11edo modes: Difference between revisions

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<h2>IMPORTED REVISION FROM WIKISPACES</h2>
Some '''modes of [[11edo]]'''. Available, of course, in [[22edo]], [[33edo]], [[44edo]], etc. Add your very favourite ones here!
This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
: This revision was by author [[User:hstraub|hstraub]] and made on <tt>2009-08-13 10:14:21 UTC</tt>.<br>
: The original revision id was <tt>84165567</tt>.<br>
: The revision comment was: <tt>MOS type 4L+3s is mish</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 of [[11edo]]. Add yr very favorite ones here!


==11edo mish (MOS 4L+3s)==  
== [[Machine]] hexatonic (MOS 5L&nbsp;1s, generator: 2\11) ==
{| class="wikitable"
|-
| 2 2 2 2 2 1
|-
| 2 2 2 2 1 2
|-
| 2 2 2 1 2 2
|-
| 2 2 1 2 2 2
|-
| 2 1 2 2 2 2
|-
| 1 2 2 2 2 2
|}


|| 2 1 2 1 2 1 2 ||
The intervals of the LLsLLL mode (harmonics in bold):
|| 1 2 1 2 1 2 2 ||
|| 2 1 2 1 2 2 1 ||
|| 1 2 1 2 2 1 2 ||
|| 2 1 2 2 1 2 1 ||
|| 1 2 2 1 2 1 2 ||
|| 2 2 1 2 1 2 1 ||


==Swooning Rushes ([[MOS Cradle]])==  
{| class="wikitable sortable sorted"
|-
! style="text-align: right;" | Degree
! Cents
! Note name on C (22edo notation)
! Approximate ratios
! #Gens up
|-
| 1
| style="text-align: right;" | 0
| C
| 1/1
| 0
|-
| 2
| style="text-align: right;" | 218.18
| D
| 8/7, 9/8, 17/15
|  +1
|-
| 3
| style="text-align: right;" | 436.36
| E
| 9/7, 14/11, 22/17
|  +2
|-
| 4
| style="text-align: right;" | 545.45
| Gb
| 11/8, 15/11
|  -3
|-
| 5
| style="text-align: right;" | 763.63
| Ab
| 11/7, 14/9, 17/11
|  -2
|-
| 6
| style="text-align: right;" | 981.81
| Bb
| 7/4, 16/9, 30/17
|  -1
|}


|| 2 3 1 3 2 ||
== [[Orgone]] heptatonic (MOS 4L+3s, generator: 3\11) ==
|| 3 1 3 2 2 ||
{{main|Smitonic}}
|| 1 3 2 2 3 ||
|| 3 2 2 3 1 ||
|| 2 2 3 1 3 ||</pre></div>
<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;11edo Modes&lt;/title&gt;&lt;/head&gt;&lt;body&gt;Some modes of &lt;a class="wiki_link" href="/11edo"&gt;11edo&lt;/a&gt;. Add yr very favorite ones here!&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:0:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc0"&gt;&lt;a name="x-11edo mish (MOS 4L+3s)"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:0 --&gt;11edo mish (MOS 4L+3s)&lt;/h2&gt;
&lt;br /&gt;


[[File:11EDO_cheat_sheet.png|400px|thumb|right|11EDO Orgone smitonic cheat sheet using modified diatonic notation (G#=A, Ab=G), and smitonic interval names]]


&lt;table class="wiki_table"&gt;
{| class="wikitable"
    &lt;tr&gt;
|-
        &lt;td&gt;2 1 2 1 2 1 2&lt;br /&gt;
| 2 1 2 1 2 1 2
&lt;/td&gt;
|-
    &lt;/tr&gt;
| 1 2 1 2 1 2 2
    &lt;tr&gt;
|-
        &lt;td&gt;1 2 1 2 1 2 2&lt;br /&gt;
| 2 1 2 1 2 2 1
&lt;/td&gt;
|-
    &lt;/tr&gt;
| 1 2 1 2 2 1 2
    &lt;tr&gt;
|-
        &lt;td&gt;2 1 2 1 2 2 1&lt;br /&gt;
| 2 1 2 2 1 2 1
&lt;/td&gt;
|-
    &lt;/tr&gt;
| 1 2 2 1 2 1 2
    &lt;tr&gt;
|-
        &lt;td&gt;1 2 1 2 2 1 2&lt;br /&gt;
| 2 2 1 2 1 2 1
&lt;/td&gt;
|}
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;2 1 2 2 1 2 1&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;1 2 2 1 2 1 2&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;2 2 1 2 1 2 1&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
&lt;/table&gt;


&lt;br /&gt;
The intervals of the symmetric LsLsLsL mode (harmonics in bold):
&lt;!-- ws:start:WikiTextHeadingRule:2:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc1"&gt;&lt;a name="x-Swooning Rushes (MOS Cradle)"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:2 --&gt;Swooning Rushes (&lt;a class="wiki_link" href="/MOS%20Cradle"&gt;MOS Cradle&lt;/a&gt;)&lt;/h2&gt;
&lt;br /&gt;


{| class="wikitable sortable sorted"
|-
! style="text-align: right;" | Degree (1 = tonic)
! Cents
! Note name on C (22edo notation)
! Approximate ratios
! #Gens up
|-
| 1
| style="text-align: right;" | 0
| C
| 1/1
| 0
|-
| 2
| style="text-align: right;" | 218.18
| D
| 8/7, 9/8, 17/15
|  -3
|-
| 3
| style="text-align: right;" | 327.27
| Eb^
| 6/5, 11/9, 17/14
|  +1
|-
| 4
| style="text-align: right;" | 545.45
| F^
| 11/8, 15/11
|  -2
|-
| 5
| style="text-align: right;" | 654.54
| Gv
| 16/11, 22/15
|  +2
|-
| 6
| style="text-align: right;" | 872.72
| Av
| 5/3, 18/11, 28/17
|  -1
|-
| 7
| style="text-align: right;" | 981.81
| Bb
| 7/4, 16/9, 30/17
|  +3
|}


&lt;table class="wiki_table"&gt;
Assuming the symmetric 2121212 mode, the 1-4-7 chord is:
    &lt;tr&gt;
* 8:11:14 on degrees 1 and 6
        &lt;td&gt;2 3 1 3 2&lt;br /&gt;
* 8:11:15 on degrees 3, 5, and 7
&lt;/td&gt;
* 44:56:77 (approx. 25:32:44) on degrees 2 and 4
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;3 1 3 2 2&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;1 3 2 2 3&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;3 2 2 3 1&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;2 2 3 1 3&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
&lt;/table&gt;


&lt;/body&gt;&lt;/html&gt;</pre></div>
=== Modal harmony ===
{{main|Smitonic}}
The seven modes are, from brightest to darkest:
{| class="wikitable"
|-
| Nerevarine mode
| 2212121
|-
| Vivecan mode
| 2122121
|-
| Lorkhanic mode
| 2121221
|-
| Sothic mode
| 2121212
|-
| Kagrenacan mode
| 1221212
|-
| Almalexian mode
| 1212212
|-
| Dagothic mode
| 1212122
|}
 
Modally, the highest to lowest [https://en.wikipedia.org/wiki/Entropy_(information_theory) entropy] scale degrees (unison = 1) are:
* 2 and 7 (equally): .99 bits
* 4 and 5 (equally): .86 bits
* 3 and 6 (equally): .59 bits
If a scale degree is high entropy it tends to be the most informative on average; the modes that have this interval as major and minor respectively are roughly a 50-50 split. This tells us that unlike in the diatonic scale, thirds and sixths are the ''least'' informative in distinguishing orgone modes. On the other hand, seconds, fourths and sevenths are highly informative, and fortunately, these scale degrees appear in the most consonant triads and tetrads of 11edo orgone, namely 8:9:11:15, 8:9:11:14 and 16:17:22:28. Those chords are therefore crucial for Orgone[7] modal harmony.
 
== [[Joan]] pentatonic (MOS 2L+3s, generator: 5\11) ==
{| class="wikitable"
|-
| 1 4 1 4 1
|-
| 4 1 4 1 1
|-
| 1 4 1 1 4
|-
| 4 1 1 4 1
|-
| 1 1 4 1 4
|}
 
== [[Joan]] heptatonic (MOS 2L+5s, generator: 5\11) ==
{| class="wikitable"
|-
| 1 1 1 3 1 1 3
|-
| 1 1 3 1 1 3 1
|-
| 1 3 1 1 3 1 1
|-
| 3 1 1 3 1 1 1
|-
| 1 1 3 1 1 1 3
|-
| 1 3 1 1 1 3 1
|-
| 3 1 1 1 3 1 1
|}
 
 
== [[Joan]] nonatonic (MOS 2L+7s, generator: 5\11) ==
 
{| class="wikitable"
|-
| 1 1 1 2 1 1 1 2 1
|-
| 1 1 2 1 1 1 2 1 1
|-
| 1 2 1 1 1 2 1 1 1
|-
| 2 1 1 1 2 1 1 1 1
|-
| 1 1 1 2 1 1 1 1 2
|-
| 1 1 2 1 1 1 1 2 1
|-
| 1 2 1 1 1 1 2 1 1
|-
| 2 1 1 1 1 2 1 1 1
|-
| 1 1 1 1 2 1 1 1 2
|}
 
The intervals of the LssssLsss mode (harmonics in bold):
{| class="wikitable sortable sorted"
|-
! style="text-align: right;" | Degree
! Cents
! Note name on C (22edo notation)
! Approximate ratios
! #Gens up
|-
| 1
| style="text-align: right;" | 0
| C
| 1/1
| 0
|-
| 2
| style="text-align: right;" | 218.18
| D
| 8/7, 9/8, 17/15
|  +7
|-
| 3
| style="text-align: right;" | 327.27
| Eb^
| 6/5, 11/9, 17/14
|  +5
|-
| 4
| style="text-align: right;" | 436.36
| E
| 9/7, 14/11, 22/17
|  +3
|-
| 5
| style="text-align: right;" | 545.45
| F^
| 11/8, 15/11
|  +1
|-
| 6
| style="text-align: right;" | 654.54
| Gv
| 16/11, 22/15
|  -1
|-
| 7
| style="text-align: right;" | 872.73
| Av
| 5/3, 18/11, 28/17
|  +6
|-
| 8
| style="text-align: right;" | 981.81
| Bb
| 7/4, 16/9, 30/17
|  +4
|-
| 9
| style="text-align: right;" | 1090.90
| Bv
| 15/8, 17/9, 28/15, 32/17
|  +2
|}
 
== Swooning Rushes ([[MOS Cradle]]) ==
{| class="wikitable"
|-
| 2 3 1 3 2
|-
| 3 1 3 2 2
|-
| 1 3 2 2 3
|-
| 3 2 2 3 1
|-
| 2 2 3 1 3
|}
 
{{Navbox scale gallery}}
 
[[Category:Lists of scales]]
[[Category:11edo]]
[[Category:Modes]]

Latest revision as of 09:08, 16 April 2025

Some modes of 11edo. Available, of course, in 22edo, 33edo, 44edo, etc. Add your very favourite ones here!

Machine hexatonic (MOS 5L 1s, generator: 2\11)

2 2 2 2 2 1
2 2 2 2 1 2
2 2 2 1 2 2
2 2 1 2 2 2
2 1 2 2 2 2
1 2 2 2 2 2

The intervals of the LLsLLL mode (harmonics in bold):

Degree Cents Note name on C (22edo notation) Approximate ratios #Gens up
1 0 C 1/1 0
2 218.18 D 8/7, 9/8, 17/15 +1
3 436.36 E 9/7, 14/11, 22/17 +2
4 545.45 Gb 11/8, 15/11 -3
5 763.63 Ab 11/7, 14/9, 17/11 -2
6 981.81 Bb 7/4, 16/9, 30/17 -1

Orgone heptatonic (MOS 4L+3s, generator: 3\11)

Main article: Smitonic
11EDO Orgone smitonic cheat sheet using modified diatonic notation (G#=A, Ab=G), and smitonic interval names
2 1 2 1 2 1 2
1 2 1 2 1 2 2
2 1 2 1 2 2 1
1 2 1 2 2 1 2
2 1 2 2 1 2 1
1 2 2 1 2 1 2
2 2 1 2 1 2 1

The intervals of the symmetric LsLsLsL mode (harmonics in bold):

Degree (1 = tonic) Cents Note name on C (22edo notation) Approximate ratios #Gens up
1 0 C 1/1 0
2 218.18 D 8/7, 9/8, 17/15 -3
3 327.27 Eb^ 6/5, 11/9, 17/14 +1
4 545.45 F^ 11/8, 15/11 -2
5 654.54 Gv 16/11, 22/15 +2
6 872.72 Av 5/3, 18/11, 28/17 -1
7 981.81 Bb 7/4, 16/9, 30/17 +3

Assuming the symmetric 2121212 mode, the 1-4-7 chord is:

  • 8:11:14 on degrees 1 and 6
  • 8:11:15 on degrees 3, 5, and 7
  • 44:56:77 (approx. 25:32:44) on degrees 2 and 4

Modal harmony

Main article: Smitonic

The seven modes are, from brightest to darkest:

Nerevarine mode 2212121
Vivecan mode 2122121
Lorkhanic mode 2121221
Sothic mode 2121212
Kagrenacan mode 1221212
Almalexian mode 1212212
Dagothic mode 1212122

Modally, the highest to lowest entropy scale degrees (unison = 1) are:

  • 2 and 7 (equally): .99 bits
  • 4 and 5 (equally): .86 bits
  • 3 and 6 (equally): .59 bits

If a scale degree is high entropy it tends to be the most informative on average; the modes that have this interval as major and minor respectively are roughly a 50-50 split. This tells us that unlike in the diatonic scale, thirds and sixths are the least informative in distinguishing orgone modes. On the other hand, seconds, fourths and sevenths are highly informative, and fortunately, these scale degrees appear in the most consonant triads and tetrads of 11edo orgone, namely 8:9:11:15, 8:9:11:14 and 16:17:22:28. Those chords are therefore crucial for Orgone[7] modal harmony.

Joan pentatonic (MOS 2L+3s, generator: 5\11)

1 4 1 4 1
4 1 4 1 1
1 4 1 1 4
4 1 1 4 1
1 1 4 1 4

Joan heptatonic (MOS 2L+5s, generator: 5\11)

1 1 1 3 1 1 3
1 1 3 1 1 3 1
1 3 1 1 3 1 1
3 1 1 3 1 1 1
1 1 3 1 1 1 3
1 3 1 1 1 3 1
3 1 1 1 3 1 1


Joan nonatonic (MOS 2L+7s, generator: 5\11)

1 1 1 2 1 1 1 2 1
1 1 2 1 1 1 2 1 1
1 2 1 1 1 2 1 1 1
2 1 1 1 2 1 1 1 1
1 1 1 2 1 1 1 1 2
1 1 2 1 1 1 1 2 1
1 2 1 1 1 1 2 1 1
2 1 1 1 1 2 1 1 1
1 1 1 1 2 1 1 1 2

The intervals of the LssssLsss mode (harmonics in bold):

Degree Cents Note name on C (22edo notation) Approximate ratios #Gens up
1 0 C 1/1 0
2 218.18 D 8/7, 9/8, 17/15 +7
3 327.27 Eb^ 6/5, 11/9, 17/14 +5
4 436.36 E 9/7, 14/11, 22/17 +3
5 545.45 F^ 11/8, 15/11 +1
6 654.54 Gv 16/11, 22/15 -1
7 872.73 Av 5/3, 18/11, 28/17 +6
8 981.81 Bb 7/4, 16/9, 30/17 +4
9 1090.90 Bv 15/8, 17/9, 28/15, 32/17 +2

Swooning Rushes (MOS Cradle)

2 3 1 3 2
3 1 3 2 2
1 3 2 2 3
3 2 2 3 1
2 2 3 1 3


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