Harmonics 9–18: Difference between revisions

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{{Infobox AFDO|steps=9}}
{{Infobox harmonics|9}}


'''9afdo''' ([[AFDO|arithmetic frequency division of the octave]]), or '''9odo''' ([[otonal division]] of the octave), divides the octave into nine parts of 1/9 each. It is a superset of [[8afdo]] and a subset of [[10afdo]]. As a scale it may be known as [[Harmonic mode|mode 9 of the harmonic series]] or the [[Overtone scale #Over-n scales|Over-9]] scale. As 9 is a small odd number, this afdo does not contain a perfect fifth above the root.
{{Harmonics intro|9}} As 9 is a small odd number, this scale does not contain a perfect fifth above the root.


== Intervals ==
== Intervals ==
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| [[File:Jid_2_1_pluck_adu_dr220.mp3]]
| [[File:Jid_2_1_pluck_adu_dr220.mp3]]
|}
|}
{{Navbox harmonics}}

Latest revision as of 01:55, 11 October 2026

Harmonics 9–18
Prime factorization 32
Dual sharp fifth 14/9 (764.916c)
Dual flat fifth 13/9 (636.618c)

The harmonics 9–18 (also harmonic series segment 9::18 or harmonic series mode 9) are a scale that consists of harmonics 9 through 18 (9:10:…:18) and repeats at the octave. Used as a tuning system, it is also called 9afdo. As 9 is a small odd number, this scale does not contain a perfect fifth above the root.

Intervals

# Cents Ratio Decimal Interval name Audio
0 0 1/1 1.0000 perfect unison
1 182.4 10/9 1.1111 small whole tone
2 347.4 11/9 1.2222 undecimal neutral third
3 498.0 4/3 1.3333 perfect fourth
4 636.6 13/9 1.4444 tridecimal diminished fifth
5 764.9 14/9 1.5556 subminor sixth
6 884.4 5/3 1.6667 just major sixth
7 996.1 16/9 1.7778 Pythagorean minor seventh
8 1101.0 17/9 1.8889 large septendecimal major seventh
9 1200.0 2/1 2.0000 perfect octave
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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