41edo modes

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This page lists some useful and/or interesting modes (subsets) of 41edo .

MOS

(maximally even scales indicated by *)

generator = 1\41

[3] [4] [5] etc.

[40*] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2

g=2 (Hemimiracle)

[3] [4] [5] etc.

[20*] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 3

[21*] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 1

g=3 (Octacot)

[3] [4] [5] etc.

[13] 3 3 3 3 3 3 3 3 3 3 3 3 5

[14*] 3 3 3 3 3 3 3 3 3 3 3 3 3 2

[27*] 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 2

g=4 (Miracle)

[3] [4] [5] etc.

[10*] 4 4 4 4 4 4 4 4 4 5

[11] 4 4 4 4 4 4 4 4 4 4 1

[21] 3 1 3 1 3 1 3 1 3 1 3 1 3 1 3 1 3 1 3 1 1

[31*] 2 1 1 2 1 1 2 1 1 2 1 1 2 1 1 2 1 1 2 1 1 2 1 1 2 1 1 2 1 1 1

g=5 (bohpier)

[8*] 5 5 5 5 5 5 5 6

[9] 5 5 5 5 5 5 5 5 1

[17] 4 1 4 1 4 1 4 1 4 1 4 1 4 1 4 1 1

[25] 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

[33*] 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

note: the non-octave Bohlen-Pierce scale is simply 5 5 5 5 5 5 5 5 5 5 5 5 5, repeating at 3/1 (65\41)

g=6 (Tetracot / Bunya / Monkey)

[7*] 6 6 6 6 6 6 5

[13] 1 5 1 5 1 5 1 5 1 5 1 5 5

[20] 1 1 4 1 1 4 1 1 4 1 1 4 1 1 4 1 1 4 1 4

[27] 1 1 1 3 1 1 1 3 1 1 1 3 1 1 1 3 1 1 1 3 1 1 1 3 1 1 3

[34*] 1 1 1 1 2 1 1 1 1 2 1 1 1 1 2 1 1 1 1 2 1 1 1 1 2 1 1 1 1 2 1 1 1 2

g=7 (Baldy)

[6*] 7 7 7 7 7 6

[11] 1 6 1 6 1 6 1 6 1 6 6

[17] 1 1 5 1 1 5 1 1 5 1 1 5 1 1 5 1 5

[23] 1 1 1 4 1 1 1 4 1 1 1 4 1 1 1 4 1 1 1 4 1 1 4

[29] [35*]

g=8 (Rodan / Guiron / Slendric?)

[5*] 8 8 8 8 9

[6] 8 8 8 8 8 1

[11] 7 1 7 1 7 1 7 1 7 1 1

[16] 6 1 1 6 1 1 6 1 1 6 1 1 6 1 1 1

[21] 5 1 1 1 5 1 1 1 5 1 1 1 5 1 1 1 5 1 1 1 1

[26] [31] [36*]

g=9 (Septimin)

[5] 9 9 9 9 5

[9*] 4 5 4 5 4 5 4 5 5

[14] 4 4 1 4 4 1 4 4 1 4 4 1 4 1

[23] 3 1 3 1 1 3 1 3 1 1 3 1 3 1 1 3 1 3 1 1 3 1 1

[32*] 2 1 1 2 1 1 1 2 1 1 2 1 1 1 2 1 1 2 1 1 1 2 1 1 2 1 1 1 2 1 1 1

g=10 (Quasitemp)

[4*] 10 10 10 11

[5] 10 10 10 10 1

[9] 9 1 9 1 9 1 9 1 1

[13] 8 1 1 8 1 1 8 1 1 8 1 1 1

[17] 7 1 1 1 7 1 1 1 7 1 1 1 7 1 1 1 1

[21] [25] [29] etc.

g=11 (Superkleismic / Orgone?)

[7] 3 8 3 8 3 8 8

[11] 3 3 5 3 3 5 3 3 5 3 5

[15*] 3 3 3 2 3 3 3 2 3 3 3 2 3 3 2

[26*] 1 2 1 2 1 2 2 1 2 1 2 1 2 2 1 2 1 2 1 2 2 1 2 1 2 2

g=12 (Hemififths / Karadeniz / Beatles?)

[7] 7 5 7 5 7 5 5

[10] 2 5 5 2 5 5 2 5 5 5

[17*] 2 2 3 2 3 2 2 3 2 3 2 2 3 2 3 2 3

[24*] 2 2 2 1 2 2 1 2 2 2 1 2 2 1 2 2 2 1 2 2 1 2 2 1

g=13 (Magic / Witchcraft)

[7] 11 2 11 2 11 2 2

[10] 9 2 2 9 2 2 9 2 2 2

[13] 7 2 2 2 7 2 2 2 7 2 2 2 2

[16] 5 2 2 2 2 5 2 2 2 2 5 2 2 2 2 2

[19*] 3 2 2 2 2 2 3 2 2 2 2 2 3 2 2 2 2 2 2

[22*] 1 2 2 2 2 2 2 1 2 2 2 2 2 2 1 2 2 2 2 2 2 2

g=14 (Hocus)

[3*] 14 14 13

[5] 1 13 1 13 13

[8] 1 1 12 1 1 12 1 12

[11] 1 1 1 11 1 1 1 11 1 1 11

[14] 1 1 1 1 10 1 1 1 1 10 1 1 1 10

[17] 1 1 1 1 1 9 1 1 1 1 1 9 1 1 1 1 9

[20] [23] [26] [29] etc.

g=15 (Stacks?)

[5] 4 11 4 11 11

[8] 4 4 7 4 4 7 4 7

[11*] 4 4 4 3 4 4 4 3 4 4 3

[19] 1 3 1 3 1 3 3 1 3 1 3 1 3 3 1 3 1 3 3

[30*] 1 1 2 1 1 2 1 1 2 1 2 1 1 2 1 1 2 1 1 2 1 2 1 1 2 1 1 2 1 2

g=16 (Barbad)

[5] 7 9 7 9 9

[8] 7 7 2 7 7 2 7 2

[13] 5 2 5 2 2 5 2 5 2 2 5 2 2

[18*] 3 2 2 3 2 2 2 3 2 2 3 2 2 2 3 2 2 2

[23*] 1 2 2 2 1 2 2 2 2 1 2 2 2 1 2 2 2 2 1 2 2 2 2

g=17 (Schismic / Schismatic / Helmholtz / Garibaldi / Cassandra)

[5] 10 7 10 7 7

[7] 3 7 7 3 7 7 7

[12*] 3 3 4 3 4 3 3 4 3 4 3 4

[17] 3 3 3 1 3 3 1 3 3 3 1 3 3 1 3 3 1

[29*] 2 1 2 1 2 1 1 2 1 2 1 1 2 1 2 1 2 1 1 2 1 2 1 1 2 1 2 1 1

g=18 (Trismegistus)

[5] 13 5 13 5 5

[7] 8 5 5 8 5 5 5

[9] 3 5 5 5 3 5 5 5 5

[16*] 3 3 2 3 2 3 2 3 3 2 3 2 3 2 3 2

[25*] 1 2 1 2 2 1 2 2 1 2 2 1 2 1 2 2 1 2 2 1 2 2 1 2 2

g=19 (Kangaroo? / Thuja?)

[5] 16 3 16 3 3

[7] 13 3 3 13 3 3 3

[9] 10 3 3 3 10 3 3 3 3

[11] 7 3 3 3 3 7 3 3 3 3 3

[13*] 4 3 3 3 3 3 4 3 3 3 3 3 3

[15] 1 3 3 3 3 3 3 1 3 3 3 3 3 3 3

[28*] 1 1 2 1 2 1 2 1 2 1 2 1 2 1 1 2 1 2 1 2 1 2 1 2 1 2 1 2

g=20 (Pluto)

[5] 19 1 19 1 1

[7] 18 1 1 18 1 1 1

[9] 17 1 1 1 17 1 1 1 1

[11] [13] [15] [17] etc.

g=21 <--> g=20

g=22 <--> g=19

etc.

Non-MOS

Harmonic series approximations

[5] 11 9 8 7 6 harmonic series 5:6:7:8:9:10

[6] 9 8 7 6 6 5 harmonic series 6::12

[7] 8 7 6 6 5 5 4 harmonic series 7::14

[8] 7 6 6 5 5 4 4 4 harmonic series 8::16

[12] 5 4 4 4 4 3 3 3 3 3 2 3 harmonic series 12::24

(reverse these for subharmonic scales)

Others

from Scala:

[7] 7 6 4 7 6 7 4 "just" major

[7] 7 4 6 7 4 7 6 "just" minor

[7] 7 4 6 7 4 6 7 natural minor

[7] 7 4 6 7 6 7 4 melodic minor

[7] 7 4 6 7 4 9 4 harmonic minor

[7] 7 6 4 7 4 9 4 harmonic major

[12] 4 3 4 2 4 3 4 4 2 4 3 4 "just" chromatic

...

Partial scales

Tetrachords

(from Scala)

1 1 15 (0-1-2-17) Wilson

1 2 14 (0-1-3-17) Wilson

1 6 10 (0-1-7-17) Wilson

1 7 9 (0-1-8-17) Barbour Chromatic

2 2 13 (0-2-4-17) Ptolemy

2 5 10 (0-2-7-17) Archytas' Chromatic

2 7 8 (0-2-9-17) Septimal Kürdi

2 8 7 (0-2-10-17) Archytas' Diatonic, Ptolemy's Diatonon Toniaion

3 4 10 (0-3-7-17) Pythagorean Chromatic, Gaudentius

3 4 10 (0-3-7-17) Boethius Chromatic

3 4 10 (0-3-7-17) Perrett Chromatic

3 5 9 (0-3-8-17) Ptolemy

3 5 9 (0-3-8-17) Hipkins

3 6 8 (0-3-9-17) Ptolemy's Diatonon Malakon, Soft Diatonic

3 7 7 (0-3-10-17) Kürdi

3 7 7 (0-3-10-17) Eratostenes' Diatonic, Pythagorean Diatonic, Ptolemy's Diatonon Ditoniaion

3 11 3 (0-3-14-17) Xenakis

4 4 9 (0-4-8-17) Avicenna

4 5 8 (0-4-9-17) Avicenna

4 6 10 (0-4-10-20) Araban

4 7 6 (0-4-11-17) Iraq, Segâh

4 9 4 (0-4-13-17) Sedaraban, Hicaz

4 9 4 (0-4-13-17) Palmer

4 10 3 (0-4-14-17) Evicârâ

5 5 7 (0-5-10-17) Ushshaq

5 5 7 (0-5-10-17) Young exquisite 3/4 tone Hellenic lyre

5 7 5 (0-5-12-17) Dudon Mohajira

5 7 5 (0-5-12-17) Mojahira, Iraq

7 2 7 (0-7-9-16) Nahawand

7 3 7 (0-7-10-17) Buselik

7 3 7 (0-7-10-17) Busalik, Nihâvend

7 4 6 (0-7-11-17) Müstear

7 4 9 (0-7-11-20) Neveser

7 5 5 (0-7-12-17) Rast

7 5 5 (0-7-12-17) Rast, Nagdi, Neutral Diatonic, Islamic Diatonic

7 5 5 (0-7-12-17) Modern Rast, Avicenna

7 6 4 (0-7-13-17) Turkish Rast

7 7 3 (0-7-14-17) Mahur

7 7 3 (0-7-14-17) Çargâh

8 7 2 (0-8-15-17) Septimal 'Ajam

Pentachords

(from Scala)

3 7 7 7 (0-3-10-17-24) Kürdi

4 4 9 7 (0-4-8-17-24) Iranian

4 6 4 7 (0-4-10-14-21) Hicaz

4 7 6 7 (0-4-11-17-24) Segâh

5 5 7 7 (0-5-10-17-24) Huseyni

7 2 7 8 (0-7-9-16-24) Busalik

7 3 7 7 (0-7-10-17-24) Buselik

7 3 7 7 (0-7-10-17-24) Busalik

7 4 6 7 (0-7-11-17-24) Müstear

7 4 9 4 (0-7-11-20-24) Nikriz

7 5 5 7 (0-7-12-17-24) Rast

7 6 4 7 (0-7-13-17-24) Turkish Rast

7 7 3 7 (0-7-14-17-24) Çargâh

7 7 6 4 (0-7-14-20-24) Pencgâh