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)
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
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, pathological)
| 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
|
| 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
|
