41edo modes: Difference between revisions

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


=MOS=
== MOS ==
(maximally even scales indicated by *)
Maximally even scales are indicated by *


'''generator = 1\41'''
'''Generator = 1\41 ([[Slendi]])'''


[3] [4] [5] etc.
[3] [4] [5] etc.
Line 11: Line 11:
[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  
[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]])'''
'''g = 2 ([[Hemimiracle]])'''


[3] [4] [5] etc.
[3] [4] [5] etc.
Line 19: Line 19:
[21*]  2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 1  
[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]])'''
'''g = 3 ([[Octacot]])'''


[3] [4] [5] etc.
[3] [4] [5] etc.
Line 29: Line 29:
[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  
[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]])'''
'''g = 4 ([[Miracle]])'''


[3] [4] [5] etc.
[3] [4] [5] etc.
Line 41: Line 41:
[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  
[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]])'''
'''g = 5 ([[Bohpier]])'''


[8*]  5 5 5 5 5 5 5 6  
[8*]  5 5 5 5 5 5 5 6  
Line 53: Line 53:
[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  
[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\[[41edo|41]])
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\[[41edo|41]])


'''g=6 ([[Tetracot]] / [[Bunya]] / [[Monkey]])'''
'''g = 6 ([[Tetracot]] / [[bunya]] / [[monkey]])'''


[7*]  6 6 6 6 6 6 5  
[7*]  6 6 6 6 6 6 5  
Line 67: Line 67:
[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  
[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]])'''
'''g = 7 ([[Baldy]], [[quadrimage]])'''


[6*]  7 7 7 7 7 6  
[6*]  7 7 7 7 7 6  
Line 79: Line 79:
[29] [35*]
[29] [35*]


'''g=8 ([[Rodan]] / [[Guiron]] / [[Slendric]]?)'''
'''g = 8 ([[Slendric]] / [[rodan]] / [[guiron]])'''


[5*]  8 8 8 8 9  
[5*]  8 8 8 8 9  
Line 93: Line 93:
[26] [31] [36*]
[26] [31] [36*]


'''g=9 ([[Septimin]])'''
'''g = 9 ([[Septimin]])'''


[5]  9 9 9 9 5  
[5]  9 9 9 9 5  
Line 105: Line 105:
[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  
[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]])'''
'''g = 10 ([[Quasitemp]])'''


[4*]  10 10 10 11  
[4*]  10 10 10 11  
Line 119: Line 119:
[21] [25] [29] etc.
[21] [25] [29] etc.


'''g=11 ([[Superkleismic]] / [[Orgone]]?)'''
'''g = 11 ([[Superkleismic]], [[orgone]])'''


[7]  3 8 3 8 3 8 8  
[7]  3 8 3 8 3 8 8  
Line 129: Line 129:
[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  
[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]]?)'''
'''g = 12 ([[Hemif]] / [[hemififths]] / [[salsa]] / [[karadeniz]])'''


[7]  7 5 7 5 7 5 5  
[7]  7 5 7 5 7 5 5  
Line 139: Line 139:
[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  
[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]])'''
'''g = 13 ([[Magic]] / [[witchcraft]])'''


[7]  11 2 11 2 11 2 2  
[7]  11 2 11 2 11 2 2  
Line 153: Line 153:
[22*]  1 2 2 2 2 2 2 1 2 2 2 2 2 2 1 2 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]])'''
'''g = 14 ([[Hocum]], [[hocus]])'''


[3*]  14 14 13  
[3*]  14 14 13  
Line 169: Line 169:
[20] [23] [26] [29] etc.
[20] [23] [26] [29] etc.


'''g=15 ([[Stacks]]?)'''
'''g = 15 ([[Superthird]], [[stacks]])'''


[5]  4 11 4 11 11  
[5]  4 11 4 11 11  
Line 181: Line 181:
[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  
[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]])'''
'''g = 16 ([[Barbad]])'''


[5]  7 9 7 9 9  
[5]  7 9 7 9 9  
Line 193: Line 193:
[23*]  1 2 2 2 1 2 2 2 2 1 2 2 2 1 2 2 2 2 1 2 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]])'''
'''g = 17 ([[Helmholtz]] / [[garibaldi]] / [[cassandra]] / [[andromeda]])'''


[5]  10 7 10 7 7  
[5]  10 7 10 7 7  
Line 205: Line 205:
[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  
[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]])'''
'''g = 18 ([[Trismegistus]])'''


[5]  13 5 13 5 5  
[5]  13 5 13 5 5  
Line 217: Line 217:
[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  
[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]]?)'''
'''g = 19 ([[Alphorn]])'''


[5]  16 3 16 3 3  
[5]  16 3 16 3 3  
Line 233: Line 233:
[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  
[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]])'''
'''g = 20 ([[Pluto]], [[merman]])'''


[5]  19 1 19 1 1  
[5]  19 1 19 1 1  
Line 242: Line 242:


[11] [13] [15] [17] etc.
[11] [13] [15] [17] etc.
g=21 <--> g=20
g=22 <--> g=19


etc.
etc.


=Non-MOS=
== Non-MOS ==
 
=== Harmonic series approximations ===
==Harmonic series approximations==
[5]  11 9 8 7 6  harmonic series 5:6:7:8:9:10
[5]  11 9 8 7 6  harmonic series 5:6:7:8:9:10


Line 262: Line 257:
[12]  5 4 4 4 4 3 3 3 3 3 2 3  harmonic series 12::24
[12]  5 4 4 4 4 3 3 3 3 3 2 3  harmonic series 12::24


(reverse these for subharmonic scales)
(Reverse these for subharmonic scales)


==Others==
=== Others ===
from Scala:
from Scala:


Line 281: Line 276:
[12]  4 3 4 2 4 3 4 4 2 4 3 4  "just" chromatic
[12]  4 3 4 2 4 3 4 4 2 4 3 4  "just" chromatic


...
…
 
=Partial scales=


==Tetrachords==
== Partial scales ==
=== Tetrachords ===
(from Scala)
(from Scala)


Line 368: Line 362:
8 7 2  (0-8-15-17)  Septimal 'Ajam     
8 7 2  (0-8-15-17)  Septimal 'Ajam     


==Pentachords==
=== Pentachords ===
(from Scala)
(from Scala)


Revision as of 06:55, 1 August 2021

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

MOS

Maximally even scales are indicated by *

Generator = 1\41 (Slendi)

[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, quadrimage)

[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 (Slendric / rodan / guiron)

[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 (Hemif / hemififths / salsa / karadeniz)

[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 (Hocum, 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 (Superthird, 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 (Helmholtz / garibaldi / cassandra / andromeda)

[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 (Alphorn)

[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, merman)

[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.

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

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