bb
|-
|-
| | 0|5
| 0{{pipe}}5
| | 3 3 3 3 3 4
| 3 3 3 3 3 4
| | 0 3 6 9 12 15
| 0 3 6 9 12 15
| | C D E F# G# A#
| C D E F# G# A#
|}
|}


Line 457: Line 453:
{| class="wikitable"
{| class="wikitable"
|-
|-
! | UDP
! UDP
! | steps
! Steps
! | degrees
! Degrees
! | note names
! Note names
|-
|-
| | 6|0
| 6{{pipe}}0
| | 3 3 3 3 3 3 1
| 3 3 3 3 3 3 1
| | 0 3 6 9 12 15 18
| 0 3 6 9 12 15 18
| | C D E F# G# A# B#
| C D E F# G# A# B#
|-
|-
| | 5|1
| 5{{pipe}}1
| | 3 3 3 3 3 1 3
| 3 3 3 3 3 1 3
| | 0 3 6 9 12 15 16
| 0 3 6 9 12 15 16
| | C D E F# G# A# Bb
| C D E F# G# A# Bb
|-
|-
| | 4|2
| 4{{pipe}}2
| | 3 3 3 3 1 3 3
| 3 3 3 3 1 3 3
| | 0 3 6 9 12 13 16
| 0 3 6 9 12 13 16
| | C D E F# G# Ab Bb
| C D E F# G# Ab Bb
|-
|-
| | 3|3
| 3{{pipe}}3
| | 3 3 3 1 3 3 3
| 3 3 3 1 3 3 3
| | 0 3 6 9 10 13 16
| 0 3 6 9 10 13 16
| | C D E F# Gb Ab Bb
| C D E F# Gb Ab Bb
|-
|-
| | 2|4
| 2{{pipe}}4
| | 3 3 1 3 3 3 3
| 3 3 1 3 3 3 3
| | 0 3 6 7 10 13 16
| 0 3 6 7 10 13 16
| | C D E E# Gb Ab Bb
| C D E E# Gb Ab Bb
|-
|-
| | 1|5
| 1{{pipe}}5
| | 3 1 3 3 3 3 3
| 3 1 3 3 3 3 3
| | 0 3 4 7 10 13 16
| 0 3 4 7 10 13 16
| | C D D# E# Gb Ab Bb
| C D D# E# Gb Ab Bb
|-
|-
| | 0|6
| 0{{pipe}}6
| | 1 3 3 3 3 3 3
| 1 3 3 3 3 3 3
| | 0 1 4 7 10 13 16
| 0 1 4 7 10 13 16
| | C C# D# E# Gb Ab Bb
| C C# D# E# Gb Ab Bb
|}
|}


Line 502: Line 498:
{| class="wikitable"
{| class="wikitable"
|-
|-
! | UDP
! UDP
! | steps
! Steps
! | degrees
! Degrees
! | note names
! Note names
|-
|-
| | 12|0
| 12{{pipe}}0
| | 2 1 2 1 2 1 2 1 2 1 2 1 1
| 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
| 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#
| C Db D Eb E F F# G G# A A# B B#
|-
|-
| | 11|1
| 11{{pipe}}1
| | 2 1 2 1 2 1 2 1 2 1 1 2 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
| 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#
| C Db D Eb E F F# G G# A A# Bb B#
|-
|-
| | 10|2
| 10{{pipe}}2
| | 2 1 2 1 2 1 2 1 1 2 1 2 1
| 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
| 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#
| C Db D Eb E F F# G G# Ab A# Bb B#
|-
|-
| | 9|3
| 9{{pipe}}3
| | 2 1 2 1 2 1 1 2 1 2 1 2 1
| 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
| 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#
| C Db D Eb E F F# Gb G# Ab A# Bb B#
|-
|-
| | 8|4
| 8{{pipe}}4
| | 2 1 2 1 1 2 1 2 1 2 1 2 1
| 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
| 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#
| C Db D Eb E E# F# Gb G# Ab A# Bb B#
|-
|-
| | 7|5
| 7{{pipe}}5
| | 2 1 1 2 1 2 1 2 1 2 1 2 1
| 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
| 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#
| C Db D D# E E# F# Gb G# Ab A# Bb B#
|-
|-
| | 6|6
| 6{{pipe}}6
| | 1 2 1 2 1 2 1 2 1 2 1 2 1
| 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
| 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#
| C C# D D# E E# F# Gb G# Ab A# Bb B#
|-
|-
| | 5|7
| 5{{pipe}}7
| | 1 2 1 2 1 2 1 2 1 2 1 1 2
| 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
| 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
| C C# D D# E E# F# Gb G# Ab A# Bb B
|-
|-
| | 4|8
| 4{{pipe}}8
| | 1 2 1 2 1 2 1 2 1 1 2 1 2
| 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
| 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
| C C# D D# E E# F# Gb G# Ab A Bb B
|-
|-
| | 3|9
| 3{{pipe}}9
| | 1 2 1 2 1 2 1 1 2 1 2 1 2
| 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
| 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
| C C# D D# E E# F# Gb G Ab A Bb B
|-
|-
| | 2|10
| 2{{pipe}}10
| | 1 2 1 2 1 1 2 1 2 1 2 1 2
| 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
| 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
| C C# D D# E E# F Gb G Ab A Bb B
|-
|-
| | 1|11
| 1{{pipe}}11
| | 1 2 1 1 2 1 2 1 2 1 2 1 2
| 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
| 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
| C C# D D# Eb E# F Gb G Ab A Bb B
|-
|-
| | 0|12
| 0{{pipe}}12
| | 1 1 2 1 2 1 2 1 2 1 2 1 2
| 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
| 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
| C C# Db D# Eb E# F Gb G Ab A Bb B
|}
|}


=== [[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)


{| class="wikitable"
{| class="wikitable"
|-
|-
! | UDP
! UDP
! | mode steps
! Mode steps
! | mode degrees
! Mode degrees
! | note names
! Note names
|-
|-
| | 4|0
| 4{{pipe}}0
| | 4 4 4 4 3
| 4 4 4 4 3
| | 0 4 8 12 16
| 0 4 8 12 16
| | C D# F G# Bb
| C D# F G# Bb
|-
|-
| | 3|1
| 3{{pipe}}1
| | 4 4 4 3 4
| 4 4 4 3 4
| | 0 4 8 12 15
| 0 4 8 12 15
| | C D# F G# A#
| C D# F G# A#
|-
|-
| | 2|2
| 2{{pipe}}2
| | 4 4 3 4 4
| 4 4 3 4 4
| | 0 4 8 11 15
| 0 4 8 11 15
| | C D# F G A#
| C D# F G A#
|-
|-
| | 1|3
| 1{{pipe}}3
| | 4 3 4 4 4
| 4 3 4 4 4
| | 0 4 7 11 15
| 0 4 7 11 15
| | C D# E# G A#
| C D# E# G A#
|-
|-
| | 0|4
| 0{{pipe}}4
| | 3 4 4 4 4
| 3 4 4 4 4
| | 0 3 7 11 15
| 0 3 7 11 15
| | C D E# G A#
| C D E# G A#
|}
|}


Line 614: Line 609:
{| class="wikitable"
{| class="wikitable"
|-
|-
! | UDP
! UDP
! | mode steps
! Mode steps
! | mode degrees
! Mode degrees
! | note names
! Note names
|-
|-
| | 8|0
| 8{{pipe}}0
| | 3 3 1 3 1 3 1 3 1
| 3 3 1 3 1 3 1 3 1
| | 0 3 6 7 10 11 14 15 18
| 0 3 6 7 10 11 14 15 18
| | C D E E# Gb G A A# B#
| C D E E# Gb G A A# B#
|-
|-
| | 7|1
| 7{{pipe}}1
| | 3 1 3 3 1 3 1 3 1
| 3 1 3 3 1 3 1 3 1
| | 0 3 4 7 10 11 14 15 18
| 0 3 4 7 10 11 14 15 18
| | C D D# E# Gb G A A# B#
| C D D# E# Gb G A A# B#
|-
|-
| | 6|2
| 6{{pipe}}2
| | 3 1 3 1 3 3 1 3 1
| 3 1 3 1 3 3 1 3 1
| | 0 3 4 7 8 11 14 15 18
| 0 3 4 7 8 11 14 15 18
| | C D D# E# F G A A# B#
| C D D# E# F G A A# B#
|-
|-
| | 5|3
| 5{{pipe}}3
| | 3 1 3 1 3 1 3 3 1
| 3 1 3 1 3 1 3 3 1
| | 0 3 4 7 8 11 12 15 18
| 0 3 4 7 8 11 12 15 18
| | C D D# E# F G G# A# B#
| C D D# E# F G G# A# B#
|-
|-
| | 4|4
| 4{{pipe}}4
| | 3 1 3 1 3 1 3 1 3
| 3 1 3 1 3 1 3 1 3
| | 0 3 4 7 8 11 12 15 16
| 0 3 4 7 8 11 12 15 16
| | C D D# E# F G G# A# Bb
| C D D# E# F G G# A# Bb
|-
|-
| | 3|5
| 3{{pipe}}5
| | 1 3 3 1 3 1 3 1 3
| 1 3 3 1 3 1 3 1 3
| | 0 1 4 7 8 11 12 15 16
| 0 1 4 7 8 11 12 15 16
| | C C# D# E# F G G# A# Bb
| C C# D# E# F G G# A# Bb
|-
|-
| | 2|6
| 2{{pipe}}6
| | 1 3 1 3 3 1 3 1 3
| 1 3 1 3 3 1 3 1 3
| | 0 1 4 5 8 11 12 15 16
| 0 1 4 5 8 11 12 15 16
| | C C# D# Eb F G G# A# Bb
| C C# D# Eb F G G# A# Bb
|-
|-
| | 1|7
| 1{{pipe}}7
| | 1 3 1 3 1 3 3 1 3
| 1 3 1 3 1 3 3 1 3
| | 0 1 4 5 8 9 12 15 16
| 0 1 4 5 8 9 12 15 16
| | C C# D# Eb F F# G# A# Bb
| C C# D# Eb F F# G# A# Bb
|-
|-
| | 0|8
| 0{{pipe}}8
| | 1 3 1 3 1 3 1 3 3
| 1 3 1 3 1 3 1 3 3
| | 0 1 4 5 8 9 12 13 16
| 0 1 4 5 8 9 12 13 16
| | C C# D# Eb F F# G# Ab Bb
| C C# D# Eb F F# G# Ab Bb
|}
|}


Line 669: Line 664:
{| class="wikitable"
{| class="wikitable"
|-
|-
! | UDP
! UDP
! | steps
! Steps
! | degrees
! Degrees
! | note names
! Note names
|-
|-
| | 13|0
| 13{{pipe}}0
| | 2 1 2 1 1 2 1 1 2 1 1 2 1 1
| 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
| 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#
| C Db D Eb E E# F# Gb G Ab A A# B B#
|-
|-
| | 12|1
| 12{{pipe}}1
| | 2 1 1 2 1 2 1 1 2 1 1 2 1 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
| 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#
| C Db D D# E E# F# Gb G Ab A A# B B#
|-
|-
| | 11|2
| 11{{pipe}}2
| | 2 1 1 2 1 1 2 1 2 1 1 2 1 1
| 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
| 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#
| C Db D D# E E# F Gb G Ab A A# B B#
|-
|-
| | 10|3
| 10{{pipe}}3
| | 2 1 1 2 1 1 2 1 1 2 1 2 1 1
| 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
| 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#
| C Db D D# E E# F Gb G G# A A# B B#
|-
|-
| | 9|4
| 9{{pipe}}4
| | 2 1 1 2 1 1 2 1 1 2 1 1 2 1
| 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
| 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#
| C Db D D# E E# F Gb G G# A A# Bb B#
|-
|-
| | 8|5
| 8{{pipe}}5
| | 1 2 1 2 1 1 2 1 1 2 1 1 2 1
| 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
| 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#
| C C# D D# E E# F Gb G G# A A# Bb B#
|-
|-
| | 7|6
| 7{{pipe}}6
| | 1 2 1 1 2 1 2 1 1 2 1 1 2 1
| 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
| 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#
| C C# D D# Eb E# F Gb G G# A A# Bb B#
|-
|-
| | 6|7
| 6{{pipe}}7
| | 1 2 1 1 2 1 1 2 1 2 1 1 2 1
| 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
| 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#
| C C# D D# Eb E# F F# G G# A A# Bb B#
|-
|-
| | 5|8
| 5{{pipe}}8
| | 1 2 1 1 2 1 1 2 1 1 2 1 2 1
| 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
| 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#
| C C# D D# Eb E# F F# G G# Ab A# Bb B#
|-
|-
| | 4|9
| 4{{pipe}}9
| | 1 2 1 1 2 1 1 2 1 1 2 1 1 2
| 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
| 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
| C C# D D# Eb E# F F# G G# Ab A# Bb B
|-
|-
| | 3|10
| 3{{pipe}}10
| | 1 1 2 1 2 1 1 2 1 1 2 1 1 2
| 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
| 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
| C C# Db D# Eb E# F F# G G# Ab A# Bb B
|-
|-
| | 2|11
| 2{{pipe}}11
| | 1 1 2 1 1 2 1 2 1 1 2 1 1 2
| 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
| 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
| C C# Db D# Eb E F F# G G# Ab A# Bb B
|-
|-
| | 1|12
| 1{{pipe}}12
| | 1 1 2 1 1 2 1 1 2 1 2 1 1 2
| 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
| 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
| C C# Db D# Eb E F F# Gb G# Ab A# Bb B
|-
|-
| | 0|13
| 0{{pipe}}13
| | 1 1 2 1 1 2 1 1 2 1 1 2 1 2
| 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
| 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
| C C# Db D# Eb E F F# Gb G# Ab A Bb B
|}
|}


=== [[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)


{| class="wikitable"
{| class="wikitable"
|-
|-
! | UDP
! UDP
! | steps
! Steps
! | degrees
! Degrees
! | note names
! Note names
! | comments
! Comments
|-
|-
| | 6|0
| 6{{pipe}}0
| | 4 4 1 4 1 4 1
| 4 4 1 4 1 4 1
| | 0 4 8 9 13 14 18
| 0 4 8 9 13 14 18
| | C D# F F# Ab A B#
| C D# F F# Ab A B#
| | has 4/3
| has 4/3
|-
|-
| | 5|1
| 5{{pipe}}1
| | 4 1 4 4 1 4 1
| 4 1 4 4 1 4 1
| | 0 4 5 9 13 14 18
| 0 4 5 9 13 14 18
| | C D# Eb F# Ab A B#
| C D# Eb F# Ab A B#
| |  
|
|-
|-
| | 4|2
| 4{{pipe}}2
| | 4 1 4 1 4 4 1
| 4 1 4 1 4 4 1
| | 0 4 5 9 10 14 18
| 0 4 5 9 10 14 18
| | C D# Eb F# Gb A B#
| C D# Eb F# Gb A B#
| |  
|
|-
|-
| | 3|3
| 3{{pipe}}3
| | 4 1 4 1 4 1 4
| 4 1 4 1 4 1 4
| | 0 4 5 9 10 14 15
| 0 4 5 9 10 14 15
| | C D# Eb F# Gb A A#
| C D# Eb F# Gb A A#
| | symmetrical
| symmetrical
|-
|-
| | 2|4
| 2{{pipe}}4
| | 1 4 4 1 4 1 4
| 1 4 4 1 4 1 4
| | 0 1 5 9 10 14 15
| 0 1 5 9 10 14 15
| | C C# Eb F# Gb A A#
| C C# Eb F# Gb A A#
| |  
|
|-
|-
| | 1|5
| 1{{pipe}}5
| | 1 4 1 4 4 1 4
| 1 4 1 4 4 1 4
| | 0 1 5 6 10 14 15
| 0 1 5 6 10 14 15
| | C C# Eb E Gb A A#
| C C# Eb E Gb A A#
| |  
|
|-
|-
| | 0|6
| 0{{pipe}}6
| | 1 4 1 4 1 4 4
| 1 4 1 4 1 4 4
| | 0 1 5 6 10 11 15
| 0 1 5 6 10 11 15
| | C C# Eb E Gb G A#
| C C# Eb E Gb G A#
| | has 3/2
| has 3/2
|}
|}


Line 804: Line 798:
{| class="wikitable"
{| class="wikitable"
|-
|-
! | UDP
! UDP
! | steps
! Steps
! | degrees
! Degrees
! | note names
! Note names
! | comments
! Comments
|-
|-
| | 10|0
| 10{{pipe}}0
| | 3 1 3 1 1 3 1 1 3 1 1
| 3 1 3 1 1 3 1 1 3 1 1
| | 0 3 4 7 8 9 12 13 14 17 18
| 0 3 4 7 8 9 12 13 14 17 18
| | C D D# E# F F# G# Ab A B B#
| C D D# E# F F# G# Ab A B B#
| |  
|
|-
|-
| | 9|1
| 9{{pipe}}1
| | 3 1 1 3 1 3 1 1 3 1 1
| 3 1 1 3 1 3 1 1 3 1 1
| | 0 3 4 5 8 9 12 13 14 17 18
| 0 3 4 5 8 9 12 13 14 17 18
| | C D D# Eb F F# G# Ab A B B#
| C D D# Eb F F# G# Ab A B B#
| |  
|
|-
|-
| | 8|2
| 8{{pipe}}2
| | 3 1 1 3 1 1 3 1 3 1 1
| 3 1 1 3 1 1 3 1 3 1 1
| | 0 3 4 5 8 9 10 13 14 17 18
| 0 3 4 5 8 9 10 13 14 17 18
| | C D D# Eb F F# Gb Ab A B B#
| C D D# Eb F F# Gb Ab A B B#
| |  
|
|-
|-
| | 7|3
| 7{{pipe}}3
| | 3 1 1 3 1 1 3 1 1 3 1
| 3 1 1 3 1 1 3 1 1 3 1
| | 0 3 4 5 8 9 10 13 14 15 18
| 0 3 4 5 8 9 10 13 14 15 18
| | C D D# Eb F F# Gb Ab A A# B#
| C D D# Eb F F# Gb Ab A A# B#
| |  
|
|-
|-
| | 6|4
| 6{{pipe}}4
| | 1 3 1 3 1 1 3 1 1 3 1
| 1 3 1 3 1 1 3 1 1 3 1
| | 0 1 4 5 8 9 10 13 14 15 18
| 0 1 4 5 8 9 10 13 14 15 18
| | C C# D# Eb F F# Gb Ab A A# B#
| C C# D# Eb F F# Gb Ab A A# B#
| |  
|
|-
|-
| | 5|5
| 5{{pipe}}5
| | 1 3 1 1 3 1 3 1 1 3 1
| 1 3 1 1 3 1 3 1 1 3 1
| | 0 1 4 5 6 9 10 13 14 15 18
| 0 1 4 5 6 9 10 13 14 15 18
| | C C# D# Eb E F# Gb Ab A A# B#
| C C# D# Eb E F# Gb Ab A A# B#
| | symmetrical, has neither 4/3 nor 3/2
| symmetrical, has neither 4/3 nor 3/2
|-
|-
| | 4|6
| 4{{pipe}}6
| | 1 3 1 1 3 1 1 3 1 3 1
| 1 3 1 1 3 1 1 3 1 3 1
| | 0 1 4 5 6 9 10 11 14 15 18
| 0 1 4 5 6 9 10 11 14 15 18
| | C C# D# Eb E F# Gb G A A# B#
| C C# D# Eb E F# Gb G A A# B#
| |  
|
|-
|-
| | 3|7
| 3{{pipe}}7
| | 1 3 1 1 3 1 1 3 1 1 3
| 1 3 1 1 3 1 1 3 1 1 3
| | 0 1 4 5 6 9 10 11 14 15 16
| 0 1 4 5 6 9 10 11 14 15 16
| | C C# D# Eb E F# Gb G A A# Bb
| C C# D# Eb E F# Gb G A A# Bb
| |  
|
|-
|-
| | 2|8
| 2{{pipe}}8
| | 1 1 3 1 3 1 1 3 1 1 3
| 1 1 3 1 3 1 1 3 1 1 3
| | 0 1 2 5 6 9 10 11 14 15 16
| 0 1 2 5 6 9 10 11 14 15 16
| | C C# Db Eb E F# Gb G A A# Bb
| C C# Db Eb E F# Gb G A A# Bb
| |  
|
|-
|-
| | 1|9
| 1{{pipe}}9
| | 1 1 3 1 1 3 1 3 1 1 3
| 1 1 3 1 1 3 1 3 1 1 3
| | 0 1 2 5 6 7 10 11 14 15 16
| 0 1 2 5 6 7 10 11 14 15 16
| | C C# Db Eb E E# Gb G A A# Bb
| C C# Db Eb E E# Gb G A A# Bb
| |  
|
|-
|-
| | 0|10
| 0{{pipe}}10
| | 1 1 3 1 1 3 1 1 3 1 3
| 1 1 3 1 1 3 1 1 3 1 3
| | 0 1 2 5 6 7 10 11 12 15 16
| 0 1 2 5 6 7 10 11 12 15 16
| | C C# Db Eb E E# Gb G G# A# Bb
| C C# Db Eb E E# Gb G G# A# Bb
| |  
|
|}
|}


Line 881: Line 875:
{| class="wikitable"
{| class="wikitable"
|-
|-
! | UDP
! UDP
! | steps
! Steps
! | degrees
! Degrees
! | note names
! Note names
|-
|-
| | 14|0
| 14{{pipe}}0
| | 2 1 1 2 1 1 1 2 1 1 1 2 1 1 1
| 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
| 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#
| C Db D D# E E# F F# G G# Ab A Bb B B#
|-
|-
| | 13|1
| 13{{pipe}}1
| | 2 1 1 1 2 1 1 2 1 1 1 2 1 1 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
| 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#
| C Db D D# Eb E# F F# G G# Ab A Bb B B#
|-
|-
| | 12|2
| 12{{pipe}}2
| | 2 1 1 1 2 1 1 1 2 1 1 2 1 1 1
| 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
| 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#
| C Db D D# Eb E# F F# Gb G# Ab A Bb B B#
|-
|-
| | 11|3
| 11{{pipe}}3
| | 2 1 1 1 2 1 1 1 2 1 1 1 2 1 1
| 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
| 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#
| C Db D D# Eb E# F F# Gb G# Ab A A# B B#
|-
|-
| | 10|4
| 10{{pipe}}4
| | 1 2 1 1 2 1 1 1 2 1 1 1 2 1 1
| 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
| 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#
| C C# D D# Eb E# F F# Gb G# Ab A A# B B#
|-
|-
| | 9|5
| 9{{pipe}}5
| | 1 2 1 1 1 2 1 1 2 1 1 1 2 1 1
| 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
| 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#
| C C# D D# Eb E F F# Gb G# Ab A A# B B#
|-
|-
| | 8|6
| 8{{pipe}}6
| | 1 2 1 1 1 2 1 1 1 2 1 1 2 1 1
| 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
| 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#
| C C# D D# Eb E F F# Gb G Ab A A# B B#
|-
|-
| | 7|7
| 7{{pipe}}7
| | 1 2 1 1 1 2 1 1 1 2 1 1 1 2 1
| 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
| 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#
| C C# D D# Eb E F F# Gb G Ab A A# Bb B#
|-
|-
| | 6|8
| 6{{pipe}}8
| | 1 1 2 1 1 2 1 1 1 2 1 1 1 2 1
| 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
| 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#
| C C# Db D# Eb E F F# Gb G Ab A A# Bb B#
|-
|-
| | 5|9
| 5{{pipe}}9
| | 1 1 2 1 1 1 2 1 1 2 1 1 1 2 1
| 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
| 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#
| C C# Db D# Eb E E# F# Gb G Ab A A# Bb B#
|-
|-
| | 4|10
| 4{{pipe}}10
| | 1 1 2 1 1 1 2 1 1 1 2 1 1 2 1
| 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
| 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#
| C C# Db D# Eb E E# F# Gb G G# A A# Bb B#
|-
|-
| | 3|11
| 3{{pipe}}11
| | 1 1 2 1 1 1 2 1 1 1 2 1 1 1 2
| 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
| 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
| C C# Db D# Eb E E# F# Gb G G# A A# Bb B
|-
|-
| | 2|12
| 2{{pipe}}12
| | 1 1 1 2 1 1 2 1 1 1 2 1 1 1 2
| 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
| 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
| C C# Db D Eb E E# F# Gb G G# A A# Bb B
|-
|-
| | 1|13
| 1{{pipe}}13
| | 1 1 1 2 1 1 1 2 1 1 2 1 1 1 2
| 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
| 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
| C C# Db D Eb E E# F Gb G G# A A# Bb B
|-
|-
| | 0|14
| 0{{pipe}}14
| | 1 1 1 2 1 1 1 2 1 1 1 2 1 1 2
| 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
| 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
| C C# Db D Eb E E# F Gb G G# Ab A# Bb B
|}
|}


=== [[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)


{| class="wikitable"
{| class="wikitable"
|-
|-
! | UDP
! UDP
! | steps
! Steps
! | degrees
! Degrees
! | note names
! Note names
|-
|-
| | 6|0
| 6{{pipe}}0
| | 5 1 5 1 5 1 1
| 5 1 5 1 5 1 1
| | 0 5 6 11 12 17 18
| 0 5 6 11 12 17 18
| | C Eb E G G# B B#
| C Eb E G G# B B#
|-
|-
| | 5|1
| 5{{pipe}}1
| | 5 1 5 1 1 5 1
| 5 1 5 1 1 5 1
| | 0 5 6 11 12 13 18
| 0 5 6 11 12 13 18
| | C Eb E G G# Ab B#
| C Eb E G G# Ab B#
|-
|-
| | 4|2
| 4{{pipe}}2
| | 5 1 1 5 1 5 1
| 5 1 1 5 1 5 1
| | 0 5 6 7 12 13 18
| 0 5 6 7 12 13 18
| | C Eb E E# G# Ab B#
| C Eb E E# G# Ab B#
|-
|-
| | 3|3
| 3{{pipe}}3
| | 1 5 1 5 1 5 1
| 1 5 1 5 1 5 1
| | 0 1 6 7 12 13 18
| 0 1 6 7 12 13 18
| | C C# E E# G# Ab B#
| C C# E E# G# Ab B#
|-
|-
| | 2|4
| 2{{pipe}}4
| | 1 5 1 5 1 1 5
| 1 5 1 5 1 1 5
| | 0 1 6 7 12 13 14
| 0 1 6 7 12 13 14
| | C C# E E# G# Ab A
| C C# E E# G# Ab A
|-
|-
| | 1|5
| 1{{pipe}}5
| | 1 5 1 1 5 1 5
| 1 5 1 1 5 1 5
| | 0 1 6 7 8 13 14
| 0 1 6 7 8 13 14
| | C C# E E# F Ab A
| C C# E E# F Ab A
|-
|-
| | 0|6
| 0{{pipe}}6
| | 1 1 5 1 5 1 5
| 1 1 5 1 5 1 5
| | 0 1 2 7 8 13 14
| 0 1 2 7 8 13 14
| | C C# Db E# F Ab A
| C C# Db E# F Ab A
|}
|}


Line 1,013: Line 1,006:
{| class="wikitable"
{| class="wikitable"
|-
|-
! | UDP
! UDP
! | steps
! Steps
! | degrees
! Degrees
! | note names
! Note names
|-
|-
| | 9|0
| 9{{pipe}}0
| | 4 1 1 4 1 1 4 1 1 1
| 4 1 1 4 1 1 4 1 1 1
| | 0 4 5 6 10 11 12 16 17 18
| 0 4 5 6 10 11 12 16 17 18
| | C D# Eb E Gb G G# Bb B B#
| C D# Eb E Gb G G# Bb B B#
|-
|-
| | 8|1
| 8{{pipe}}1
| | 4 1 1 4 1 1 1 4 1 1
| 4 1 1 4 1 1 1 4 1 1
| | 0 4 5 6 10 11 12 13 17 18
| 0 4 5 6 10 11 12 13 17 18
| | C D# Eb E Gb G G# Ab B B#
| C D# Eb E Gb G G# Ab B B#
|-
|-
| | 7|2
| 7{{pipe}}2
| | 4 1 1 1 4 1 1 4 1 1
| 4 1 1 1 4 1 1 4 1 1
| | 0 4 5 6 7 11 12 13 17 18
| 0 4 5 6 7 11 12 13 17 18
| | C D# Eb E E# G G# Ab B B#
| C D# Eb E E# G G# Ab B B#
|-
|-
| | 6|3
| 6{{pipe}}3
| | 1 4 1 1 4 1 1 4 1 1
| 1 4 1 1 4 1 1 4 1 1
| | 0 1 5 6 7 11 12 13 17 18
| 0 1 5 6 7 11 12 13 17 18
| | C C# Eb E E# G G# Ab B B#
| C C# Eb E E# G G# Ab B B#
|-
|-
| | 5|4
| 5{{pipe}}4
| | 1 4 1 1 4 1 1 1 4 1
| 1 4 1 1 4 1 1 1 4 1
| | 0 1 5 6 7 11 12 13 14 18
| 0 1 5 6 7 11 12 13 14 18
| | C C# Eb E E# G G# Ab A B#
| C C# Eb E E# G G# Ab A B#
|-
|-
| | 4|5
| 4{{pipe}}5
| | 1 4 1 1 1 4 1 1 4 1
| 1 4 1 1 1 4 1 1 4 1
| | 0 1 5 6 7 8 12 13 14 18
| 0 1 5 6 7 8 12 13 14 18
| | C C# Eb E E# F G# Ab A B#
| C C# Eb E E# F G# Ab A B#
|-
|-
| | 3|6
| 3{{pipe}}6
| | 1 1 4 1 1 4 1 1 4 1
| 1 1 4 1 1 4 1 1 4 1
| | 0 1 2 6 7 8 12 13 14 18
| 0 1 2 6 7 8 12 13 14 18
| | C C# Db E E# F G# Ab A B#
| C C# Db E E# F G# Ab A B#
|-
|-
| | 2|7
| 2{{pipe}}7
| | 1 1 4 1 1 4 1 1 1 4
| 1 1 4 1 1 4 1 1 1 4
| | 0 1 2 6 7 8 12 13 14 15
| 0 1 2 6 7 8 12 13 14 15
| | C C# Db E E# F G# Ab A A#
| C C# Db E E# F G# Ab A A#
|-
|-
| | 1|8
| 1{{pipe}}8
| | 1 1 4 1 1 1 4 1 1 4
| 1 1 4 1 1 1 4 1 1 4
| | 0 1 2 6 7 8 9 13 14 15
| 0 1 2 6 7 8 9 13 14 15
| | C C# Db E E# F F# Ab A A#
| C C# Db E E# F F# Ab A A#
|-
|-
| | 0|9
| 0{{pipe}}9
| | 1 1 1 4 1 1 4 1 1 4
| 1 1 1 4 1 1 4 1 1 4
| | 0 1 2 3 7 8 9 13 14 15
| 0 1 2 3 7 8 9 13 14 15
| | C C# Db D E# F F# Ab A A#
| C C# Db D E# F F# Ab A A#
|}
|}


Line 1,073: Line 1,066:
{| class="wikitable"
{| class="wikitable"
|-
|-
! | UDP
! UDP
! | steps
! Steps
! | degrees
! Degrees
! | note names
! Note names
|-
|-
| | 12|0
| 12{{pipe}}0
| | 3 1 1 1 3 1 1 1 3 1 1 1 1
| 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
| 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#
| C D D# Eb E F# Gb G G# A# Bb B B#
|-
|-
| | 11|1
| 11{{pipe}}1
| | 3 1 1 1 3 1 1 1 1 3 1 1 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
| 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#
| C D D# Eb E F# Gb G G# Ab Bb B B#
|-
|-
| | 10|2
| 10{{pipe}}2
| | 3 1 1 1 1 3 1 1 1 3 1 1 1
| 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
| 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#
| C D D# Eb E E# Gb G G# Ab Bb B B#
|-
|-
| | 9|3
| 9{{pipe}}3
| | 1 3 1 1 1 3 1 1 1 3 1 1 1
| 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
| 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#
| C C# D# Eb E E# Gb G G# Ab Bb B B#
|-
|-
| | 8|4
| 8{{pipe}}4
| | 1 3 1 1 1 3 1 1 1 1 3 1 1
| 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
| 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#
| C C# D# Eb E E# Gb G G# Ab A B B#
|-
|-
| | 7|5
| 7{{pipe}}5
| | 1 3 1 1 1 1 3 1 1 1 3 1 1
| 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
| 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#
| C C# D# Eb E E# F G G# Ab A B B#
|-
|-
| | 6|6
| 6{{pipe}}6
| | 1 1 3 1 1 1 3 1 1 1 3 1 1
| 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
| 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#
| C C# Db Eb E E# F G G# Ab A B B#
|-
|-
| | 5|7
| 5{{pipe}}7
| | 1 1 3 1 1 1 3 1 1 1 1 3 1
| 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
| 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#
| C C# Db Eb E E# F G G# Ab A A# B#
|-
|-
| | 4|8
| 4{{pipe}}8
| | 1 1 3 1 1 1 1 3 1 1 1 3 1
| 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
| 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#
| C C# Db Eb E E# F F# G# Ab A A# B#
|-
|-
| | 3|9
| 3{{pipe}}9
| | 1 1 1 3 1 1 1 3 1 1 1 3 1
| 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
| 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#
| C C# Db D E E# F F# G# Ab A A# B#
|-
|-
| | 2|10
| 2{{pipe}}10
| | 1 1 1 3 1 1 1 3 1 1 1 1 3
| 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
| 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
| C C# Db D E E# F F# G# Ab A A# Bb
|-
|-
| | 1|11
| 1{{pipe}}11
| | 1 1 1 3 1 1 1 1 3 1 1 1 3
| 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
| 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
| C C# Db D E E# F F# Gb Ab A A# Bb
|-
|-
| | 0|12
| 0{{pipe}}12
| | 1 1 1 1 3 1 1 1 3 1 1 1 3
| 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
| 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
| C C# Db D D# E# F F# Gb Ab A A# Bb
|}
|}


Line 1,148: Line 1,141:
{| class="wikitable"
{| class="wikitable"
|-
|-
! | UDP
! UDP
! | steps
! Steps
! | degrees
! Degrees
! | note names
! Note names
|-
|-
| | 15|0
| 15{{pipe}}0
| | 2 1 1 1 1 2 1 1 1 1 2 1 1 1 1 1
| 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
| 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#
| C Db D D# Eb E F F# Gb G G# A A# Bb B B#
|-
|-
| | 14|1
| 14{{pipe}}1
| | 2 1 1 1 1 2 1 1 1 1 1 2 1 1 1 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
| 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#
| C Db D D# Eb E F F# Gb G G# Ab A# Bb B B#
|-
|-
| | 13|2
| 13{{pipe}}2
| | 2 1 1 1 1 1 2 1 1 1 1 2 1 1 1 1
| 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
| 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#
| C Db D D# Eb E E# F# Gb G G# Ab A# Bb B B#
|-
|-
| | 12|3
| 12{{pipe}}3
| | 1 2 1 1 1 1 2 1 1 1 1 2 1 1 1 1
| 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
| 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#
| C C# D D# Eb E E# F# Gb G G# Ab A# Bb B B#
|-
|-
| | 11|4
| 11{{pipe}}4
| | 1 2 1 1 1 1 2 1 1 1 1 1 2 1 1 1
| 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
| 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#
| C C# D D# Eb E E# F# Gb G G# Ab A Bb B B#
|-
|-
| | 10|5
| 10{{pipe}}5
| | 1 2 1 1 1 1 1 2 1 1 1 1 2 1 1 1
| 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
| 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#
| C C# D D# Eb E E# F Gb G G# Ab A Bb B B#
|-
|-
| | 9|6
| 9{{pipe}}6
| | 1 1 2 1 1 1 1 2 1 1 1 1 2 1 1 1
| 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
| 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#
| C C# Db D# Eb E E# F Gb G G# Ab A Bb B B#
|-
|-
| | 8|7
| 8{{pipe}}7
| | 1 1 2 1 1 1 1 2 1 1 1 1 1 2 1 1
| 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
| 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#
| C C# Db D# Eb E E# F Gb G G# Ab A A# B B#
|-
|-
| | 7|8
| 7{{pipe}}8
| | 1 1 2 1 1 1 1 1 2 1 1 1 1 2 1 1
| 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
| 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#
| C C# Db D# Eb E E# F F# G G# Ab A A# B B#
|-
|-
| | 6|9
| 6{{pipe}}9
| | 1 1 1 2 1 1 1 1 2 1 1 1 1 2 1 1
| 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
| 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#
| C C# Db D Eb E E# F F# G G# Ab A A# B B#
|-
|-
| | 5|10
| 5{{pipe}}10
| | 1 1 1 2 1 1 1 1 2 1 1 1 1 1 2 1
| 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
| 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#
| C C# Db D Eb E E# F F# G G# Ab A A# Bb B#
|-
|-
| | 4|11
| 4{{pipe}}11
| | 1 1 1 2 1 1 1 1 1 2 1 1 1 1 2 1
| 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
| 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#
| C C# Db D Eb E E# F F# Gb G# Ab A A# Bb B#
|-
|-
| | 3|12
| 3{{pipe}}12
| | 1 1 1 1 2 1 1 1 1 2 1 1 1 1 2 1
| 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
| 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#
| C C# Db D D# E E# F F# Gb G# Ab A A# Bb B#
|-
|-
| | 2|13
| 2{{pipe}}13
| | 1 1 1 1 2 1 1 1 1 2 1 1 1 1 1 2
| 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
| 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
| C C# Db D D# E E# F F# Gb G# Ab A A# Bb B
|-
|-
| | 1|14
| 1{{pipe}}14
| | 1 1 1 1 2 1 1 1 1 1 2 1 1 1 1 2
| 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
| 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
| C C# Db D D# E E# F F# Gb G Ab A A# Bb B
|-
|-
| | 0|15
| 0{{pipe}}15
| | 1 1 1 1 1 2 1 1 1 1 2 1 1 1 1 2
| 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
| 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
| C C# Db D D# Eb E# F F# Gb G Ab A A# Bb B
|}
|}


=== [[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)


{| class="wikitable"
{| class="wikitable"
|-
|-
! | UDP
! UDP
! | mode steps
! Mode steps
! | mode degrees
! Mode degrees
! | note names
! Note names
|-
|-
| | 4|0
| 4{{pipe}}0
| | 5 5 2 5 2
| 5 5 2 5 2
| | 0 5 10 12 17
| 0 5 10 12 17
| | C Eb Gb G# B
| C Eb Gb G# B
|-
|-
| | 3|1
| 3{{pipe}}1
| | 5 2 5 5 2
| 5 2 5 5 2
| | 0 5 7 12 17
| 0 5 7 12 17
| | C Eb E# G# B
| C Eb E# G# B
|-
|-
| | 2|2
| 2{{pipe}}2
| | 5 2 5 2 5
| 5 2 5 2 5
| | 0 5 7 12 14
| 0 5 7 12 14
| | C Eb E# G# A
| C Eb E# G# A
|-
|-
| | 1|3
| 1{{pipe}}3
| | 2 5 5 2 5
| 2 5 5 2 5
| | 0 2 7 12 14
| 0 2 7 12 14
| | C Db E# G# A
| C Db E# G# A
|-
|-
| | 0|4
| 0{{pipe}}4
| | 2 5 2 5 5
| 2 5 2 5 5
| | 0 2 7 9 14
| 0 2 7 9 14
| | C Db E# F# A
| C Db E# F# A
|}
|}


Line 1,275: Line 1,267:
{| class="wikitable"
{| class="wikitable"
|-
|-
! | UDP
! UDP
! | mode steps
! Mode steps
! | mode degrees
! Mode degrees
! | note names
! Note names
|-
|-
| | 7|0
| 7{{pipe}}0
| | 3 2 3 2 2 3 2 2
| 3 2 3 2 2 3 2 2
| | 0 3 5 8 10 12 15 17
| 0 3 5 8 10 12 15 17
| | C D Eb F Gb G# A# B
| C D Eb F Gb G# A# B
|-
|-
| | 6|1
| 6{{pipe}}1
| | 3 2 2 3 2 3 2 2
| 3 2 2 3 2 3 2 2
| | 0 3 5 7 10 12 15 17
| 0 3 5 7 10 12 15 17
| | C D Eb E# Gb G# A# B
| C D Eb E# Gb G# A# B
|-
|-
| | 5|2
| 5{{pipe}}2
| | 3 2 2 3 2 2 3 2
| 3 2 2 3 2 2 3 2
| | 0 3 5 7 10 12 14 17
| 0 3 5 7 10 12 14 17
| | C D Eb E# Gb G# A B
| C D Eb E# Gb G# A B
|-
|-
| | 4|3
| 4{{pipe}}3
| | 2 3 2 3 2 2 3 2
| 2 3 2 3 2 2 3 2
| | 0 2 5 7 10 12 14 17
| 0 2 5 7 10 12 14 17
| | C Db Eb E# Gb G# A B
| C Db Eb E# Gb G# A B
|-
|-
| | 3|4
| 3{{pipe}}4
| | 2 3 2 2 3 2 3 2
| 2 3 2 2 3 2 3 2
| | 0 2 5 7 9 12 14 17
| 0 2 5 7 9 12 14 17
| | C Db Eb E# F# G# A B
| C Db Eb E# F# G# A B
|-
|-
| | 2|5
| 2{{pipe}}5
| | 2 3 2 2 3 2 2 3
| 2 3 2 2 3 2 2 3
| | 0 2 5 7 9 12 14 16
| 0 2 5 7 9 12 14 16
| | C Db Eb E# F# G# A Bb
| C Db Eb E# F# G# A Bb
|-
|-
| | 1|6
| 1{{pipe}}6
| | 2 2 3 2 3 2 2 3
| 2 2 3 2 3 2 2 3
| | 0 2 4 7 9 12 14 16
| 0 2 4 7 9 12 14 16
| | C Db D# E# F# G# A Bb
| C Db D# E# F# G# A Bb
|-
|-
| | 0|7
| 0{{pipe}}7
| | 2 2 3 2 2 3 2 3
| 2 2 3 2 2 3 2 3
| | 0 2 4 7 9 11 14 16
| 0 2 4 7 9 11 14 16
| | C Db D# E# F# G A Bb
| C Db D# E# F# G A Bb
|}
|}


Line 1,325: Line 1,317:
{| class="wikitable"
{| class="wikitable"
|-
|-
! | UDP
! UDP
! | mode steps
! Mode steps
! | mode degrees
! Mode degrees
! | note names
! Note names
|-
|-
| | 10|0
| 10{{pipe}}0
| | 2 2 2 1 2 2 2 1 2 2 1
| 2 2 2 1 2 2 2 1 2 2 1
| | 0 2 4 6 7 9 11 13 14 16 18
| 0 2 4 6 7 9 11 13 14 16 18
| | C Db D# E E# F# G Ab A Bb B#
| C Db D# E E# F# G Ab A Bb B#
|-
|-
| | 9|1
| 9{{pipe}}1
| | 2 2 2 1 2 2 1 2 2 2 1
| 2 2 2 1 2 2 1 2 2 2 1
| | 0 2 4 6 7 9 11 12 14 16 18
| 0 2 4 6 7 9 11 12 14 16 18
| | C Db D# E E# F# G G# A Bb B#
| C Db D# E E# F# G G# A Bb B#
|-
|-
| | 8|2
| 8{{pipe}}2
| | 2 2 1 2 2 2 1 2 2 2 1
| 2 2 1 2 2 2 1 2 2 2 1
| | 0 2 4 5 7 9 11 12 14 16 18
| 0 2 4 5 7 9 11 12 14 16 18
| | C Db D# Eb E# F# G G# A Bb B#
| C Db D# Eb E# F# G G# A Bb B#
|-
|-
| | 7|3
| 7{{pipe}}3
| | 2 2 1 2 2 2 1 2 2 1 2
| 2 2 1 2 2 2 1 2 2 1 2
| | 0 2 4 5 7 9 11 12 14 16 17
| 0 2 4 5 7 9 11 12 14 16 17
| | C Db D# Eb E# F# G G# A Bb B
| C Db D# Eb E# F# G G# A Bb B
|-
|-
| | 6|4
| 6{{pipe}}4
| | 2 2 1 2 2 1 2 2 2 1 2
| 2 2 1 2 2 1 2 2 2 1 2
| | 0 2 4 5 7 9 10 12 14 16 17
| 0 2 4 5 7 9 10 12 14 16 17
| | C Db D# Eb E# F# Gb G# A Bb B
| C Db D# Eb E# F# Gb G# A Bb B
|-
|-
| | 5|5
| 5{{pipe}}5
| | 2 1 2 2 2 1 2 2 2 1 2
| 2 1 2 2 2 1 2 2 2 1 2
| | 0 2 3 5 7 9 10 12 14 16 17
| 0 2 3 5 7 9 10 12 14 16 17
| | C Db D Eb E# F# Gb G# A Bb B
| C Db D Eb E# F# Gb G# A Bb B
|-
|-
| | 4|6
| 4{{pipe}}6
| | 2 1 2 2 2 1 2 2 1 2 2
| 2 1 2 2 2 1 2 2 1 2 2
| | 0 2 3 5 7 9 10 12 14 15 17
| 0 2 3 5 7 9 10 12 14 15 17
| | C Db D Eb E# F# Gb G# A A# B
| C Db D Eb E# F# Gb G# A A# B
|-
|-
| | 3|7
| 3{{pipe}}7
| | 2 1 2 2 1 2 2 2 1 2 2
| 2 1 2 2 1 2 2 2 1 2 2
| | 0 2 3 5 7 8 10 12 14 15 17
| 0 2 3 5 7 8 10 12 14 15 17
| | C Db D Eb E# F Gb G# A A# B
| C Db D Eb E# F Gb G# A A# B
|-
|-
| | 2|8
| 2{{pipe}}8
| | 1 2 2 2 1 2 2 2 1 2 2
| 1 2 2 2 1 2 2 2 1 2 2
| | 0 1 3 5 7 8 10 12 14 15 17
| 0 1 3 5 7 8 10 12 14 15 17
| | C C# D Eb E# F Gb G# A A# B
| C C# D Eb E# F Gb G# A A# B
|-
|-
| | 1|9
| 1{{pipe}}9
| | 1 2 2 2 1 2 2 1 2 2 2
| 1 2 2 2 1 2 2 1 2 2 2
| | 0 1 3 5 7 8 10 12 13 15 17
| 0 1 3 5 7 8 10 12 13 15 17
| | C C# D Eb E# F Gb G# Ab A# B
| C C# D Eb E# F Gb G# Ab A# B
|-
|-
| | 0|10
| 0{{pipe}}10
| | 1 2 2 1 2 2 2 1 2 2 2
| 1 2 2 1 2 2 2 1 2 2 2
| | 0 1 3 5 6 8 10 12 13 15 17
| 0 1 3 5 6 8 10 12 13 15 17
| | C C# D Eb E F Gb G# Ab A# B
| C C# D Eb E F Gb G# Ab A# B
|}
|}


=== [[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)


{| class="wikitable"
{| class="wikitable"
|-
|-
! | UDP
! UDP
! | steps
! Steps
! | degrees
! Degrees
! | note names
! Note names
|-
|-
| | 4|0
| 4{{pipe}}0
| | 8 1 8 1 1
| 8 1 8 1 1
| | 0 8 9 17 18
| 0 8 9 17 18
| | C F F# B B#
| C F F# B B#
|-
|-
| | 3|1
| 3{{pipe}}1
| | 8 1 1 8 1
| 8 1 1 8 1
| | 0 8 9 10 18
| 0 8 9 10 18
| | C F F# Gb B#
| C F F# Gb B#
|-
|-
| | 2|2
| 2{{pipe}}2
| | 1 8 1 8 1
| 1 8 1 8 1
| | 0 1 9 10 18
| 0 1 9 10 18
| | C C# F# Gb B#
| C C# F# Gb B#
|-
|-
| | 1|3
| 1{{pipe}}3
| | 1 8 1 1 8
| 1 8 1 1 8
| | 0 1 9 10 11
| 0 1 9 10 11
| | C C# F# Gb G
| C C# F# Gb G
|-
|-
| | 0|4
| 0{{pipe}}4
| | 1 1 8 1 8
| 1 1 8 1 8
| | 0 1 2 10 11
| 0 1 2 10 11
| | C C# Db Gb G
| C C# Db Gb G
|}
|}


Line 1,427: Line 1,418:
{| class="wikitable"
{| class="wikitable"
|-
|-
! | UDP
! UDP
! | steps
! Steps
! | degrees
! Degrees
! | note names
! Note names
|-
|-
| | 6|0
| 6{{pipe}}0
| | 7 1 1 7 1 1 1
| 7 1 1 7 1 1 1
| | 0 7 8 9 16 17 18
| 0 7 8 9 16 17 18
| | C E# F F# Bb B B#
| C E# F F# Bb B B#
|-
|-
| | 5|1
| 5{{pipe}}1
| | 7 1 1 1 7 1 1
| 7 1 1 1 7 1 1
| | 0 7 8 9 10 17 18
| 0 7 8 9 10 17 18
| | C E# F F# Gb B B#
| C E# F F# Gb B B#
|-
|-
| | 4|2
| 4{{pipe}}2
| | 1 7 1 1 7 1 1
| 1 7 1 1 7 1 1
| | 0 1 8 9 10 17 18
| 0 1 8 9 10 17 18
| | C C# F F# Gb B B#
| C C# F F# Gb B B#
|-
|-
| | 3|3
| 3{{pipe}}3
| | 1 7 1 1 1 7 1
| 1 7 1 1 1 7 1
| | 0 1 8 9 10 11 18
| 0 1 8 9 10 11 18
| | C C# F F# Gb G B#
| C C# F F# Gb G B#
|-
|-
| | 2|4
| 2{{pipe}}4
| | 1 1 7 1 1 7 1
| 1 1 7 1 1 7 1
| | 0 1 2 9 10 11 18
| 0 1 2 9 10 11 18
| | C C# Db F# Gb G B#
| C C# Db F# Gb G B#
|-
|-
| | 1|5
| 1{{pipe}}5
| | 1 1 7 1 1 1 7
| 1 1 7 1 1 1 7
| | 0 1 2 9 10 11 12
| 0 1 2 9 10 11 12
| | C C# Db F# Gb G G#
| C C# Db F# Gb G G#
|-
|-
| | 0|6
| 0{{pipe}}6
| | 1 1 1 7 1 1 7
| 1 1 1 7 1 1 7
| | 0 1 2 3 10 11 12
| 0 1 2 3 10 11 12
| | C C# Db D Gb G G#
| C C# Db D Gb G G#
|}
|}


Line 1,472: Line 1,463:
{| class="wikitable"
{| class="wikitable"
|-
|-
! | UDP
! UDP
! | steps
! Steps
! | degrees
! Degrees
! | note names
! Note names
|-
|-
| | 8|0
| 8{{pipe}}0
| | 6 1 1 1 6 1 1 1 1
| 6 1 1 1 6 1 1 1 1
| | 0 6 7 8 9 15 16 17 18
| 0 6 7 8 9 15 16 17 18
| | C E E# F F# A# Bb B B#
| C E E# F F# A# Bb B B#
|-
|-
| | 7|1
| 7{{pipe}}1
| | 6 1 1 1 1 6 1 1 1
| 6 1 1 1 1 6 1 1 1
| | 0 6 7 8 9 10 16 17 18
| 0 6 7 8 9 10 16 17 18
| | C E E# F F# Gb Bb B B#
| C E E# F F# Gb Bb B B#
|-
|-
| | 6|2
| 6{{pipe}}2
| | 1 6 1 1 1 6 1 1 1
| 1 6 1 1 1 6 1 1 1
| | 0 1 7 8 9 10 16 17 18
| 0 1 7 8 9 10 16 17 18
| | C C# E# F F# Gb Bb B B#
| C C# E# F F# Gb Bb B B#
|-
|-
| | 5|3
| 5{{pipe}}3
| | 1 6 1 1 1 1 6 1 1
| 1 6 1 1 1 1 6 1 1
| | 0 1 7 8 9 10 11 17 18
| 0 1 7 8 9 10 11 17 18
| | C C# E# F F# Gb G B B#
| C C# E# F F# Gb G B B#
|-
|-
| | 4|4
| 4{{pipe}}4
| | 1 1 6 1 1 1 6 1 1
| 1 1 6 1 1 1 6 1 1
| | 0 1 2 8 9 10 11 17 18
| 0 1 2 8 9 10 11 17 18
| | C C# Db F F# Gb G B B#
| C C# Db F F# Gb G B B#
|-
|-
| | 3|5
| 3{{pipe}}5
| | 1 1 6 1 1 1 1 6 1
| 1 1 6 1 1 1 1 6 1
| | 0 1 2 8 9 10 11 12 18
| 0 1 2 8 9 10 11 12 18
| | C C# Db F F# Gb G G# B#
| C C# Db F F# Gb G G# B#
|-
|-
| | 2|6
| 2{{pipe}}6
| | 1 1 1 6 1 1 1 6 1
| 1 1 1 6 1 1 1 6 1
| | 0 1 2 3 9 10 11 12 18
| 0 1 2 3 9 10 11 12 18
| | C C# Db D F# Gb G G# B#
| C C# Db D F# Gb G G# B#
|-
|-
| | 1|7
| 1{{pipe}}7
| | 1 1 1 6 1 1 1 1 6
| 1 1 1 6 1 1 1 1 6
| | 0 1 2 3 9 10 11 12 13
| 0 1 2 3 9 10 11 12 13
| | C C# Db D F# Gb G G# Ab
| C C# Db D F# Gb G G# Ab
|-
|-
| | 0|8
| 0{{pipe}}8
| | 1 1 1 1 6 1 1 1 6
| 1 1 1 1 6 1 1 1 6
| | 0 1 2 3 4 10 11 12 13
| 0 1 2 3 4 10 11 12 13
| | C C# Db D D# Gb G G# Ab
| C C# Db D D# Gb G G# Ab
|}
|}


Line 1,527: Line 1,518:
{| class="wikitable"
{| class="wikitable"
|-
|-
! | UDP
! UDP
! | steps
! Steps
! | degrees
! Degrees
! | note names
! Note names
|-
|-
| | 10|0
| 10{{pipe}}0
| | 5 1 1 1 1 5 1 1 1 1 1
| 5 1 1 1 1 5 1 1 1 1 1
| | 0 5 6 7 8 9 14 15 16 17 18
| 0 5 6 7 8 9 14 15 16 17 18
| | C Eb E E# F F# A A# Bb B B#
| C Eb E E# F F# A A# Bb B B#
|-
|-
| | 9|1
| 9{{pipe}}1
| | 5 1 1 1 1 1 5 1 1 1 1
| 5 1 1 1 1 1 5 1 1 1 1
| | 0 5 6 7 8 9 10 15 16 17 18
| 0 5 6 7 8 9 10 15 16 17 18
| | C Eb E E# F F# Gb A# Bb B B#
| C Eb E E# F F# Gb A# Bb B B#
|-
|-
| | 8|2
| 8{{pipe}}2
| | 1 5 1 1 1 1 5 1 1 1 1
| 1 5 1 1 1 1 5 1 1 1 1
| | 0 1 6 7 8 9 10 15 16 17 18
| 0 1 6 7 8 9 10 15 16 17 18
| | C C# E E# F F# Gb A# Bb B B#
| C C# E E# F F# Gb A# Bb B B#
|-
|-
| | 7|3
| 7{{pipe}}3
| | 1 5 1 1 1 1 1 5 1 1 1
| 1 5 1 1 1 1 1 5 1 1 1
| | 0 1 6 7 8 9 10 11 16 17 18
| 0 1 6 7 8 9 10 11 16 17 18
| | C C# E E# F F# Gb G Bb B B#
| C C# E E# F F# Gb G Bb B B#
|-
|-
| | 6|4
| 6{{pipe}}4
| | 1 1 5 1 1 1 1 5 1 1 1
| 1 1 5 1 1 1 1 5 1 1 1
| | 0 1 2 7 8 9 10 11 16 17 18
| 0 1 2 7 8 9 10 11 16 17 18
| | C C# Db E# F F# Gb G Bb B B#
| C C# Db E# F F# Gb G Bb B B#
|-
|-
| | 5|5
| 5{{pipe}}5
| | 1 1 5 1 1 1 1 1 5 1 1
| 1 1 5 1 1 1 1 1 5 1 1
| | 0 1 2 7 8 9 10 11 12 17 18
| 0 1 2 7 8 9 10 11 12 17 18
| | C C# Db E# F F# Gb G G# B B#
| C C# Db E# F F# Gb G G# B B#
|-
|-
| | 4|6
| 4{{pipe}}6
| | 1 1 1 5 1 1 1 1 5 1 1
| 1 1 1 5 1 1 1 1 5 1 1
| | 0 1 2 3 8 9 10 11 12 17 18
| 0 1 2 3 8 9 10 11 12 17 18
| | C C# Db D F F# Gb G G# B B#
| C C# Db D F F# Gb G G# B B#
|-
|-
| | 3|7
| 3{{pipe}}7
| | 1 1 1 5 1 1 1 1 1 5 1
| 1 1 1 5 1 1 1 1 1 5 1
| | 0 1 2 3 8 9 10 11 12 13 18
| 0 1 2 3 8 9 10 11 12 13 18
| | C C# Db D F F# Gb G G# Ab B#
| C C# Db D F F# Gb G G# Ab B#
|-
|-
| | 2|8
| 2{{pipe}}8
| | 1 1 1 1 5 1 1 1 1 5 1
| 1 1 1 1 5 1 1 1 1 5 1
| | 0 1 2 3 4 9 10 11 12 13 18
| 0 1 2 3 4 9 10 11 12 13 18
| | C C# Db D D# F# Gb G G# Ab B#
| C C# Db D D# F# Gb G G# Ab B#
|-
|-
| | 1|9
| 1{{pipe}}9
| | 1 1 1 1 5 1 1 1 1 1 5
| 1 1 1 1 5 1 1 1 1 1 5
| | 0 1 2 3 4 9 10 11 12 13 14
| 0 1 2 3 4 9 10 11 12 13 14
| | C C# Db D D# F# Gb G G# Ab A
| C C# Db D D# F# Gb G G# Ab A
|-
|-
| | 0|10
| 0{{pipe}}10
| | 1 1 1 1 1 5 1 1 1 1 5
| 1 1 1 1 1 5 1 1 1 1 5
| | 0 1 2 3 4 5 10 11 12 13 14
| 0 1 2 3 4 5 10 11 12 13 14
| | C C# Db D D# Eb Gb G G# Ab A
| C C# Db D D# Eb Gb G G# Ab A
|}
|}


Line 1,600: Line 1,591:


== 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
1 1 6 3 1 1 6 – E# F Gbb A# B# C Dbb E# – enharmonic approximation
 
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]])
5 3 1 2 4 1 3 – C Eb F F# G A# B – Hyperblue Dorian (approximated from [[31edo]])


<br>
<br />
{{Scale gallery}}
{{Scale gallery}}


[[Category:19edo]]
[[Category:19edo]]
[[Category:modes]]
[[Category:modes]]

Revision as of 14:18, 17 January 2025

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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