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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"
|-
|-
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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|Orgone}}
{{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
*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:
*z mode: 2212121
{| class="wikitable"
*y mode: 2122121
|-
*x mode: 2121221
| Nerevarine mode
*V mode: 2121212
| 2212121
*U mode: 1221212
|-
*T mode: 1212212
| Vivecan mode
*S 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 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.
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"
|-
|-
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== [[Joan]] heptatonic (MOS 2L+5s, generator: 5\11) ==
== [[Joan]] heptatonic (MOS 2L+5s, generator: 5\11) ==
{| class="wikitable"
{| class="wikitable"
|-
|-
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{| 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"
|-
|-
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|}
|}


{{Navbox scale gallery}}
[[Category:Lists of scales]]
[[Category:11edo]]
[[Category:11edo]]
[[Category:Catalog]]
[[Category:Modes]]
[[Category:Edo]]
[[Category:Theory]]
Retrieved from "https://en.xen.wiki/w/11edo_modes"