22edo modes

Some modes available in 22edo. Please add more, discovered or newly-composed! Note also that 22edo can play all 11edo modes as well.

Orwell

5 notes MOS, 4L+1s (Grumpy pentatonic)

2	5	5	5	5
5	2	5	5	5
5	5	2	5	5
5	5	5	2	5
5	5	5	5	2

9 notes MOS, 4L+5s (fair bug)

2 3 2 3 2 3 2 3 2
3 2 3 2 3 2 3 2 2	*
2 3 2 3 2 3 2 2 3
3 2 3 2 3 2 2 3 2
2 3 2 3 2 2 3 2 3
3 2 3 2 2 3 2 3 2
2 3 2 2 3 2 3 2 3
3 2 2 3 2 3 2 3 2
2 2 3 2 3 2 3 2 3

*Audio example:

13 notes MOS, 9L+4s

1	2	2	1	2	2	1	2	2	1	2	2	2
2	2	1	2	2	1	2	2	1	2	2	2	1
2	1	2	2	1	2	2	1	2	2	2	1	2
1	2	2	1	2	2	1	2	2	2	1	2	2
2	2	1	2	2	1	2	2	2	1	2	2	1
2	1	2	2	1	2	2	2	1	2	2	1	2
1	2	2	1	2	2	2	1	2	2	1	2	2
2	2	1	2	2	2	1	2	2	1	2	2	1
2	1	2	2	2	1	2	2	1	2	2	1	2
1	2	2	2	1	2	2	1	2	2	1	2	2
2	2	2	1	2	2	1	2	2	1	2	2	1
2	2	1	2	2	1	2	2	1	2	2	1	2
2	1	2	2	1	2	2	1	2	2	1	2	2

Porcupine

See also Porcupine Temperament Modal Harmony for many more MODMOS modes.

7 notes MOS, 1L+6s (Happy heptatonic)

3 3 3 3 3 3 4	Magical seventh mode
3 3 3 3 3 4 3	Diminished
3 3 3 3 4 3 3	Diminished
3 3 3 4 3 3 3	symmetric minor ("dorian")	*
3 3 4 3 3 3 3	bright minor
3 4 3 3 3 3 3	dark major
4 3 3 3 3 3 3	bright otonal major	#

*Audio example:

#Audio example:

MODMOS of 7 notes MOS

• Porcupine bright harmonic 11th mode - Porcupine[7] 6|0 b7 4 3 3 3 3 2 4
• Porcupine bright major #6 #7 - Porcupine[7] 6|0 #6 #7 - 4 3 3 3 4 3 2
• Porcupine bright major #7 - Porcupine[7] 6|0 #7 - 4 3 3 3 3 4 2
• Porcupine bright minor #2 - Porcupine[7] 4|2 #2 4 2 4 3 3 3 3 (mode of bright major #7)
• Porcupine dark minor #2 - Porcupine[7] 3|3 #2 4 2 3 4 3 3 3 (inverse of bright major #6 #7)

8 notes MOS, 7L+1s (Grumpy octatonic)

3 3 3 3 3 3 3 1
3 3 3 3 3 3 1 3
3 3 3 3 3 1 3 3
3 3 3 3 1 3 3 3	kind of minor
3 3 3 1 3 3 3 3	kind of minor
3 3 1 3 3 3 3 3	both minor and major
3 1 3 3 3 3 3 3	kind of major
1 3 3 3 3 3 3 3	kind of major

15 notes MOS, 7L+8s

1 2 1 2 1 2 1 2 1 2 1 2 1 2 1
2 1 2 1 2 1 2 1 2 1 2 1 2 1 1
1 2 1 2 1 2 1 2 1 2 1 2 1 1 2
2 1 2 1 2 1 2 1 2 1 2 1 1 2 1
1 2 1 2 1 2 1 2 1 2 1 1 2 1 2
2 1 2 1 2 1 2 1 2 1 1 2 1 2 1
1 2 1 2 1 2 1 2 1 1 2 1 2 1 2
2 1 2 1 2 1 2 1 1 2 1 2 1 2 1
1 2 1 2 1 2 1 1 2 1 2 1 2 1 2
2 1 2 1 2 1 1 2 1 2 1 2 1 2 1
1 2 1 2 1 1 2 1 2 1 2 1 2 1 2
2 1 2 1 1 2 1 2 1 2 1 2 1 2 1
1 2 1 1 2 1 2 1 2 1 2 1 2 1 2
2 1 1 2 1 2 1 2 1 2 1 2 1 2 1
1 1 2 1 2 1 2 1 2 1 2 1 2 1 2

Hedgehog

6 notes MOS, 2L+4s (Rice hexatonic)

3	5	3	3	5	3
3	3	5	3	3	5
5	3	3	5	3	3

8 notes MOS, 6L+2s (Biggie octatonic)

3 3 3 2 3 3 3 2

3 3 2 3 3 3 2 3

3 2 3 3 3 2 3 3

2 3 3 3 2 3 3 3

14 notes MOS, 8L+6s

2 1 2 1 2 1 2 2 1 2 1 2 1 2

1 2 1 2 1 2 2 1 2 1 2 1 2 2

2 1 2 1 2 2 1 2 1 2 1 2 2 1

1 2 1 2 2 1 2 1 2 1 2 2 1 2

2 1 2 2 1 2 1 2 1 2 2 1 2 1

1 2 2 1 2 1 2 1 2 2 1 2 1 2

2 2 1 2 1 2 1 2 2 1 2 1 2 1

Superpyth

5 notes MOS, 2L+3s (classic pentatonic)

4	5	4	5	4
4	4	5	4	5
5	4	4	5	4
4	5	4	4	5
5	4	5	4	4

7 notes MOS, 5L+2s (diatonic)

4 4 1 4 4 4 1	Major (Ionian)
4 1 4 4 4 1 4	Dorian
1 4 4 4 1 4 4	Phrygian
4 4 4 1 4 4 1	Lydian
4 4 1 4 4 1 4	Mixolydian
4 1 4 4 1 4 4	Minor (Aeolian)
1 4 4 1 4 4 4	Locrian

Subsets of 7 notes MOS

• Manohari - 5 4 4 4 1 4
• Shailaja - 5 8 1 4 4
• Subminor hexatonic - 4 1 4 4 5 4

MODMOS of 7 notes MOS

• Superpyth double harmonic major - Superpyth[7] 5|1 b2 b6 - 1 7 1 4 1 7 1
• Superpyth harmonic major - Superpyth[7] 5|1 b6 - 4 4 1 4 1 7 1 (inverse of harmonic minor)
• Superpyth harmonic minor - Superpyth[7] 2|4 #7 - 4 1 4 4 1 7 1
• Superpyth melodic minor - Superpyth[7] 5|1 b3 - 4 1 4 4 4 4 1

12 notes MOS, 5L+7s

1	3	1	3	1	3	1	1	3	1	3	1
1	1	3	1	3	1	3	1	1	3	1	3
3	1	1	3	1	3	1	3	1	1	3	1
1	3	1	1	3	1	3	1	3	1	1	3
3	1	3	1	1	3	1	3	1	3	1	1
1	3	1	3	1	1	3	1	3	1	3	1
1	1	3	1	3	1	1	3	1	3	1	3
3	1	1	3	1	3	1	1	3	1	3	1
1	3	1	1	3	1	3	1	1	3	1	3
3	1	3	1	1	3	1	3	1	1	3	1
1	3	1	3	1	1	3	1	3	1	1	3
3	1	3	1	3	1	1	3	1	3	1	1

Scala files for all 12 modes

Audio comparison of the 12 modes

17 notes MOS

1 2 1 1 1 2 1 1 2 1 1 2 1 1 1 2 1

Pajara

10 notes

"Symmetrical" modes are MOS, 2L+8s (Rice decatonic); "Pentachordal" modes are not MOS.

(The names of the modes are Paul Erlich's - see http://lumma.org/tuning/erlich/erlich-decatonic.pdf.)

2 2 3 2 2 2 3 2 2 2	Standard Pentachordal Major	*
2 2 3 2 2 2 2 3 2 2	Static Symmetrical Major
2 3 2 2 2 2 2 3 2 2	Alternate Pentachordal Major
2 3 2 2 2 2 3 2 2 2	Dynamic Symmetrical Major
2 2 2 3 2 2 2 2 2 3	Standard Pentachordal Minor
2 2 2 3 2 2 2 2 3 2	Static Symmetrical Minor
2 2 2 2 3 2 2 2 3 2	Alternate Pentachordal Minor
2 2 2 2 3 2 2 2 2 3	Dynamic Symmetrical Minor

*Audio example:

MODMOS of 10 notes MOS

• Pentachordal decatonic - Pajara[10] 2|2 (2) #8 - 2 2 3 2 2 2 3 2 2 2

12 notes MOS, 10L+2s

2	2	1	2	2	2	2	2	1	2	2	2
2	2	2	1	2	2	2	2	2	1	2	2
2	2	2	2	1	2	2	2	2	2	1	2
2	2	2	2	2	1	2	2	2	2	2	1
1	2	2	2	2	2	1	2	2	2	2	2
2	1	2	2	2	2	2	1	2	2	2	2

MODMOS of 12 notes MOS

• Hexachordal dodecatonic - Pajara[12] 3|2 (2) b10 or Pajara[12] 2|3 (2) #4 - 2 2 2 1 2 2 2 2 1 2 2 2

Doublewide/Fleetwood

6 notes MOS, 4L+2s (bicycle)

5	1	5	5	1	5
5	5	1	5	5	1
1	5	5	1	5	5

10 notes MOS, 4L+6s (fair bicycle)

1	4	1	4	1	1	4	1	4	1
1	1	4	1	4	1	1	4	1	4
4	1	1	4	1	4	1	1	4	1
1	4	1	1	4	1	4	1	1	4
4	1	4	1	1	4	1	4	1	1

14 notes MOS, 4L+10s

1	3	1	1	1	3	1	1	3	1	1	1	3	1
1	1	3	1	1	1	3	1	1	3	1	1	1	3
3	1	1	3	1	1	1	3	1	1	3	1	1	1
1	3	1	1	3	1	1	1	3	1	1	3	1	1
1	1	3	1	1	3	1	1	1	3	1	1	3	1
1	1	1	3	1	1	3	1	1	1	3	1	1	3
3	1	1	1	3	1	1	3	1	1	1	3	1	1

18 notes MOS

2 1 1 1 2 1 1 1 1 2 1 1 1 2 1 1 1 1

Astrology

6 notes MOS, 4L+2s (bicycle)

4	3	4	4	3	4	*
4	4	3	4	4	3
3	4	4	3	4	4

*Audio example:

10 notes MOS, 6L+4s (unfair bicycle)

3	1	3	1	3	3	1	3	1	3
3	3	1	3	1	3	3	1	3	1
1	3	3	1	3	1	3	3	1	3
3	1	3	3	1	3	1	3	3	1
1	3	1	3	3	1	3	1	3	3

16 notes MOS

2 1 2 1 1 2 1 1 2 1 2 1 1 2 1 1

Magic/Telepathy

7 notes MOS, 3L+4s (mosh)

1	6	1	6	1	6	1
1	1	6	1	6	1	6
6	1	1	6	1	6	1
1	6	1	1	6	1	6
6	1	6	1	1	6	1
1	6	1	6	1	1	6
6	1	6	1	6	1	1

10 notes MOS, 3L+7s (fair mosh)

1	5	1	1	5	1	1	1	5	1
1	1	5	1	1	5	1	1	1	5
5	1	1	5	1	1	5	1	1	1
1	5	1	1	5	1	1	5	1	1
1	1	5	1	1	5	1	1	5	1
1	1	1	5	1	1	5	1	1	5
5	1	1	1	5	1	1	5	1	1
1	5	1	1	1	5	1	1	5	1
1	1	5	1	1	1	5	1	1	5
5	1	1	5	1	1	1	5	1	1

13 notes MOS, 3L+10s

1	1	4	1	1	1	4	1	1	1	4	1	1
1	1	1	4	1	1	1	4	1	1	1	4	1
1	1	1	1	4	1	1	1	4	1	1	1	4
4	1	1	1	1	4	1	1	1	4	1	1	1
1	4	1	1	1	1	4	1	1	1	4	1	1
1	1	4	1	1	1	1	4	1	1	1	4	1
1	1	1	4	1	1	1	1	4	1	1	1	4
4	1	1	1	4	1	1	1	1	4	1	1	1
1	4	1	1	1	4	1	1	1	1	4	1	1
1	1	4	1	1	1	4	1	1	1	1	4	1
1	1	1	4	1	1	1	4	1	1	1	1	4
4	1	1	1	4	1	1	1	4	1	1	1	1
1	4	1	1	1	4	1	1	1	4	1	1	1

16 notes MOS

3 1 1 1 1 3 1 1 1 1 3 1 1 1 1 1

19 notes MOS

1 1 1 2 1 1 1 1 1 2 1 1 1 1 1 2 1 1 1

Marvel

• Marvel double harmonic major - 2 5 2 4 2 5 2
• Marvel detempering of Negri[9] and August[9] - 2 3 2 2 4 2 2 3 2
• Marvel hexatonic - 5 2 6 2 5 2

Further variations of major and minor

• "just" harmonic major - 4 3 2 4 2 5 2
• "just" harmonic minor - 4 2 3 4 2 5 2
• "just" major pentatonic - 4 3 6 3 6
• "just" melodic minor - 4 2 3 4 3 4 2
• "just" minor pentatonic (inverse of "just" major pentatonic) - 6 3 4 6 3
• tetrachordal major, Sa grama - 4 3 2 4 4 3 2
• inverse of tetrachordal major, "just"/tetrachordal minor - 4 2 3 4 2 3 4
• Zarlino/Ptolemy diatonic, "just" major, Ma grama - 4 3 2 4 3 4 2
• inverse of Zarlino/Ptolemy diatonic, natural minor - 4 2 3 4 2 4 3

Others

• 2.3.7.11 4-SN octatonic - 3 2 3 5 3 2 3 1
• Aurora scale - 2 5 6 4 5
• Blackdye / Syntonic dipentatonic - 1 3 2 3 1 3 2 3 1 3
• Chromatic tetrachord octave species - 2 2 5 4 2 2 5, 5 2 2 4 5 2 2, 2 5 2 4 2 5 2
• Enharmonic tetrachord octave species - 1 1 7 4 1 1 7, 7 1 1 4 7 1 1, 1 7 1 4 1 7 1
• Enharmonic trichord octave species - 2 7 4 2 7, 7 2 4 7 2
• Kai Lugheidh's mode - 2 5 3 3 5 2 2