41edo modes: Difference between revisions

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<h2>IMPORTED REVISION FROM WIKISPACES</h2>
__FORCETOC__
This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
This page lists some useful and/or interesting modes (subsets) of [[41edo]].
: This revision was by author [[User:spt3125|spt3125]] and made on <tt>2016-04-24 15:56:59 UTC</tt>.<br>
: The original revision id was <tt>581046433</tt>.<br>
: The revision comment was: <tt></tt><br>
The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<br>
<h4>Original Wikitext content:</h4>
<div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;white-space: pre-wrap ! important" class="old-revision-html">[[toc]]
This page lists some useful and/or interesting modes (subsets) of [[41edo]] .


== MOS ==
Maximally even scales are indicated by *


=MOS=
'''Generator = 1\41 ([[Slendi]])'''
(maximally even scales indicated by *)


**generator = 1\41**
[3] [4] [5] etc.
[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  
[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.
[20*]  2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 3  
[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  
[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.
[13]  3 3 3 3 3 3 3 3 3 3 3 3 5  
[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
[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  
[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.
[10*]  4 4 4 4 4 4 4 4 4 5
[10*]  4 4 4 4 4 4 4 4 4 5
[11]  4 4 4 4 4 4 4 4 4 4 1  
[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  
[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  
[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  
[9]  5 5 5 5 5 5 5 5 1  
[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  
[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  
[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  
[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|3/1]] (65\[[41edo|41]])


**g=6 ([[tetracot]] / [[bunya]] / [[monkey]])**
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]])'''
 
[7*]  6 6 6 6 6 6 5  
[7*]  6 6 6 6 6 6 5  
[13]  1 5 1 5 1 5 1 5 1 5 1 5 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  
[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  
[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  
[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  
[11]  1 6 1 6 1 6 1 6 1 6 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  
[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  
[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*]
[29] [35*]


**g=8 ([[rodan]] / [[guiron]] / [[slendric]]?)**
'''g = 8 ([[Slendric]] / [[rodan]] / [[guiron]])'''
 
[5*]  8 8 8 8 9  
[5*]  8 8 8 8 9  
[6]  8 8 8 8 8 1  
[6]  8 8 8 8 8 1  
[11]  7 1 7 1 7 1 7 1 7 1 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  
[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  
[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*]
[26] [31] [36*]


**g=9 ([[septimin]])**
'''g = 9 ([[Septimin]])'''
 
[5]  9 9 9 9 5  
[5]  9 9 9 9 5  
[9*]  4 5 4 5 4 5 4 5 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
[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  
[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  
[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  
[5]  10 10 10 10 1  
[5]  10 10 10 10 1  
[9]  9 1 9 1 9 1 9 1 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  
[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  
[17]  7 1 1 1 7 1 1 1 7 1 1 1 7 1 1 1 1  
[21] [25] [29] etc.
[21] [25] [29] etc.


**g=11 ([[superkleismic]] / [[rgone]]?)**
'''g = 11 ([[Superkleismic]], [[orgone]])'''
 
[7]  3 8 3 8 3 8 8  
[7]  3 8 3 8 3 8 8  
[11]  3 3 5 3 3 5 3 3 5 3 5  
[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  
[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  
[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  
[10]  2 5 5 2 5 5 2 5 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  
[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  
[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  
[10]  9 2 2 9 2 2 9 2 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
[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  
[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  
[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  
[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  
[5]  1 13 1 13 13  
[5]  1 13 1 13 13  
[8]  1 1 12 1 1 12 1 12  
[8]  1 1 12 1 1 12 1 12  
[11]  1 1 1 11 1 1 1 11 1 1 11  
[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  
[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  
[17]  1 1 1 1 1 9 1 1 1 1 1 9 1 1 1 1 9  
[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  
[8]  4 4 7 4 4 7 4 7  
[8]  4 4 7 4 4 7 4 7  
[11*]  4 4 4 3 4 4 4 3 4 4 3  
[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  
[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  
[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  
[8]  7 7 2 7 7 2 7 2  
[8]  7 7 2 7 7 2 7 2  
[13]  5 2 5 2 2 5 2 5 2 2 5 2 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  
[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  
[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 (temperament)|Helmholtz]] / [[garibaldi]] / [[cassandra]] / [[andromeda]])'''
 
[5]  10 7 10 7 7  
[5]  10 7 10 7 7  
[7]  3 7 7 3 7 7 7  
[7]  3 7 7 3 7 7 7  
[12*]  3 3 4 3 4 3 3 4 3 4 3 4  
[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  
[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  
[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  
[7]  8 5 5 8 5 5 5  
[7]  8 5 5 8 5 5 5  
[9]  3 5 5 5 3 5 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  
[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  
[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  
[7]  13 3 3 13 3 3 3  
[7]  13 3 3 13 3 3 3  
[9]  10 3 3 3 10 3 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  
[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  
[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  
[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  
[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  
[7]  18 1 1 18 1 1 1  
[7]  18 1 1 18 1 1 1  
[9]  17 1 1 1 17 1 1 1 1  
[9]  17 1 1 1 17 1 1 1 1  
[11] [13] [15] [17] etc.
[11] [13] [15] [17] etc.


g=21 &lt;--&gt; g=20
g=22 &lt;--&gt; g=19
etc.
etc.


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


=Non-MOS=
[6]  9 8 7 6 6 5  harmonic series 6::12


==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
[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
[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
[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:
[7]  7 6 4 7 6 7 4  "just" major
[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 7 6  "just" minor
[7]  7 4 6 7 4 6 7  natural 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 6 7 4  melodic minor
[7]  7 4 6 7 4 9 4  harmonic minor
[7]  7 4 6 7 4 9 4  harmonic minor
[7]  7 6 4 7 4 9 4  harmonic major
[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
[12]  4 3 4 2 4 3 4 4 2 4 3 4  "just" chromatic


...
…


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


=Partial scales=
1 1 15  (0-1-2-17)  Wilson     


==Tetrachords==
(from Scala)
1 1 15  (0-1-2-17)  Wilson     
1 2 14  (0-1-3-17)  Wilson       
1 2 14  (0-1-3-17)  Wilson       
1 6 10  (0-1-7-17)  Wilson       
1 6 10  (0-1-7-17)  Wilson       
1 7 9  (0-1-8-17)  Barbour Chromatic     
1 7 9  (0-1-8-17)  Barbour Chromatic     
2 2 13  (0-2-4-17)  Ptolemy       
2 2 13  (0-2-4-17)  Ptolemy       
2 5 10  (0-2-7-17)  Archytas' Chromatic     
2 5 10  (0-2-7-17)  Archytas' Chromatic     
2 7 8  (0-2-9-17)  Septimal Kürdi     
2 7 8  (0-2-9-17)  Septimal Kürdi     
2 8 7  (0-2-10-17)  Archytas' Diatonic, Ptolemy's Diatonon Toniaion   
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)  Pythagorean Chromatic, Gaudentius     
3 4 10  (0-3-7-17)  Boethius Chromatic     
3 4 10  (0-3-7-17)  Boethius Chromatic     
3 4 10  (0-3-7-17)  Perrett 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)  Ptolemy       
3 5 9  (0-3-8-17)  Hipkins       
3 5 9  (0-3-8-17)  Hipkins       
3 6 8  (0-3-9-17)  Ptolemy's Diatonon Malakon, Soft Diatonic   
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)  Kürdi       
3 7 7  (0-3-10-17)  Eratostenes' Diatonic, Pythagorean Diatonic, Ptolemy's Diatonon Ditoniaion
3 7 7  (0-3-10-17)  Eratostenes' Diatonic, Pythagorean Diatonic, Ptolemy's Diatonon Ditoniaion
3 11 3  (0-3-14-17)  Xenakis       
 
3 11 3  (0-3-14-17)  [[Xenakis]]      
 
4 4 9  (0-4-8-17)  Avicenna       
4 4 9  (0-4-8-17)  Avicenna       
4 5 8  (0-4-9-17)  Avicenna       
4 5 8  (0-4-9-17)  Avicenna       
4 6 10  (0-4-10-20)  Araban       
4 6 10  (0-4-10-20)  Araban       
4 7 6  (0-4-11-17)  Iraq, Segâh     
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)  Sedaraban, Hicaz     
4 9 4  (0-4-13-17)  Palmer       
4 9 4  (0-4-13-17)  Palmer       
4 10 3  (0-4-14-17)  Evicârâ       
4 10 3  (0-4-14-17)  Evicârâ       
5 5 7  (0-5-10-17)  Ushshaq       
5 5 7  (0-5-10-17)  Ushshaq       
5 5 7  (0-5-10-17)  Young exquisite 3/4 tone Hellenic lyre  
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)  Dudon Mohajira     
5 7 5  (0-5-12-17)  Mojahira, Iraq     
5 7 5  (0-5-12-17)  Mojahira, Iraq     
7 2 7  (0-7-9-16)  Nahawand       
7 2 7  (0-7-9-16)  Nahawand       
7 3 7  (0-7-10-17)  Buselik       
7 3 7  (0-7-10-17)  Buselik       
7 3 7  (0-7-10-17)  Busalik, Nihâvend     
7 3 7  (0-7-10-17)  Busalik, Nihâvend     
7 4 6  (0-7-11-17)  Müstear       
7 4 6  (0-7-11-17)  Müstear       
7 4 9  (0-7-11-20)  Neveser       
7 4 9  (0-7-11-20)  Neveser       
7 5 5  (0-7-12-17)  Rast       
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)  Rast, Nagdi, Neutral Diatonic, Islamic Diatonic  
7 5 5  (0-7-12-17)  Modern Rast, Avicenna     
7 5 5  (0-7-12-17)  Modern Rast, Avicenna     
7 6 4  (0-7-13-17)  Turkish Rast     
7 6 4  (0-7-13-17)  Turkish Rast     
7 7 3  (0-7-14-17)  Mahur       
7 7 3  (0-7-14-17)  Mahur       
7 7 3  (0-7-14-17)  Çargâh       
7 7 3  (0-7-14-17)  Çargâh       
8 7 2  (0-8-15-17)  Septimal 'Ajam     
8 7 2  (0-8-15-17)  Septimal 'Ajam     


==Pentachords==
=== Pentachords ===
(from Scala)
(from Scala)
3 7 7 7  (0-3-10-17-24)  Kürdi  
3 7 7 7  (0-3-10-17-24)  Kürdi  
4 4 9 7  (0-4-8-17-24)  Iranian  
4 4 9 7  (0-4-8-17-24)  Iranian  
4 6 4 7  (0-4-10-14-21)  Hicaz  
4 6 4 7  (0-4-10-14-21)  Hicaz  
4 7 6 7  (0-4-11-17-24)  Segâh  
4 7 6 7  (0-4-11-17-24)  Segâh  
5 5 7 7  (0-5-10-17-24)  Huseyni  
5 5 7 7  (0-5-10-17-24)  Huseyni  
7 2 7 8  (0-7-9-16-24)  Busalik  
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)  Buselik  
7 3 7 7  (0-7-10-17-24)  Busalik  
7 3 7 7  (0-7-10-17-24)  Busalik  
7 4 6 7  (0-7-11-17-24)  Müstear  
7 4 6 7  (0-7-11-17-24)  Müstear  
7 4 9 4  (0-7-11-20-24)  Nikriz  
7 4 9 4  (0-7-11-20-24)  Nikriz  
7 5 5 7  (0-7-12-17-24)  Rast  
7 5 5 7  (0-7-12-17-24)  Rast  
7 6 4 7  (0-7-13-17-24)  Turkish Rast
7 6 4 7  (0-7-13-17-24)  Turkish Rast
7 7 3 7  (0-7-14-17-24)  Çargâh  
7 7 3 7  (0-7-14-17-24)  Çargâh  
7 7 6 4  (0-7-14-20-24)  Pencgâh  
 
</pre></div>
7 7 6 4  (0-7-14-20-24)  Pencgâh
<h4>Original HTML content:</h4>
 
<div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;width:200%;white-space: pre-wrap ! important" class="old-revision-html">&lt;html&gt;&lt;head&gt;&lt;title&gt;41edo modes&lt;/title&gt;&lt;/head&gt;&lt;body&gt;&lt;!-- ws:start:WikiTextTocRule:14:&amp;lt;img id=&amp;quot;wikitext@@toc@@normal&amp;quot; class=&amp;quot;WikiMedia WikiMediaToc&amp;quot; title=&amp;quot;Table of Contents&amp;quot; src=&amp;quot;/site/embedthumbnail/toc/normal?w=225&amp;amp;h=100&amp;quot;/&amp;gt; --&gt;&lt;div id="toc"&gt;&lt;h1 class="nopad"&gt;Table of Contents&lt;/h1&gt;&lt;!-- ws:end:WikiTextTocRule:14 --&gt;&lt;!-- ws:start:WikiTextTocRule:15: --&gt;&lt;div style="margin-left: 1em;"&gt;&lt;a href="#MOS"&gt;MOS&lt;/a&gt;&lt;/div&gt;
{{Navbox scale gallery}}
&lt;!-- ws:end:WikiTextTocRule:15 --&gt;&lt;!-- ws:start:WikiTextTocRule:16: --&gt;&lt;div style="margin-left: 1em;"&gt;&lt;a href="#Non-MOS"&gt;Non-MOS&lt;/a&gt;&lt;/div&gt;
[[Category:41edo]]
&lt;!-- ws:end:WikiTextTocRule:16 --&gt;&lt;!-- ws:start:WikiTextTocRule:17: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Non-MOS-Harmonic series approximations"&gt;Harmonic series approximations&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:17 --&gt;&lt;!-- ws:start:WikiTextTocRule:18: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Non-MOS-Others"&gt;Others&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:18 --&gt;&lt;!-- ws:start:WikiTextTocRule:19: --&gt;&lt;div style="margin-left: 1em;"&gt;&lt;a href="#Partial scales"&gt;Partial scales&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:19 --&gt;&lt;!-- ws:start:WikiTextTocRule:20: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Partial scales-Tetrachords"&gt;Tetrachords&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:20 --&gt;&lt;!-- ws:start:WikiTextTocRule:21: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Partial scales-Pentachords"&gt;Pentachords&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:21 --&gt;&lt;!-- ws:start:WikiTextTocRule:22: --&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:22 --&gt;This page lists some useful and/or interesting modes (subsets) of &lt;a class="wiki_link" href="/41edo"&gt;41edo&lt;/a&gt; .&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:0:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc0"&gt;&lt;a name="MOS"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:0 --&gt;MOS&lt;/h1&gt;
(maximally even scales indicated by *)&lt;br /&gt;
&lt;br /&gt;
&lt;strong&gt;generator = 1\41&lt;/strong&gt;&lt;br /&gt;
[3] [4] [5] etc.&lt;br /&gt;
[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 &lt;br /&gt;
&lt;br /&gt;
&lt;strong&gt;g=2 (&lt;a class="wiki_link" href="/hemimiracle"&gt;hemimiracle&lt;/a&gt;)&lt;/strong&gt;&lt;br /&gt;
[3] [4] [5] etc.&lt;br /&gt;
[20*]  2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 3 &lt;br /&gt;
[21*]  2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 1 &lt;br /&gt;
&lt;br /&gt;
&lt;strong&gt;g=3 (&lt;a class="wiki_link" href="/octacot"&gt;octacot&lt;/a&gt;)&lt;/strong&gt;&lt;br /&gt;
[3] [4] [5] etc.&lt;br /&gt;
[13]  3 3 3 3 3 3 3 3 3 3 3 3 5 &lt;br /&gt;
[14*]  3 3 3 3 3 3 3 3 3 3 3 3 3 2&lt;br /&gt;
[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 &lt;br /&gt;
&lt;br /&gt;
&lt;strong&gt;g=4 (&lt;a class="wiki_link" href="/miracle"&gt;miracle&lt;/a&gt;)&lt;/strong&gt;&lt;br /&gt;
[3] [4] [5] etc.&lt;br /&gt;
[10*]  4 4 4 4 4 4 4 4 4 5&lt;br /&gt;
[11]  4 4 4 4 4 4 4 4 4 4 1 &lt;br /&gt;
[21]  3 1 3 1 3 1 3 1 3 1 3 1 3 1 3 1 3 1 3 1 1 &lt;br /&gt;
[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 &lt;br /&gt;
&lt;br /&gt;
&lt;strong&gt;g=5 (&lt;a class="wiki_link" href="/bohpier"&gt;bohpier&lt;/a&gt;)&lt;/strong&gt;&lt;br /&gt;
[8*]  5 5 5 5 5 5 5 6 &lt;br /&gt;
[9]  5 5 5 5 5 5 5 5 1 &lt;br /&gt;
[17]  4 1 4 1 4 1 4 1 4 1 4 1 4 1 4 1 1 &lt;br /&gt;
[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 &lt;br /&gt;
[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 &lt;br /&gt;
note: the non-octave &lt;a class="wiki_link" href="/Bohlen-Pierce"&gt;Bohlen-Pierce&lt;/a&gt; scale is simply 5 5 5 5 5 5 5 5 5 5 5 5 5, repeating at &lt;a class="wiki_link" href="/3_1"&gt;3/1&lt;/a&gt; (65\&lt;a class="wiki_link" href="/41edo"&gt;41&lt;/a&gt;)&lt;br /&gt;
&lt;br /&gt;
&lt;strong&gt;g=6 (&lt;a class="wiki_link" href="/tetracot"&gt;tetracot&lt;/a&gt; / &lt;a class="wiki_link" href="/bunya"&gt;bunya&lt;/a&gt; / &lt;a class="wiki_link" href="/monkey"&gt;monkey&lt;/a&gt;)&lt;/strong&gt;&lt;br /&gt;
[7*]  6 6 6 6 6 6 5 &lt;br /&gt;
[13]  1 5 1 5 1 5 1 5 1 5 1 5 5&lt;br /&gt;
[20]  1 1 4 1 1 4 1 1 4 1 1 4 1 1 4 1 1 4 1 4 &lt;br /&gt;
[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 &lt;br /&gt;
[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 &lt;br /&gt;
&lt;br /&gt;
&lt;strong&gt;g=7 (&lt;a class="wiki_link" href="/baldy"&gt;baldy&lt;/a&gt;)&lt;/strong&gt;&lt;br /&gt;
[6*]  7 7 7 7 7 6 &lt;br /&gt;
[11]  1 6 1 6 1 6 1 6 1 6 6 &lt;br /&gt;
[17]  1 1 5 1 1 5 1 1 5 1 1 5 1 1 5 1 5 &lt;br /&gt;
[23]  1 1 1 4 1 1 1 4 1 1 1 4 1 1 1 4 1 1 1 4 1 1 4 &lt;br /&gt;
[29] [35*]&lt;br /&gt;
&lt;br /&gt;
&lt;strong&gt;g=8 (&lt;a class="wiki_link" href="/rodan"&gt;rodan&lt;/a&gt; / &lt;a class="wiki_link" href="/guiron"&gt;guiron&lt;/a&gt; / &lt;a class="wiki_link" href="/slendric"&gt;slendric&lt;/a&gt;?)&lt;/strong&gt;&lt;br /&gt;
[5*]  8 8 8 8 9 &lt;br /&gt;
[6]  8 8 8 8 8 1 &lt;br /&gt;
[11]  7 1 7 1 7 1 7 1 7 1 1 &lt;br /&gt;
[16]  6 1 1 6 1 1 6 1 1 6 1 1 6 1 1 1 &lt;br /&gt;
[21]  5 1 1 1 5 1 1 1 5 1 1 1 5 1 1 1 5 1 1 1 1 &lt;br /&gt;
[26] [31] [36*]&lt;br /&gt;
&lt;br /&gt;
&lt;strong&gt;g=9 (&lt;a class="wiki_link" href="/septimin"&gt;septimin&lt;/a&gt;)&lt;/strong&gt;&lt;br /&gt;
[5]  9 9 9 9 5 &lt;br /&gt;
[9*]  4 5 4 5 4 5 4 5 5 &lt;br /&gt;
[14]  4 4 1 4 4 1 4 4 1 4 4 1 4 1&lt;br /&gt;
[23]  3 1 3 1 1 3 1 3 1 1 3 1 3 1 1 3 1 3 1 1 3 1 1 &lt;br /&gt;
[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 &lt;br /&gt;
&lt;br /&gt;
&lt;strong&gt;g=10 (&lt;a class="wiki_link" href="/quasitemp"&gt;quasitemp&lt;/a&gt;)&lt;/strong&gt;&lt;br /&gt;
[4*]  10 10 10 11 &lt;br /&gt;
[5]  10 10 10 10 1 &lt;br /&gt;
[9]  9 1 9 1 9 1 9 1 1 &lt;br /&gt;
[13]  8 1 1 8 1 1 8 1 1 8 1 1 1 &lt;br /&gt;
[17]  7 1 1 1 7 1 1 1 7 1 1 1 7 1 1 1 1 &lt;br /&gt;
[21] [25] [29] etc.&lt;br /&gt;
&lt;br /&gt;
&lt;strong&gt;g=11 (&lt;a class="wiki_link" href="/superkleismic"&gt;superkleismic&lt;/a&gt; / &lt;a class="wiki_link" href="/rgone"&gt;rgone&lt;/a&gt;?)&lt;/strong&gt;&lt;br /&gt;
[7]  3 8 3 8 3 8 8 &lt;br /&gt;
[11]  3 3 5 3 3 5 3 3 5 3 5 &lt;br /&gt;
[15*]  3 3 3 2 3 3 3 2 3 3 3 2 3 3 2 &lt;br /&gt;
[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 &lt;br /&gt;
&lt;br /&gt;
&lt;strong&gt;g=12 (&lt;a class="wiki_link" href="/hemififths"&gt;hemififths&lt;/a&gt; / &lt;a class="wiki_link" href="/karadeniz"&gt;karadeniz&lt;/a&gt; / &lt;a class="wiki_link" href="/beatles"&gt;beatles&lt;/a&gt;?)&lt;/strong&gt;&lt;br /&gt;
[7]  7 5 7 5 7 5 5 &lt;br /&gt;
[10]  2 5 5 2 5 5 2 5 5 5 &lt;br /&gt;
[17*]  2 2 3 2 3 2 2 3 2 3 2 2 3 2 3 2 3 &lt;br /&gt;
[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 &lt;br /&gt;
&lt;br /&gt;
&lt;strong&gt;g=13 (&lt;a class="wiki_link" href="/magic"&gt;magic&lt;/a&gt; / &lt;a class="wiki_link" href="/witchcraft"&gt;witchcraft&lt;/a&gt;)&lt;/strong&gt;&lt;br /&gt;
[7]  11 2 11 2 11 2 2 &lt;br /&gt;
[10]  9 2 2 9 2 2 9 2 2 2 &lt;br /&gt;
[13]  7 2 2 2 7 2 2 2 7 2 2 2 2&lt;br /&gt;
[16]  5 2 2 2 2 5 2 2 2 2 5 2 2 2 2 2 &lt;br /&gt;
[19*]  3 2 2 2 2 2 3 2 2 2 2 2 3 2 2 2 2 2 2 &lt;br /&gt;
[22*]  1 2 2 2 2 2 2 1 2 2 2 2 2 2 1 2 2 2 2 2 2 2 &lt;br /&gt;
&lt;br /&gt;
&lt;strong&gt;g=14 (&lt;a class="wiki_link" href="/hocus"&gt;hocus&lt;/a&gt;)&lt;/strong&gt;&lt;br /&gt;
[3*]  14 14 13 &lt;br /&gt;
[5]  1 13 1 13 13 &lt;br /&gt;
[8]  1 1 12 1 1 12 1 12 &lt;br /&gt;
[11]  1 1 1 11 1 1 1 11 1 1 11 &lt;br /&gt;
[14]  1 1 1 1 10 1 1 1 1 10 1 1 1 10 &lt;br /&gt;
[17]  1 1 1 1 1 9 1 1 1 1 1 9 1 1 1 1 9 &lt;br /&gt;
[20] [23] [26] [29] etc.&lt;br /&gt;
&lt;br /&gt;
&lt;strong&gt;g=15 (&lt;a class="wiki_link" href="/stacks"&gt;stacks&lt;/a&gt;?)&lt;/strong&gt;&lt;br /&gt;
[5]  4 11 4 11 11 &lt;br /&gt;
[8]  4 4 7 4 4 7 4 7 &lt;br /&gt;
[11*]  4 4 4 3 4 4 4 3 4 4 3 &lt;br /&gt;
[19]  1 3 1 3 1 3 3 1 3 1 3 1 3 3 1 3 1 3 3 &lt;br /&gt;
[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 &lt;br /&gt;
&lt;br /&gt;
&lt;strong&gt;g=16 (&lt;a class="wiki_link" href="/barbad"&gt;barbad&lt;/a&gt;)&lt;/strong&gt;&lt;br /&gt;
[5]  7 9 7 9 9 &lt;br /&gt;
[8]  7 7 2 7 7 2 7 2 &lt;br /&gt;
[13]  5 2 5 2 2 5 2 5 2 2 5 2 2 &lt;br /&gt;
[18*]  3 2 2 3 2 2 2 3 2 2 3 2 2 2 3 2 2 2 &lt;br /&gt;
[23*]  1 2 2 2 1 2 2 2 2 1 2 2 2 1 2 2 2 2 1 2 2 2 2 &lt;br /&gt;
&lt;br /&gt;
&lt;strong&gt;g=17 (&lt;a class="wiki_link" href="/schismic"&gt;schismic&lt;/a&gt; / &lt;a class="wiki_link" href="/schismatic"&gt;schismatic&lt;/a&gt; / &lt;a class="wiki_link" href="/helmholtz"&gt;helmholtz&lt;/a&gt; / &lt;a class="wiki_link" href="/garibaldi"&gt;garibaldi&lt;/a&gt; / &lt;a class="wiki_link" href="/cassandra"&gt;cassandra&lt;/a&gt;)&lt;/strong&gt;&lt;br /&gt;
[5]  10 7 10 7 7 &lt;br /&gt;
[7]  3 7 7 3 7 7 7 &lt;br /&gt;
[12*]  3 3 4 3 4 3 3 4 3 4 3 4 &lt;br /&gt;
[17]  3 3 3 1 3 3 1 3 3 3 1 3 3 1 3 3 1 &lt;br /&gt;
[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 &lt;br /&gt;
&lt;br /&gt;
&lt;strong&gt;g=18 (&lt;a class="wiki_link" href="/trismegistus"&gt;trismegistus&lt;/a&gt;)&lt;/strong&gt;&lt;br /&gt;
[5]  13 5 13 5 5 &lt;br /&gt;
[7]  8 5 5 8 5 5 5 &lt;br /&gt;
[9]  3 5 5 5 3 5 5 5 5 &lt;br /&gt;
[16*]  3 3 2 3 2 3 2 3 3 2 3 2 3 2 3 2 &lt;br /&gt;
[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 &lt;br /&gt;
&lt;br /&gt;
&lt;strong&gt;g=19 (&lt;a class="wiki_link" href="/kangaroo"&gt;kangaroo&lt;/a&gt;? / &lt;a class="wiki_link" href="/thuja"&gt;thuja&lt;/a&gt;?)&lt;/strong&gt;&lt;br /&gt;
[5]  16 3 16 3 3 &lt;br /&gt;
[7]  13 3 3 13 3 3 3 &lt;br /&gt;
[9]  10 3 3 3 10 3 3 3 3 &lt;br /&gt;
[11]  7 3 3 3 3 7 3 3 3 3 3 &lt;br /&gt;
[13*]  4 3 3 3 3 3 4 3 3 3 3 3 3 &lt;br /&gt;
[15]  1 3 3 3 3 3 3 1 3 3 3 3 3 3 3 &lt;br /&gt;
[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 &lt;br /&gt;
&lt;br /&gt;
&lt;strong&gt;g=20 (&lt;a class="wiki_link" href="/pluto"&gt;pluto&lt;/a&gt;)&lt;/strong&gt;&lt;br /&gt;
[5]  19 1 19 1 1 &lt;br /&gt;
[7]  18 1 1 18 1 1 1 &lt;br /&gt;
[9]  17 1 1 1 17 1 1 1 1 &lt;br /&gt;
[11] [13] [15] [17] etc.&lt;br /&gt;
&lt;br /&gt;
g=21 &amp;lt;--&amp;gt; g=20&lt;br /&gt;
g=22 &amp;lt;--&amp;gt; g=19&lt;br /&gt;
etc.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:2:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc1"&gt;&lt;a name="Non-MOS"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:2 --&gt;Non-MOS&lt;/h1&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:4:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc2"&gt;&lt;a name="Non-MOS-Harmonic series approximations"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:4 --&gt;Harmonic series approximations&lt;/h2&gt;
[5]   11 9 8 7 6  harmonic series 5:6:7:8:9:10&lt;br /&gt;
[6]   9 8 7 6 6 5  harmonic series 6::12&lt;br /&gt;
[7]  8 7 6 6 5 5 4  harmonic series 7::14&lt;br /&gt;
[8]  7 6 6 5 5 4 4 4  harmonic series 8::16&lt;br /&gt;
[12]  5 4 4 4 4 3 3 3 3 3 2 3  harmonic series 12::24&lt;br /&gt;
(reverse these for subharmonic scales)&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:6:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc3"&gt;&lt;a name="Non-MOS-Others"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:6 --&gt;Others&lt;/h2&gt;
from Scala:&lt;br /&gt;
[7]  7 6 4 7 6 7 4  &amp;quot;just&amp;quot; major&lt;br /&gt;
[7]  7 4 6 7 4 7 6  &amp;quot;just&amp;quot; minor&lt;br /&gt;
[7]  7 4 6 7 4 6 7  natural minor&lt;br /&gt;
[7]  7 4 6 7 6 7 4  melodic minor&lt;br /&gt;
[7]  7 4 6 7 4 9 4  harmonic minor&lt;br /&gt;
[7]  7 6 4 7 4 9 4  harmonic major&lt;br /&gt;
[12]  4 3 4 2 4 3 4 4 2 4 3 4  &amp;quot;just&amp;quot; chromatic&lt;br /&gt;
&lt;br /&gt;
...&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:8:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc4"&gt;&lt;a name="Partial scales"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:8 --&gt;Partial scales&lt;/h1&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:10:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc5"&gt;&lt;a name="Partial scales-Tetrachords"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:10 --&gt;Tetrachords&lt;/h2&gt;
(from Scala)&lt;br /&gt;
1 1 15  (0-1-2-17)  Wilson      &lt;br /&gt;
1 2 14  (0-1-3-17)  Wilson      &lt;br /&gt;
1 6 10  (0-1-7-17)  Wilson      &lt;br /&gt;
1 7 9  (0-1-8-17)  Barbour Chromatic    &lt;br /&gt;
2 2 13  (0-2-4-17)  Ptolemy      &lt;br /&gt;
2 5 10  (0-2-7-17)  Archytas' Chromatic    &lt;br /&gt;
2 7 8  (0-2-9-17)  Septimal Kürdi    &lt;br /&gt;
2 8 7  (0-2-10-17)  Archytas' Diatonic, Ptolemy's Diatonon Toniaion  &lt;br /&gt;
3 4 10  (0-3-7-17)  Pythagorean Chromatic, Gaudentius    &lt;br /&gt;
3 4 10  (0-3-7-17)  Boethius Chromatic    &lt;br /&gt;
3 4 10  (0-3-7-17)  Perrett Chromatic    &lt;br /&gt;
3 5 9  (0-3-8-17)  Ptolemy      &lt;br /&gt;
3 5 9  (0-3-8-17)  Hipkins      &lt;br /&gt;
3 6 8  (0-3-9-17)  Ptolemy's Diatonon Malakon, Soft Diatonic  &lt;br /&gt;
3 7 7  (0-3-10-17)  Kürdi      &lt;br /&gt;
3 7 7  (0-3-10-17)  Eratostenes' Diatonic, Pythagorean Diatonic, Ptolemy's Diatonon Ditoniaion&lt;br /&gt;
3 11 3  (0-3-14-17)  Xenakis      &lt;br /&gt;
4 4 9  (0-4-8-17)  Avicenna      &lt;br /&gt;
4 5 8  (0-4-9-17)  Avicenna      &lt;br /&gt;
4 6 10  (0-4-10-20)  Araban      &lt;br /&gt;
4 7 6  (0-4-11-17)  Iraq, Segâh    &lt;br /&gt;
4 9 4  (0-4-13-17)  Sedaraban, Hicaz    &lt;br /&gt;
4 9 4  (0-4-13-17)  Palmer      &lt;br /&gt;
4 10 3  (0-4-14-17)  Evicârâ      &lt;br /&gt;
5 5 7  (0-5-10-17)  Ushshaq      &lt;br /&gt;
5 5 7  (0-5-10-17)  Young exquisite 3/4 tone Hellenic lyre &lt;br /&gt;
5 7 5  (0-5-12-17)  Dudon Mohajira    &lt;br /&gt;
5 7 5  (0-5-12-17)  Mojahira, Iraq    &lt;br /&gt;
7 2 7  (0-7-9-16)  Nahawand      &lt;br /&gt;
7 3 7  (0-7-10-17)  Buselik      &lt;br /&gt;
7 3 7  (0-7-10-17)  Busalik, Nihâvend    &lt;br /&gt;
7 4 6  (0-7-11-17)  Müstear      &lt;br /&gt;
7 4 9  (0-7-11-20)  Neveser      &lt;br /&gt;
7 5 5  (0-7-12-17)  Rast      &lt;br /&gt;
7 5 5  (0-7-12-17)  Rast, Nagdi, Neutral Diatonic, Islamic Diatonic &lt;br /&gt;
7 5 5  (0-7-12-17)  Modern Rast, Avicenna    &lt;br /&gt;
7 6 4  (0-7-13-17)  Turkish Rast    &lt;br /&gt;
7 7 3  (0-7-14-17)  Mahur      &lt;br /&gt;
7 7 3  (0-7-14-17)  Çargâh      &lt;br /&gt;
8 7 2  (0-8-15-17)  Septimal 'Ajam    &lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:12:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc6"&gt;&lt;a name="Partial scales-Pentachords"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:12 --&gt;Pentachords&lt;/h2&gt;
(from Scala)&lt;br /&gt;
3 7 7 7  (0-3-10-17-24)  Kürdi &lt;br /&gt;
4 4 9 7  (0-4-8-17-24)  Iranian &lt;br /&gt;
4 6 4 7  (0-4-10-14-21)  Hicaz &lt;br /&gt;
4 7 6 7  (0-4-11-17-24)  Segâh &lt;br /&gt;
5 5 7 7  (0-5-10-17-24)  Huseyni &lt;br /&gt;
7 2 7 8  (0-7-9-16-24)  Busalik &lt;br /&gt;
7 3 7 7  (0-7-10-17-24)  Buselik &lt;br /&gt;
7 3 7 7  (0-7-10-17-24)  Busalik &lt;br /&gt;
7 4 6 7  (0-7-11-17-24)  Müstear &lt;br /&gt;
7 4 9 4  (0-7-11-20-24)  Nikriz &lt;br /&gt;
7 5 5 7  (0-7-12-17-24)  Rast &lt;br /&gt;
7 6 4 7  (0-7-13-17-24)  Turkish Rast&lt;br /&gt;
7 7 3 7  (0-7-14-17-24)  Çargâh &lt;br /&gt;
7 7 6 4  (0-7-14-20-24)  Pencgâh&lt;/body&gt;&lt;/html&gt;</pre></div>

Latest revision as of 04:22, 28 September 2025

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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Full list: Category:Tempered scales
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