Harmonics 20–40: Difference between revisions

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{{Infobox AFDO|steps=20}}
{{Infobox harmonics|20}}


'''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.
{{Harmonics intro|20}}
 
== Intervals ==
{| 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
|}
 
=== Internal intervals ===
 
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 }}
 
== Scales ==
 
* [[3-5-7-9 hexany]]
* 20:21:24:28:30:35:40 Rotated [[Ternessbabdec]]
 
{{Navbox harmonics}}

Latest revision as of 00:12, 11 October 2026

Harmonics 20–40
Prime factorization 22 × 5
Fifth 30/20 (701.955c)

The harmonic segment 20::40 (also harmonics 20–40) consists of harmonics 20 through 40 (20:21:…:40) and spans one octave above the root. Used as a scale, it is also called mode 20 of the harmonic series.

Intervals

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

Internal intervals

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

Scales

View • Talk • EditOvertone scales 
Small modes 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24
Larger modes 30 • 32 • 36 • 48 • 60 • 128
Families /2: 2 • 4 • 8 • 16 • 32 • 128
/3: 3 • 6 • 9 • 12 • 15 • 18 • 21 • 24
/5: 5 • 10 • 15 • 20 • 25 • 30 • 35 • 60 • 80
/7: 7 • 14 • 21 • 28 • 35 • 56
/11: 11 • 22 • 33
/13: 13 • 26
Related Harmonic series • Subharmonic series • Carlos harmonic scale • Ringer scale • Primodality
Retrieved from "https://en.xen.wiki/index.php?title=Harmonics_20–40&oldid=239221"