20afdo: Difference between revisions

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'''20afdo''' ([[AFDO|arithmetic frequency division of the octave]]), or '''20odo''' ([[otonal division]] of the octave), divides the octave into 20 parts of 1/20 each. As a scale it may be known as [[Harmonic mode|mode 20 of the harmonic series]] or the [[Overtone scale #Over-n scales|Over-20]] scale.
'''20afdo''' ([[AFDO|arithmetic frequency division of the octave]]), or '''20odo''' ([[otonal division]] of the octave), divides the octave into 20 parts of 1/20 each. As a scale it may be known as [[Harmonic mode|mode 20 of the harmonic series]] or the [[Overtone scale #Over-n scales|Over-20]] scale.
{| class="wikitable"
|-
| | otone
| | 20
| | 21
| | 22
| | 23
| | 24
| | 25
| | 26
| | 27
| | 28
| | 29
| | 30
| | 31
| | 32
| | 33
| | 34
| | 35
| | 36
| | 37
| | 38
| | 39
| | 40
|-
| | freq. ratio
| | 1/1
| | 21/20
| | 11/10
| | 23/20
| | 6/5
| | 5/4
| | 13/10
| | 27/20
| | 7/5
| | 29/20
| | 3/2
| | 31/20
| | 8/5
| | 33/20
| | 17/10
| | 7/4
| | 9/5
| | 37/20
| | 19/10
| | 39/20
| | 2/1
|-
| | cents
| | 0
| | 84
| | 165
| | 242
| | 316
| | 386
| | 454
| | 520
| | 583
| | 643
| | 702
| | 759
| | 814
| | 867
| | 919
| | 969
| | 1018
| | 1065
| | 1111
| | 1156
| | 1200
|}
A reference chart to find cents values for every interval available in this scale:
{| class="wikitable"
|-
| |
| | 20
| | 21
| | 22
| | 23
| | 24
| | 25
| | 26
| | 27
| | 28
| | 29
| | 30
| | 31
| | 32
| | 33
| | 34
| | 35
| | 36
| | 37
| | 38
| | 39
|-
| | 20
| | 0
| | 84
| | 165
| | 242
| | 316
| | 386
| | 454
| | 520
| | 583
| | 643
| | 702
| | 759
| | 814
| | 867
| | 919
| | 969
| | 1018
| | 1065
| | 1111
| | 1156
|-
| | 21
| | 1116
| | 0
| | 81
| | 157
| | 231
| | 302
| | 370
| | 435
| | 498
| | 559
| | 617
| | 674
| | 729
| | 782
| | 834
| | 884
| | 933
| | 981
| | 1027
| | 1072
|-
| | 22
| | 1035
| | 1119
| | 0
| | 77
| | 151
| | 221
| | 289
| | 355
| | 418
| | 478
| | 537
| | 594
| | 649
| | 702
| | 754
| | 804
| | 853
| | 900
| | 946
| | 991
|-
| | 23
| | 958
| | 1043
| | 1123
| | 0
| | 74
| | 144
| | 212
| | 278
| | 341
| | 401
| | 460
| | 517
| | 572
| | 625
| | 677
| | 727
| | 776
| | 823
| | 869
| | 914
|-
| | 24
| | 884
| | 969
| | 1049
| | 1126
| | 0
| | 71
| | 139
| | 204
| | 267
| | 328
| | 386
| | 443
| | 498
| | 551
| | 603
| | 653
| | 702
| | 749
| | 796
| | 841
|-
| | 25
| | 814
| | 583
| | 979
| | 1056
| | 1129
| | 0
| | 68
| | 133
| | 196
| | 257
| | 316
| | 372
| | 427
| | 481
| | 532
| | 583
| | 631
| | 679
| | 725
| | 770
|-
| | 26
| | 746
| | 830
| | 911
| | 988
| | 1061
| | 1132
| | 0
| |
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|-
| | 27
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| | 28
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| | 29
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| | 30
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| | 31
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| | 32
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| | 33
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| | 34
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| | 35
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| | 36
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| | 37
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| | 38
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| | 39
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|}
{{Todo| complete table }}

Revision as of 10:54, 20 September 2023

← 19afdo 20afdo 21afdo →
Prime factorization 22 × 5
Fifth 30/20 (701.955c)

20afdo (arithmetic frequency division of the octave), or 20odo (otonal division of the octave), divides the octave into 20 parts of 1/20 each. As a scale it may be known as mode 20 of the harmonic series or the Over-20 scale.

otone 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40
freq. ratio 1/1 21/20 11/10 23/20 6/5 5/4 13/10 27/20 7/5 29/20 3/2 31/20 8/5 33/20 17/10 7/4 9/5 37/20 19/10 39/20 2/1
cents 0 84 165 242 316 386 454 520 583 643 702 759 814 867 919 969 1018 1065 1111 1156 1200

A reference chart to find cents values for every interval available in this scale:

20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39
20 0 84 165 242 316 386 454 520 583 643 702 759 814 867 919 969 1018 1065 1111 1156
21 1116 0 81 157 231 302 370 435 498 559 617 674 729 782 834 884 933 981 1027 1072
22 1035 1119 0 77 151 221 289 355 418 478 537 594 649 702 754 804 853 900 946 991
23 958 1043 1123 0 74 144 212 278 341 401 460 517 572 625 677 727 776 823 869 914
24 884 969 1049 1126 0 71 139 204 267 328 386 443 498 551 603 653 702 749 796 841
25 814 583 979 1056 1129 0 68 133 196 257 316 372 427 481 532 583 631 679 725 770
26 746 830 911 988 1061 1132 0
27
28
29
30
31
32
33
34
35
36
37
38
39