11edo modes
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)
| 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
- 17:22:30 or 25:32:44 on degrees 2 and 4
Modal harmony
The seven modes are, from brightest to darkest:
- z mode: 2212121
- y mode: 2122121
- x mode: 2121221
- V mode: 2121212
- U mode: 1221212
- T mode: 1212212
- S 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, 16:17:22:28, and (the most "minor" version of 1-2-4-7) 28:30:32:49.
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 |