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:
- 2212121
- 2122121
- 2121221
- 2121212
- 1221212
- 1212212
- 1212122
Modally, the least to most entropic scale degrees are:
- 2 and 7 (equally): .99 bits
- 4 and 5 (equally): .86 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.
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 |