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List of distinct EDO scales: Difference between revisions

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Each [[Equal_division_of_the_octave|EDO]] has a finite number of distinct scales, assuming that the scales are equivalent up to cyclical permutation and that they are also irreducible. By irreducible is meant a scale that is not supported by a smaller EDO (e.g. 4424442, the diatonic scale in 24-EDO, is reducible because it is also contained in 12-EDO).
Each [[Equal_division_of_the_octave|EDO]] has a finite number of distinct scales, assuming that the scales are equivalent up to cyclical permutation and that they are also irreducible. By irreducible is meant a scale that is not supported by a smaller EDO (e.g. 4424442, the diatonic scale in 24-EDO, is reducible because it is also contained in 12-EDO).


Below is a table which counts every possible scale for a given EDO (columns) and number of steps/notes (rows). Note that the total number of scales for each EDO is given by OEIS entries [http://oeis.org/A059966 A059966] and [http://oeis.org/A001037 A001037].
Below is a table which counts every possible scale for a given EDO (columns) and number of steps/notes (rows). Note that the total number of scales for each EDO is given by {{OEIS|A059966}} and {{OEIS|A001037}}.  


==Breakdown of Scales by EDO and Number of Notes==
==Breakdown of Scales by EDO and Number of Notes==


{| class="wikitable"
{| class="wikitable"
! colspan="2" rowspan="2"|
! colspan="16" |EDO
|-
|-
| |
| |
| |
| |
| |
| |
| |
| |
| |
| |
| | EDO
| |
| |
| |
| |
| |
| |
| |
|-
| |
| |
| | 1
| | 1
| | 2
| | 2
Line 45: Line 26:
| | 16
| | 16
|-
|-
| |
!  rowspan="16"| N
| | 1
| | 1
| | 1
| | 1
Line 64: Line 45:
| |  
| |  
|-
|-
| |
| | 2
| | 2
| |  
| |  
Line 83: Line 63:
| | 4
| | 4
|-
|-
| |
| | 3
| | 3
| |  
| |  
Line 102: Line 81:
| | 28
| | 28
|-
|-
| |
| | 4
| | 4
| |  
| |  
Line 121: Line 99:
| | 106
| | 106
|-
|-
| |
| | 5
| | 5
| |  
| |  
Line 140: Line 117:
| | 266
| | 266
|-
|-
| |
| | 6
| | 6
| |  
| |  
Line 159: Line 135:
| | 500
| | 500
|-
|-
| |
| | 7
| | 7
| |  
| |  
Line 178: Line 153:
| | 714
| | 714
|-
|-
| | N
| | 8
| | 8
| |  
| |  
Line 197: Line 171:
| | 809
| | 809
|-
|-
| |
| | 9
| | 9
| |  
| |  
Line 216: Line 189:
| | 715
| | 715
|-
|-
| |
| | 10
| | 10
| |  
| |  
Line 235: Line 207:
| | 504
| | 504
|-
|-
| |
| | 11
| | 11
| |  
| |  
Line 254: Line 225:
| | 273
| | 273
|-
|-
| |
| | 12
| | 12
| |  
| |  
Line 273: Line 243:
| | 116
| | 116
|-
|-
| |
| | 13
| | 13
| |  
| |  
Line 292: Line 261:
| | 35
| | 35
|-
|-
| |
| | 14
| | 14
| |  
| |  
Line 311: Line 279:
| | 8
| | 8
|-
|-
| |
| | 15
| | 15
| |  
| |  
Line 330: Line 297:
| | 1
| | 1
|-
|-
| |
| | 16
| | 16
| |  
| |  
Line 349: Line 315:
| | 1
| | 1
|-
|-
| |
| colspan="2"| Total
| |
| |
| |
| |
| |
| |
| |
| |
| |
| |
| |
| |
| |
| |
| |
| |
| |
|-
| |
| | Total
| | 1
| | 1
| | 1
| | 1
Line 387: Line 333:
| | 4080
| | 4080
|}
|}
(if someone could format this table a little better, it would be greatly appreciated)


==Breakdown of Scales by EDO Only==
==Breakdown of Scales by EDO Only==
Retrieved from "https://en.xen.wiki/w/List_of_distinct_EDO_scales"