Harmonics 3–6: Difference between revisions

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{{Infobox AFDO|steps=3}}
{{Infobox harmonics|3}}
'''3afdo''' ([[AFDO|arithmetic frequency division of the octave]]), or '''3odo''' ([[otonal division]] of the octave), if the attempt is made to use it as an actual [[tuning system]], would divide the [[octave]] into three arithmetically equal parts. It is a superset of [[2afdo]] and a subset of [[4afdo]]. It is the first nontrivial afdo since it is the first afdo to demonstrate [[chirality]]. Its inverse is [[3ifdo]]. As a [[scale]] it may also be known as [[harmonic mode|mode 3 of the harmonic series]] or the [[overtone scale #Over-n scales|Over-3]] scale. The notes of this afdo form a 3:4:5 triad (first rotation of the [[just major triad]]) on root position.
{{Harmonics intro|3}} It is the first nontrivial scale of the series, since it is the first to demonstrate [[chirality]]. The notes of this scale form a 3:4:5 triad (first rotation of the [[just major triad]]) in root position.


== 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 23:49, 10 October 2026

Harmonics 3–6
Prime factorization 3 (prime)
Dual sharp fifth 5/3 (884.359c)
Dual flat fifth 4/3 (498.045c)

The harmonics 3–6 (also harmonic series segment 3::6 or harmonic series mode 3) are a scale that consists of harmonics 3 through 6 (3:4:5:6) and repeats at the octave. Used as a tuning system, it is also called 3afdo. The inverse consists of subharmonics 3–6. It is the first nontrivial scale of the series, since it is the first to demonstrate chirality. The notes of this scale form a 3:4:5 triad (first rotation of the just major triad) in root position.

Intervals

# Cents Ratio Decimal Interval name Audio
0 0.0 1/1 1.0000 perfect unison
1 498.0 4/3 1.3333 just perfect fourth
2 884.4 5/3 1.6667 just major sixth
3 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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