11edo modes: Difference between revisions

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Some '''modes of [[11edo]]'''. Available, of course, in [[22edo]], [[33edo]], [[44edo]], etc. Add your very favourite ones here!
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) ==
== [[Machine]] hexatonic (MOS 5L 1s, generator: 2\11) ==
 
{| class="wikitable"
{| class="wikitable"
|-
|-
Line 19: Line 18:


The intervals of the LLsLLL mode (harmonics in bold):
The intervals of the LLsLLL mode (harmonics in bold):
{| class="wikitable sortable sorted"
{| class="wikitable sortable sorted"
|-
|-
! style="text-align:right" | Degree
! style="text-align: right;" | Degree
! | Cents
! Cents
! | Note name on C (22edo notation)
! Note name on C (22edo notation)
! | Approximate ratios
! Approximate ratios
! | #Gens up
! #Gens up
|-
|-
| | 1
| 1
| style="text-align:right;" | 0
| style="text-align: right;" | 0
| | C
| C
| | '''1/1'''
| 1/1
| | 0
| 0
|-
|-
| | 2
| 2
| style="text-align:right;" | 218.18
| style="text-align: right;" | 218.18
| | D
| D
| | 8/7, '''9/8''', 17/15
| 8/7, 9/8, 17/15
| | +1
| +1
|-
|-
| | 3
| 3
| style="text-align:right;" | 436.36
| style="text-align: right;" | 436.36
| | E
| E
| | 9/7, 14/11, 22/17
| 9/7, 14/11, 22/17
| | +2
| +2
|-
|-
| | 4
| 4
| style="text-align:right;" | 545.45
| style="text-align: right;" | 545.45
| | Gb
| Gb
| | '''11/8''', 15/11
| 11/8, 15/11
| | -3
| -3
|-
|-
| | 5
| 5
| style="text-align:right;" | 763.63
| style="text-align: right;" | 763.63
| | Ab
| Ab
| | 11/7, 14/9, 17/11
| 11/7, 14/9, 17/11
| | -2
| -2
|-
|-
| | 6
| 6
| style="text-align:right;" | 981.81
| style="text-align: right;" | 981.81
| | Bb
| Bb
| | '''7/4''', 16/9, 30/17
| 7/4, 16/9, 30/17
| | -1
| -1
|}
|}


== [[Orgone]] heptatonic (MOS 4L+3s, generator: 3\11) ==
== [[Orgone]] heptatonic (MOS 4L+3s, generator: 3\11) ==
{{main|Smitonic}}
[[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]]


{| class="wikitable"
{| class="wikitable"
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|}
|}


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


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


Assuming the symmetric 2121212 mode, the 1-4-7 chord is:
Assuming the symmetric 2121212 mode, the 1-4-7 chord is:
*8:11:14 on degrees 1 and 6
* 8:11:14 on degrees 1 and 6
*8:11:15 on degrees 3, 5, and 7
* 8:11:15 on degrees 3, 5, and 7
*17:22:30 or 25:32:44 on degrees 2 and 4
* 44:56:77 (approx. 25:32:44) on degrees 2 and 4
 


===Modal harmony===
=== Modal harmony ===
{{main|Smitonic}}
The seven modes are, from brightest to darkest:
The seven modes are, from brightest to darkest:
*2212121
{| class="wikitable"
*2122121
|-
*2121221
| Nerevarine mode
*2121212
| 2212121
*1221212
|-
*1212212
| Vivecan mode
*1212122
| 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:
Modally, the highest to lowest [https://en.wikipedia.org/wiki/Entropy_(information_theory) entropy] scale degrees (unison = 1) are:
Line 156: Line 175:
* 4 and 5 (equally): .86 bits
* 4 and 5 (equally): .86 bits
* 3 and 6 (equally): .59 bits
* 3 and 6 (equally): .59 bits
(if a scale degree is highly entropic 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, 16:17:22:28, and (the most "minor" version of 1-2-4-7) 32:34:41:56.
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) ==
== [[Joan]] pentatonic (MOS 2L+3s, generator: 5\11) ==
{| class="wikitable"
{| class="wikitable"
|-
|-
Line 174: Line 192:


== [[Joan]] heptatonic (MOS 2L+5s, generator: 5\11) ==
== [[Joan]] heptatonic (MOS 2L+5s, generator: 5\11) ==
{| class="wikitable"
{| class="wikitable"
|-
|-
Line 219: Line 236:
{| class="wikitable sortable sorted"
{| class="wikitable sortable sorted"
|-
|-
! style="text-align:right" | Degree
! style="text-align: right;" | Degree
! | Cents
! Cents
! | Note name on C (22edo notation)
! Note name on C (22edo notation)
! | Approximate ratios
! Approximate ratios
! | #Gens up
! #Gens up
|-
|-
| | 1
| 1
| style="text-align:right;" | 0
| style="text-align: right;" | 0
| | C
| C
| | '''1/1'''
| 1/1
| | 0
| 0
|-
|-
| | 2
| 2
| style="text-align:right;" | 218.18
| style="text-align: right;" | 218.18
| | D
| D
| | 8/7, '''9/8''', 17/15
| 8/7, 9/8, 17/15
| | +7
| +7
|-
|-
| | 3
| 3
| style="text-align:right;" | 327.27
| style="text-align: right;" | 327.27
| | Eb^
| Eb^
| | 6/5, 11/9, 17/14
| 6/5, 11/9, 17/14
| | +5
| +5
|-
|-
| | 4
| 4
| style="text-align:right;" | 436.36
| style="text-align: right;" | 436.36
| | E
| E
| | 9/7, 14/11, 22/17
| 9/7, 14/11, 22/17
| | +3
| +3
|-
|-
| | 5
| 5
| style="text-align:right;" | 545.45
| style="text-align: right;" | 545.45
| | F^
| F^
| | '''11/8''', 15/11
| 11/8, 15/11
| | +1
| +1
|-
|-
| | 6
| 6
| style="text-align:right;" | 654.54
| style="text-align: right;" | 654.54
| | Gv
| Gv
| | 16/11, 22/15
| 16/11, 22/15
| | -1
| -1
|-
|-
| | 7
| 7
| style="text-align:right;" | 872.73
| style="text-align: right;" | 872.73
| | Av
| Av
| | 5/3, 18/11, 28/17
| 5/3, 18/11, 28/17
| | +6
| +6
|-
|-
| | 8
| 8
| style="text-align:right;" | 981.81
| style="text-align: right;" | 981.81
| | Bb
| Bb
| | '''7/4''', 16/9, 30/17
| 7/4, 16/9, 30/17
| | +4
| +4
|-
|-
| | 9
| 9
| style="text-align:right;" | 1090.90
| style="text-align: right;" | 1090.90
| | Bv
| Bv
| | '''15/8''', 17/9, 28/15, 32/17
| 15/8, 17/9, 28/15, 32/17
| | +2
| +2
|}
|}


== Swooning Rushes ([[MOS Cradle]]) ==
== Swooning Rushes ([[MOS Cradle]]) ==
{| class="wikitable"
{| class="wikitable"
|-
|-
Line 295: Line 311:
|}
|}


{{Navbox scale gallery}}
[[Category:Lists of scales]]
[[Category:11edo]]
[[Category:11edo]]
[[Category:Catalog]]
[[Category:Modes]]
[[Category:Edo]]
[[Category:Theory]]

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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