Harmonics 17–34: Difference between revisions

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{{Infobox AFDO|steps=17}}
{{Infobox harmonics|17}}


'''17afdo''' ([[AFDO|arithmetic frequency division of the octave]]), or '''17odo''' ([[otonal division]] of the octave), divides the octave into 17 parts of 1/17 each. As a scale it may be known as [[Harmonic mode|mode 17 of the harmonic series]] or the [[Overtone scale #Over-n scales|Over-17]] scale.
{{Harmonics intro|17}}
 
== Intervals ==
{| class="wikitable center-all"
! #
! Cents
! Ratio
! Decimal
! Interval name
! Audio
|-
| 0
| 0.00
| 1/1
| 1.0000
| Perfect unison
|
|-
| 1
| 98.96
| 18/17
| 1.0588
| Small septendecimal semitone
|
|-
| 2
| 192.56
| 19/17
| 1.1176
| Large undevicesimal whole tone
|
|-
| 3
| 281.36
| 20/17
| 1.1765
| Diatismic minor third
|
|-
| 4
| 365.83
| 21/17
| 1.2353
| Septendecimal submajor third
|
|-
| 5
| 446.36
| 22/17
| 1.2941
| Septendecimal supermajor third
|
|-
| 6
| 523.32
| 23/17
| 1.3529
| Vicesimotertial acute fourth
|
|-
| 7
| 597.00
| 24/17
| 1.4118
| Small septendecimal tritone
|
|-
| 8
| 667.67
| 25/17
| 1.4706
| Vengeance subfifth
|
|-
| 9
| 735.57
| 26/17
| 1.5294
| Septendecimal superfifth
|
|-
| 10
| 800.91
| 27/17
| 1.5882
| Septendecimal quasi-tempered minor sixth
|
|-
| 11
| 863.87
| 28/17
| 1.6471
| Septendecimal submajor sixth
|
|-
| 12
| 924.62
| 29/17
| 1.7059
| Vicesimononal supermajor sixth
|
|-
| 13
| 983.31
| 30/17
| 1.7647
| Diatismic minor seventh
|
|-
| 14
| 1040.08
| 31/17
| 1.8235
| Untrigesimal submajor seventh
|
|-
| 15
| 1095.04
| 32/17
| 1.8824
| Septendecimal major seventh
|
|-
| 16
| 1148.31
| 33/17
| 1.9412
| Septendecimal ultramajor seventh
|
|-
| 17
| 1200.00
| 2/1
| 2.0000
| Perfect octave
|
|}
 
 
{{todo|inline=1|add sound example|expand|text=Add audio examples to the table, and write some more page body text about this scale.}}
 
{{Navbox harmonics}}

Latest revision as of 00:10, 11 October 2026

Harmonics 17–34
Prime factorization 17 (prime)
Dual sharp fifth 26/17 (735.572c)
Dual flat fifth 25/17 (667.672c)

The harmonics 17–34 (also harmonic series segment 17::34 or harmonic series mode 17) are a scale that consists of harmonics 17 through 34 (17:18:…:34) and repeats at the octave. Used as a tuning system, it is also called 17afdo.

Intervals

# Cents Ratio Decimal Interval name Audio
0 0.00 1/1 1.0000 Perfect unison
1 98.96 18/17 1.0588 Small septendecimal semitone
2 192.56 19/17 1.1176 Large undevicesimal whole tone
3 281.36 20/17 1.1765 Diatismic minor third
4 365.83 21/17 1.2353 Septendecimal submajor third
5 446.36 22/17 1.2941 Septendecimal supermajor third
6 523.32 23/17 1.3529 Vicesimotertial acute fourth
7 597.00 24/17 1.4118 Small septendecimal tritone
8 667.67 25/17 1.4706 Vengeance subfifth
9 735.57 26/17 1.5294 Septendecimal superfifth
10 800.91 27/17 1.5882 Septendecimal quasi-tempered minor sixth
11 863.87 28/17 1.6471 Septendecimal submajor sixth
12 924.62 29/17 1.7059 Vicesimononal supermajor sixth
13 983.31 30/17 1.7647 Diatismic minor seventh
14 1040.08 31/17 1.8235 Untrigesimal submajor seventh
15 1095.04 32/17 1.8824 Septendecimal major seventh
16 1148.31 33/17 1.9412 Septendecimal ultramajor seventh
17 1200.00 2/1 2.0000 Perfect octave


Todo: add sound example, expand

Add audio examples to the table, and write some more page body text about this scale.

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
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