19edo modes: Difference between revisions

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<h2>IMPORTED REVISION FROM WIKISPACES</h2>
__FORCETOC__
This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
Some scales and modes available in [[19edo]]. Please add more, discovered or newly-composed! See also [[19edo#Scales]].
: This revision was by author [[User:spt3125|spt3125]] and made on <tt>2014-01-21 21:04:42 UTC</tt>.<br>
: The original revision id was <tt>484391678</tt>.<br>
: The revision comment was: <tt></tt><br>
The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<br>
<h4>Original Wikitext content:</h4>
<div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;white-space: pre-wrap ! important" class="old-revision-html">Some modes available in [[19edo]]. Please add more, discovered or newly-composed!


=MOS scales of rank-2 temperaments=  
== Note names in 19edo ==
The charts below primarily use the following note names (based on standard meantone/Pythagorean notation):


==[[negri]]==
{| class="wikitable" style="text-align: center;"
(2\19; 16/15~15/14)
|-
**[9]** 222222223
! 0
**[10]** 2222222221
! 1
! 2
! 3
! 4
! 5
! 6
! 7
! 8
! 9
! 10
! 11
! 12
! 13
! 14
! 15
! 16
! 17
! 18
|-
| C
| Ç


==[[deutone]]==
C# (<span style="font-size: calc(40px / 3);">Δb)</span>
(3\19; 9/8~10/9)
| <span style="display: block; text-align: center;"><span style="font-size: calc(40px / 3);">Δ</span></span><span style="display: block; text-align: center;">Ç# (Db)</span>
**[6]** 333334
| D
**[7]** 3333331
| Þ
**[13]** 2121212121211


==[[Semaphore and Godzilla|godzilla/semaphore]]==
D# (<span style="font-size: calc(40px / 3);">εb, Sb)</span>
(4\19; 8/7~7/6)
| <span style="font-size: calc(40px / 3);">ε, S</span>
**[5]** 44443
**[9]** 131313133
**[14]** 12112112112121


==[[Kleismic family|kleismic/hanson/etc]]==
<span style="display: block; text-align: center;">Þ# (Eb)</span>
(5\19; ~6/5)
| E
**[7]** 1414144
| E# (Fb)
**[11]** 11311311313
| F
**[15]** 112111211121121
| ϕ


==[[Magic|magic]]==
F# (Γb)
(6\19; ~5/4)
| <span style="display: block; text-align: center;">Γ</span>ϕ# (Gb)
**[7]** 5151511
| G
**[10]** 4114114111
| Z
**[13]** 3111311131111
**[16]** 2111121111211111


==[[sensi]]==
G# (<span style="font-size: calc(40px / 3);">αb)</span>
(7\19; 9/7~13/10)
| <span style="display: block; font-size: calc(40px / 3); text-align: center;">α</span><span style="line-height: 1.5;">Z# (</span>Ab)
**[5]** 25255
| A
**[8]** 22322323
| Æ
**[11]** 22212221221


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


**meantone[5]** (2L+3s / chroma-positive generator = 8\19; ~4/3)
Other systems of notation are of course possible, and may be preferred depending on the scales you are working with!
|| UDP || mode steps || mode name ||
|| 4|0 || 33535 || major pentatonic ||
|| 3|1 || 53353 || minor pentatonic ||
|| 2|2 || 35335 ||  ||
|| 1|3 || 53533 ||  ||
|| 0|4 || 35353 ||  ||


**meantone[7]** (5L+2s / CPG = 11\19; ~3/2)
== MOS scales and modes of rank-2 temperaments ==
|| UDP || mode steps || mode name ||
=== [[Meantone|Meantone]] ===
|| 6|0 || 3332332 || Lydian ||
'''meantone[5]''' ([[2L&nbsp;3s]] / [[Modal_UDP_Notation|chroma-positive generator]] = 8\19 ~= 4/3)
|| 5|1 || 2333233 || Ionian ||
|| 4|2 || 3233323 || Mixolydian ||
|| 3|3 || 3323332 || Dorian ||
|| 2|4 || 2332333 || Aeolian ||
|| 1|5 || 3233233 || Phrygian ||
|| 0|6 || 3323323 || Locrian ||


**meantone[12]** (7L+5s / CPG = 8\19; ~4/3)
{| class="wikitable"
|| UDP... || mode steps........ || notes || mode name ||
|-
|| 11|0 || 221212212121 || C Db D# Eb E# F Gb G# Ab A# Bb B# ||   ||
! UDP
|| 10|1 || 122121221212 || C C# D Eb E F F# G Ab A Bb B ||   ||
! Steps
|| 9|2 || 212212122121 || C Db D Eb E# F Gb G Ab A# Bb B# ||  ||
! Degrees
|| 8|3 || 121221212212 || C C# D D# E F F# G G# A Bb B ||   ||
! Note names
|| 7|4 || 212122121221 || C Db D Eb E F Gb G Ab A Bb B# ||  ||
! Comments
|| 6|5 || 121212212122 || C C# D D# E E# F# G G# A A# B ||  ||
! Audio
|| 5|6 || 212121221212 || C Db D Eb E F F# G Ab A Bb B ||  ||
|-
|| 4|7 || 221212122121 || C Db D# Eb E# F Gb G Ab A# Bb B# ||  ||
| 4{{pipe}}0
|| 3|8 || 122121212212 || C C# D Eb E F F# G G# A Bb B ||   ||
| 5 3 5 3 3
|| 2|9 || 212212121221 || C Db D Eb E# F Gb G Ab A Bb B# ||  ||
| 0 5 8 13 16
|| 1|10 || 121221212122 || C C# D D# E F F# G G# A A# B ||  ||
| C Eb F Ab Bb
|| 0|11 || 212122121212 || C Db D Eb E F Gb G Ab A Bb B || Yasser's Supradiatonic ||
| minor pentatonic (2)
&lt;span style="font-size: 90%;"&gt;Note: in 19edo, E#=Fb and B#=Cb; other notes are not enharmonic (for example, C# and Db are different).&lt;/span&gt;
| [[File:Minor 2 Pentatonic (19-EDO).mp3|frameless]]
|-
| 3{{pipe}}1
| 5 3 3 5 3
| 0 5 8 11 16
| C Eb F G Bb
| minor pentatonic
| [[File:Minor Pentatonic (19-EDO).mp3|frameless]]
|-
| 2{{pipe}}2
| 3 5 3 5 3
| 0 3 8 11 16
| C D F G Bb
| "mixolydian" pentatonic
| [[File:Mixolydian Pentatonic (19-EDO).mp3|frameless]]
|-
| 1{{pipe}}3
| 3 5 3 3 5
| 0 3 8 11 14
| C D F G A
| "suspended" pentatonic
| [[File:Suspended Pentatonic (19-EDO).mp3|frameless]]
|-
| 0{{pipe}}4
| 3 3 5 3 5
| 0 3 6 11 14
| C D E G A
| major pentatonic
| [[File:Major Pentatonic (19-EDO).mp3|frameless]]
|}


'''meantone[7]''' ([[5L&nbsp;2s]] / CPG = 11\19 ~= 3/2)


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


==[[Meantone family#Liese|liese]]/[[Marvel temperaments#Triton|triton]]==
'''meantone[12]''' ([[7L&nbsp;5s]] / CPG = 8\19)
(9\19; ~7/5)
**[11]** 51111511111
**[13]** 4111114111111
**[15]** 311111131111111
**[17]** 21111111211111111


[[media type="custom" key="24914728"]]</pre></div>
{| class="wikitable"
<h4>Original HTML content:</h4>
|-
<div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;width:200%;white-space: pre-wrap ! important" class="old-revision-html">&lt;html&gt;&lt;head&gt;&lt;title&gt;19edo Modes&lt;/title&gt;&lt;/head&gt;&lt;body&gt;Some modes available in &lt;a class="wiki_link" href="/19edo"&gt;19edo&lt;/a&gt;. Please add more, discovered or newly-composed!&lt;br /&gt;
! UDP
&lt;br /&gt;
! Steps
&lt;!-- ws:start:WikiTextHeadingRule:1:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc0"&gt;&lt;a name="MOS scales of rank-2 temperaments"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:1 --&gt;MOS scales of rank-2 temperaments&lt;/h1&gt;
! Degrees
&lt;br /&gt;
! Note names
&lt;!-- ws:start:WikiTextHeadingRule:3:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc1"&gt;&lt;a name="MOS scales of rank-2 temperaments-negri"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:3 --&gt;&lt;a class="wiki_link" href="/negri"&gt;negri&lt;/a&gt;&lt;/h2&gt;
! Comments
(2\19; 16/15~15/14)&lt;br /&gt;
|-
&lt;strong&gt;[9]&lt;/strong&gt; 222222223&lt;br /&gt;
| 11{{pipe}}0
&lt;strong&gt;[10]&lt;/strong&gt; 2222222221&lt;br /&gt;
| 2 2 1 2 1 2 2 1 2 1 2 1
&lt;br /&gt;
| 0 2 4 5 7 8 10 12 13 15 16 18
&lt;!-- ws:start:WikiTextHeadingRule:5:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc2"&gt;&lt;a name="MOS scales of rank-2 temperaments-deutone"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:5 --&gt;&lt;a class="wiki_link" href="/deutone"&gt;deutone&lt;/a&gt;&lt;/h2&gt;
| C Db D# Eb E# F Gb G# Ab A# Bb B#
(3\19; 9/8~10/9)&lt;br /&gt;
&lt;strong&gt;[6]&lt;/strong&gt; 333334&lt;br /&gt;
&lt;strong&gt;[7]&lt;/strong&gt; 3333331&lt;br /&gt;
&lt;strong&gt;[13]&lt;/strong&gt; 2121212121211&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:7:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc3"&gt;&lt;a name="MOS scales of rank-2 temperaments-godzilla/semaphore"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:7 --&gt;&lt;a class="wiki_link" href="/Semaphore%20and%20Godzilla"&gt;godzilla/semaphore&lt;/a&gt;&lt;/h2&gt;
(4\19; 8/7~7/6)&lt;br /&gt;
&lt;strong&gt;[5]&lt;/strong&gt; 44443&lt;br /&gt;
&lt;strong&gt;[9]&lt;/strong&gt; 131313133&lt;br /&gt;
&lt;strong&gt;[14]&lt;/strong&gt; 12112112112121&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:9:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc4"&gt;&lt;a name="MOS scales of rank-2 temperaments-kleismic/hanson/etc"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:9 --&gt;&lt;a class="wiki_link" href="/Kleismic%20family"&gt;kleismic/hanson/etc&lt;/a&gt;&lt;/h2&gt;
(5\19; ~6/5)&lt;br /&gt;
&lt;strong&gt;[7]&lt;/strong&gt; 1414144&lt;br /&gt;
&lt;strong&gt;[11]&lt;/strong&gt; 11311311313&lt;br /&gt;
&lt;strong&gt;[15]&lt;/strong&gt; 112111211121121&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:11:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc5"&gt;&lt;a name="MOS scales of rank-2 temperaments-magic"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:11 --&gt;&lt;a class="wiki_link" href="/Magic"&gt;magic&lt;/a&gt;&lt;/h2&gt;
(6\19; ~5/4)&lt;br /&gt;
&lt;strong&gt;[7]&lt;/strong&gt; 5151511&lt;br /&gt;
&lt;strong&gt;[10]&lt;/strong&gt; 4114114111&lt;br /&gt;
&lt;strong&gt;[13]&lt;/strong&gt; 3111311131111&lt;br /&gt;
&lt;strong&gt;[16]&lt;/strong&gt; 2111121111211111&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:13:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc6"&gt;&lt;a name="MOS scales of rank-2 temperaments-sensi"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:13 --&gt;&lt;a class="wiki_link" href="/sensi"&gt;sensi&lt;/a&gt;&lt;/h2&gt;
(7\19; 9/7~13/10)&lt;br /&gt;
&lt;strong&gt;[5]&lt;/strong&gt; 25255&lt;br /&gt;
&lt;strong&gt;[8]&lt;/strong&gt; 22322323&lt;br /&gt;
&lt;strong&gt;[11]&lt;/strong&gt; 22212221221&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:15:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc7"&gt;&lt;a name="MOS scales of rank-2 temperaments-meantone"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:15 --&gt;&lt;a class="wiki_link" href="/meantone"&gt;meantone&lt;/a&gt;&lt;/h2&gt;
&lt;br /&gt;
&lt;strong&gt;meantone[5]&lt;/strong&gt; (2L+3s / chroma-positive generator = 8\19; ~4/3)&lt;br /&gt;


C <span style="font-size: calc(40px / 3);">Δ </span>Þ S E# F Γ Z <span style="font-size: calc(40px / 3);">α Æ </span>β B#
|
|-
| 10{{pipe}}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#


&lt;table class="wiki_table"&gt;
C <span style="font-size: calc(40px / 3);">Δ </span>Þ S E# F Γ G <span style="font-size: calc(40px / 3);">α Æ </span>β B#
    &lt;tr&gt;
|
        &lt;td&gt;UDP&lt;br /&gt;
|-
&lt;/td&gt;
| 9{{pipe}}2
        &lt;td&gt;mode steps&lt;br /&gt;
| 2 1 2 2 1 2 1 2 2 1 2 1
&lt;/td&gt;
| 0 2 3 5 7 8 10 11 13 15 16 18
        &lt;td&gt;mode name&lt;br /&gt;
| C Db D Eb E# F Gb G Ab A# Bb B#
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;4|0&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;33535&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;major pentatonic&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;3|1&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;53353&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;minor pentatonic&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;2|2&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;35335&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;1|3&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;53533&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;0|4&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;35353&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
&lt;/table&gt;


&lt;br /&gt;
C <span style="font-size: calc(40px / 3);">Δ D</span> S E# F Γ G <span style="font-size: calc(40px / 3);">α Æ </span>β B#
&lt;strong&gt;meantone[7]&lt;/strong&gt; (5L+2s / CPG = 11\19; ~3/2)&lt;br /&gt;
|
|-
| 8{{pipe}}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 <span style="font-size: calc(40px / 3);">Δ D</span> S E# F Γ G <span style="font-size: calc(40px / 3);">α A </span>β B#
|
|-
| 7{{pipe}}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#


&lt;table class="wiki_table"&gt;
C <span style="font-size: calc(40px / 3);">Δ D</span> S E F Γ G <span style="font-size: calc(40px / 3);">α A </span>β B#
    &lt;tr&gt;
|
        &lt;td&gt;UDP&lt;br /&gt;
|-
&lt;/td&gt;
| 6{{pipe}}5
        &lt;td&gt;mode steps&lt;br /&gt;
| 2 1 2 1 2 2 1 2 1 2 1 2
&lt;/td&gt;
| 0 2 3 5 6 8 10 11 13 14 16 17
        &lt;td&gt;mode name&lt;br /&gt;
| C Db D Eb E F Gb G Ab A Bb B
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;6|0&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;3332332&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;Lydian&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;5|1&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;2333233&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;Ionian&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;4|2&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;3233323&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;Mixolydian&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;3|3&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;3323332&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;Dorian&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;2|4&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;2332333&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;Aeolian&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;1|5&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;3233233&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;Phrygian&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;0|6&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;3323323&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;Locrian&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
&lt;/table&gt;


&lt;br /&gt;
C <span style="font-size: calc(40px / 3);">Δ D</span> S E F Γ G <span style="font-size: calc(40px / 3);">α A </span>β B
&lt;strong&gt;meantone[12]&lt;/strong&gt; (7L+5s / CPG = 8\19; ~4/3)&lt;br /&gt;
| 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>
|-
| 5{{pipe}}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


&lt;table class="wiki_table"&gt;
C <span style="font-size: calc(40px / 3);">Δ D</span> S E F ϕ G <span style="font-size: calc(40px / 3);">α A </span>β B
    &lt;tr&gt;
| fifths of 12-5 chords form C Ionian mode
        &lt;td&gt;UDP...&lt;br /&gt;
|-
&lt;/td&gt;
| 4{{pipe}}7
        &lt;td&gt;mode steps........&lt;br /&gt;
| 1 2 2 1 2 1 2 2 1 2 1 2
&lt;/td&gt;
| 0 1 3 5 6 8 9 11 13 14 16 17
        &lt;td&gt;notes&lt;br /&gt;
| C C# D Eb E F F# G Ab A Bb B
&lt;/td&gt;
        &lt;td&gt;mode name&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;11|0&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;221212212121&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;C Db D# Eb E# F Gb G# Ab A# Bb B#&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;10|1&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;122121221212&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;C C# D Eb E F F# G Ab A Bb B&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;9|2&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;212212122121&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;C Db D Eb E# F Gb G Ab A# Bb B#&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;8|3&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;121221212212&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;C C# D D# E F F# G G# A Bb B&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;7|4&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;212122121221&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;C Db D Eb E F Gb G Ab A Bb B#&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;6|5&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;121212212122&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;C C# D D# E E# F# G G# A A# B&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;5|6&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;212121221212&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;C Db D Eb E F F# G Ab A Bb B&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;4|7&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;221212122121&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;C Db D# Eb E# F Gb G Ab A# Bb B#&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;3|8&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;122121212212&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;C C# D Eb E F F# G G# A Bb B&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;2|9&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;212212121221&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;C Db D Eb E# F Gb G Ab A Bb B#&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;1|10&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;121221212122&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;C C# D D# E F F# G G# A A# B&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;0|11&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;212122121212&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;C Db D Eb E F Gb G Ab A Bb B&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;Yasser's Supradiatonic&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
&lt;/table&gt;


&lt;span style="font-size: 90%;"&gt;Note: in 19edo, E#=Fb and B#=Cb; other notes are not enharmonic (for example, C# and Db are different).&lt;/span&gt;&lt;br /&gt;
C Ç<span style="font-size: calc(40px / 3); line-height: 1.5;"> D</span><span style="line-height: 1.5;"> S E F ϕ G </span><span style="font-size: calc(40px / 3); line-height: 1.5;">α A </span><span style="line-height: 1.5;">β B</span>
&lt;br /&gt;
| octaves of 11-5 chords form C Mixolydian mode
&lt;br /&gt;
|-
&lt;br /&gt;
| 3{{pipe}}8
&lt;!-- ws:start:WikiTextHeadingRule:17:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc8"&gt;&lt;a name="MOS scales of rank-2 temperaments-liese/triton"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:17 --&gt;&lt;a class="wiki_link" href="/Meantone%20family#Liese"&gt;liese&lt;/a&gt;/&lt;a class="wiki_link" href="/Marvel%20temperaments#Triton"&gt;triton&lt;/a&gt;&lt;/h2&gt;
| 1 2 2 1 2 1 2 1 2 2 1 2
(9\19; ~7/5)&lt;br /&gt;
| 0 1 3 5 6 8 9 11 12 14 16 17
&lt;strong&gt;[11]&lt;/strong&gt; 51111511111&lt;br /&gt;
| C C# D Eb E F F# G G# A Bb B
&lt;strong&gt;[13]&lt;/strong&gt; 4111114111111&lt;br /&gt;
 
&lt;strong&gt;[15]&lt;/strong&gt; 311111131111111&lt;br /&gt;
C Ç<span style="font-size: calc(40px / 3);"> D</span> S E F ϕ G Z<span style="font-size: calc(40px / 3);"> A </span>β B
&lt;strong&gt;[17]&lt;/strong&gt; 21111111211111111&lt;br /&gt;
|
&lt;br /&gt;
|-
&lt;!-- ws:start:WikiTextMediaRule:0:&amp;lt;img src=&amp;quot;http://www.wikispaces.com/site/embedthumbnail/custom/24914728?h=0&amp;amp;w=0&amp;quot; class=&amp;quot;WikiMedia WikiMediaCustom&amp;quot; id=&amp;quot;wikitext@@media@@type=&amp;amp;quot;custom&amp;amp;quot; key=&amp;amp;quot;24914728&amp;amp;quot;&amp;quot; title=&amp;quot;Custom Media&amp;quot;/&amp;gt; --&gt;&lt;!-- this adds some padding to the tables for better readability --&gt;
| 2{{pipe}}9
&lt;script type="text/javascript"&gt;
| 1 2 1 2 2 1 2 1 2 2 1 2
/*&lt;![CDATA[*/
| 0 1 3 4 6 8 9 11 12 14 16 17
document.write('&lt;style type="text/css"&gt; .wiki_table td { padding: 5px; } &lt;\/style&gt;');
| C C# D D# E F F# G G# A Bb B
/*]]&gt;*/
 
&lt;/script&gt;&lt;!-- ws:end:WikiTextMediaRule:0 --&gt;&lt;/body&gt;&lt;/html&gt;</pre></div>
C Ç<span style="font-size: calc(40px / 3);"> D</span> Þ E F ϕ G Z<span style="font-size: calc(40px / 3);"> A </span>β B
| octaves of 12-5 chords form C Ionian mode
|-
| 1{{pipe}}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<span style="font-size: calc(40px / 3);"> D</span> Þ E F ϕ G Z A<span style="font-size: calc(40px / 3);"> Æ B</span>
| roots of 12-5 chords form C Ionian mode
|-
| 0{{pipe}}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<span style="font-size: calc(40px / 3);"> D</span> Þ E Fb ϕ G Z A<span style="font-size: calc(40px / 3);"> Æ B</span>
|
|}
 
=== [[Negri|Negri]] ===
'''negri[9]''' ([[1L&nbsp;8s]] / [[Modal_UDP_Notation|chroma-positive generator]] = 17\19)
 
{| class="wikitable"
|-
! UDP
! Steps
! Degrees
! Note names
! Comments
|-
| 8{{pipe}}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{{pipe}}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{{pipe}}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{{pipe}}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{{pipe}}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{{pipe}}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{{pipe}}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{{pipe}}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{{pipe}}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&nbsp;1s]] / CPG = 2\19)
 
{| class="wikitable"
|-
! UDP
! Steps
! Degrees
! Note names
|-
| 9{{pipe}}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{{pipe}}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{{pipe}}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{{pipe}}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{{pipe}}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{{pipe}}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{{pipe}}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{{pipe}}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{{pipe}}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{{pipe}}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]] ===
'''deutone[6]''' ([[1L&nbsp;5s ]]/ [[Modal_UDP_Notation|chroma-positive generator]] = 16\19)
 
{| class="wikitable"
|-
! UDP
! Steps
! Degrees
! Note names
|-
| 5{{pipe}}0
| 4 3 3 3 3 3
| 0 4 7 10 13 16
| C D# E# Gb Ab Bb
|-
| 4{{pipe}}1
| 3 4 3 3 3 3
| 0 3 7 10 13 16
| C D E# Gb Ab Bb
|-
| 3{{pipe}}2
| 3 3 4 3 3 3
| 0 3 6 10 13 16
| C D E Gb Ab Bb
|-
| 2{{pipe}}3
| 3 3 3 4 3 3
| 0 3 6 9 13 16
| C D E F# Ab Bb
|-
| 1{{pipe}}4
| 3 3 3 3 4 3
| 0 3 6 9 12 16
| C D E F# G# Bb
|-
| 0{{pipe}}5
| 3 3 3 3 3 4
| 0 3 6 9 12 15
| C D E F# G# A#
|}
 
'''deutone[7]''' ([[6L&nbsp;1s]]/ CPG = 3\19)
 
{| class="wikitable"
|-
! UDP
! Steps
! Degrees
! Note names
|-
| 6{{pipe}}0
| 3 3 3 3 3 3 1
| 0 3 6 9 12 15 18
| C D E F# G# A# B#
|-
| 5{{pipe}}1
| 3 3 3 3 3 1 3
| 0 3 6 9 12 15 16
| C D E F# G# A# Bb
|-
| 4{{pipe}}2
| 3 3 3 3 1 3 3
| 0 3 6 9 12 13 16
| C D E F# G# Ab Bb
|-
| 3{{pipe}}3
| 3 3 3 1 3 3 3
| 0 3 6 9 10 13 16
| C D E F# Gb Ab Bb
|-
| 2{{pipe}}4
| 3 3 1 3 3 3 3
| 0 3 6 7 10 13 16
| C D E E# Gb Ab Bb
|-
| 1{{pipe}}5
| 3 1 3 3 3 3 3
| 0 3 4 7 10 13 16
| C D D# E# Gb Ab Bb
|-
| 0{{pipe}}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&nbsp;7s]]/ CPG = 3\19)
 
{| class="wikitable"
|-
! UDP
! Steps
! Degrees
! Note names
|-
| 12{{pipe}}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{{pipe}}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{{pipe}}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{{pipe}}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{{pipe}}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{{pipe}}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{{pipe}}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{{pipe}}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{{pipe}}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{{pipe}}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{{pipe}}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{{pipe}}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{{pipe}}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
|}
 
=== [[Semaphore_and_Godzilla|Godzilla / Semaphore]] ===
'''godzilla[5]''' ([[4L&nbsp;1s]]/ [[Modal_UDP_Notation|chroma-positive generator]] = 4\19 ~= 8/7 ~= 7/6)
 
{| class="wikitable"
|-
! UDP
! Mode steps
! Mode degrees
! Note names
|-
| 4{{pipe}}0
| 4 4 4 4 3
| 0 4 8 12 16
| C D# F G# Bb
|-
| 3{{pipe}}1
| 4 4 4 3 4
| 0 4 8 12 15
| C D# F G# A#
|-
| 2{{pipe}}2
| 4 4 3 4 4
| 0 4 8 11 15
| C D# F G A#
|-
| 1{{pipe}}3
| 4 3 4 4 4
| 0 4 7 11 15
| C D# E# G A#
|-
| 0{{pipe}}4
| 3 4 4 4 4
| 0 3 7 11 15
| C D E# G A#
|}
 
'''godzilla[9]''' ([[5L&nbsp;4s]]/ CPG = 15\19 ~= 7/4 ~= 12/7)
 
{| class="wikitable"
|-
! UDP
! Mode steps
! Mode degrees
! Note names
|-
| 8{{pipe}}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{{pipe}}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{{pipe}}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{{pipe}}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{{pipe}}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{{pipe}}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{{pipe}}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{{pipe}}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{{pipe}}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&nbsp;9s]]/ CPG = 4\19)
 
{| class="wikitable"
|-
! UDP
! Steps
! Degrees
! Note names
|-
| 13{{pipe}}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{{pipe}}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{{pipe}}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{{pipe}}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{{pipe}}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{{pipe}}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{{pipe}}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{{pipe}}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{{pipe}}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{{pipe}}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{{pipe}}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{{pipe}}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{{pipe}}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{{pipe}}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_family|Kleismic / Hanson]] ===
'''kleismic[7]''' ([[4L&nbsp;3s]]/ [[Modal_UDP_Notation|chroma-positive generator]] = 14\19 ~= 5/3)
 
{| class="wikitable"
|-
! UDP
! Steps
! Degrees
! Note names
! Comments
|-
| 6{{pipe}}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{{pipe}}1
| 4 1 4 4 1 4 1
| 0 4 5 9 13 14 18
| C D# Eb F# Ab A B#
|
|-
| 4{{pipe}}2
| 4 1 4 1 4 4 1
| 0 4 5 9 10 14 18
| C D# Eb F# Gb A B#
|
|-
| 3{{pipe}}3
| 4 1 4 1 4 1 4
| 0 4 5 9 10 14 15
| C D# Eb F# Gb A A#
| symmetrical
|-
| 2{{pipe}}4
| 1 4 4 1 4 1 4
| 0 1 5 9 10 14 15
| C C# Eb F# Gb A A#
|
|-
| 1{{pipe}}5
| 1 4 1 4 4 1 4
| 0 1 5 6 10 14 15
| C C# Eb E Gb A A#
|
|-
| 0{{pipe}}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&nbsp;7s]]/ CPG = 14\19)
 
{| class="wikitable"
|-
! UDP
! Steps
! Degrees
! Note names
! Comments
|-
| 10{{pipe}}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{{pipe}}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{{pipe}}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{{pipe}}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{{pipe}}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{{pipe}}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{{pipe}}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{{pipe}}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{{pipe}}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{{pipe}}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{{pipe}}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&nbsp;11s]]/ CPG = 14\19)
 
{| class="wikitable"
|-
! UDP
! Steps
! Degrees
! Note names
|-
| 14{{pipe}}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{{pipe}}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{{pipe}}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{{pipe}}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{{pipe}}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{{pipe}}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{{pipe}}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{{pipe}}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{{pipe}}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{{pipe}}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{{pipe}}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{{pipe}}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{{pipe}}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{{pipe}}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{{pipe}}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]] ===
'''magic[7]''' ([[3L&nbsp;4s]] / [[Modal_UDP_Notation|chroma-positive generator]] = 6\19 ~=5/4)
 
{| class="wikitable"
|-
! UDP
! Steps
! Degrees
! Note names
|-
| 6{{pipe}}0
| 5 1 5 1 5 1 1
| 0 5 6 11 12 17 18
| C Eb E G G# B B#
|-
| 5{{pipe}}1
| 5 1 5 1 1 5 1
| 0 5 6 11 12 13 18
| C Eb E G G# Ab B#
|-
| 4{{pipe}}2
| 5 1 1 5 1 5 1
| 0 5 6 7 12 13 18
| C Eb E E# G# Ab B#
|-
| 3{{pipe}}3
| 1 5 1 5 1 5 1
| 0 1 6 7 12 13 18
| C C# E E# G# Ab B#
|-
| 2{{pipe}}4
| 1 5 1 5 1 1 5
| 0 1 6 7 12 13 14
| C C# E E# G# Ab A
|-
| 1{{pipe}}5
| 1 5 1 1 5 1 5
| 0 1 6 7 8 13 14
| C C# E E# F Ab A
|-
| 0{{pipe}}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&nbsp;7s]] / CPG = 6\19)
 
{| class="wikitable"
|-
! UDP
! Steps
! Degrees
! Note names
|-
| 9{{pipe}}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{{pipe}}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{{pipe}}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{{pipe}}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{{pipe}}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{{pipe}}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{{pipe}}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{{pipe}}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{{pipe}}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{{pipe}}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&nbsp;10s]] / CPG = 6\19 ~=5/4)
 
{| class="wikitable"
|-
! UDP
! Steps
! Degrees
! Note names
|-
| 12{{pipe}}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{{pipe}}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{{pipe}}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{{pipe}}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{{pipe}}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{{pipe}}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{{pipe}}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{{pipe}}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{{pipe}}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{{pipe}}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{{pipe}}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{{pipe}}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{{pipe}}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&nbsp;13s]] / CPG = 6\19)
 
{| class="wikitable"
|-
! UDP
! Steps
! Degrees
! Note names
|-
| 15{{pipe}}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{{pipe}}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{{pipe}}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{{pipe}}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{{pipe}}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{{pipe}}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{{pipe}}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{{pipe}}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{{pipe}}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{{pipe}}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{{pipe}}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{{pipe}}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{{pipe}}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{{pipe}}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{{pipe}}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{{pipe}}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]] ===
'''sensi[5]''' ([[3L&nbsp;2s]] / [[Modal_UDP_Notation|chroma-positive generator]] = 12\19)
 
{| class="wikitable"
|-
! UDP
! Mode steps
! Mode degrees
! Note names
|-
| 4{{pipe}}0
| 5 5 2 5 2
| 0 5 10 12 17
| C Eb Gb G# B
|-
| 3{{pipe}}1
| 5 2 5 5 2
| 0 5 7 12 17
| C Eb E# G# B
|-
| 2{{pipe}}2
| 5 2 5 2 5
| 0 5 7 12 14
| C Eb E# G# A
|-
| 1{{pipe}}3
| 2 5 5 2 5
| 0 2 7 12 14
| C Db E# G# A
|-
| 0{{pipe}}4
| 2 5 2 5 5
| 0 2 7 9 14
| C Db E# F# A
|}
 
'''sensi[8]''' ([[3L&nbsp;5s]] / CPG = 12\19)
 
{| class="wikitable"
|-
! UDP
! Mode steps
! Mode degrees
! Note names
|-
| 7{{pipe}}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{{pipe}}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{{pipe}}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{{pipe}}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{{pipe}}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{{pipe}}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{{pipe}}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{{pipe}}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&nbsp;3s]] / CPG = 7\19)
 
{| class="wikitable"
|-
! UDP
! Mode steps
! Mode degrees
! Note names
|-
| 10{{pipe}}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{{pipe}}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{{pipe}}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{{pipe}}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{{pipe}}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{{pipe}}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{{pipe}}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{{pipe}}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{{pipe}}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{{pipe}}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{{pipe}}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
|}
 
=== [[Meantone_family#Liese|Liese]] / [[Marvel_temperaments#Triton|Triton]] ===
'''liese[5]''' ([[2L&nbsp;3s]] / [[Modal_UDP_Notation|chroma-positive generator]] = 9\19 ~= 7/5)
 
{| class="wikitable"
|-
! UDP
! Steps
! Degrees
! Note names
|-
| 4{{pipe}}0
| 8 1 8 1 1
| 0 8 9 17 18
| C F F# B B#
|-
| 3{{pipe}}1
| 8 1 1 8 1
| 0 8 9 10 18
| C F F# Gb B#
|-
| 2{{pipe}}2
| 1 8 1 8 1
| 0 1 9 10 18
| C C# F# Gb B#
|-
| 1{{pipe}}3
| 1 8 1 1 8
| 0 1 9 10 11
| C C# F# Gb G
|-
| 0{{pipe}}4
| 1 1 8 1 8
| 0 1 2 10 11
| C C# Db Gb G
|}
 
'''liese[7]''' ([[2L&nbsp;5s]] / CPG = 9\19)
 
{| class="wikitable"
|-
! UDP
! Steps
! Degrees
! Note names
|-
| 6{{pipe}}0
| 7 1 1 7 1 1 1
| 0 7 8 9 16 17 18
| C E# F F# Bb B B#
|-
| 5{{pipe}}1
| 7 1 1 1 7 1 1
| 0 7 8 9 10 17 18
| C E# F F# Gb B B#
|-
| 4{{pipe}}2
| 1 7 1 1 7 1 1
| 0 1 8 9 10 17 18
| C C# F F# Gb B B#
|-
| 3{{pipe}}3
| 1 7 1 1 1 7 1
| 0 1 8 9 10 11 18
| C C# F F# Gb G B#
|-
| 2{{pipe}}4
| 1 1 7 1 1 7 1
| 0 1 2 9 10 11 18
| C C# Db F# Gb G B#
|-
| 1{{pipe}}5
| 1 1 7 1 1 1 7
| 0 1 2 9 10 11 12
| C C# Db F# Gb G G#
|-
| 0{{pipe}}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&nbsp;7s]] / CPG = 9\19)
 
{| class="wikitable"
|-
! UDP
! Steps
! Degrees
! Note names
|-
| 8{{pipe}}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{{pipe}}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{{pipe}}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{{pipe}}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{{pipe}}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{{pipe}}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{{pipe}}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{{pipe}}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{{pipe}}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&nbsp;9s]] / CPG = 9\19)
 
{| class="wikitable"
|-
! UDP
! Steps
! Degrees
! Note names
|-
| 10{{pipe}}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{{pipe}}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{{pipe}}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{{pipe}}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{{pipe}}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{{pipe}}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{{pipe}}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{{pipe}}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{{pipe}}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{{pipe}}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{{pipe}}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]])
 
{{Navbox scale gallery}}
 
[[Category:19edo]]
[[Category:modes]]

Latest revision as of 03:35, 28 September 2025

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

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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