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)

Main article: Smitonic

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

Main article: Smitonic

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

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