Harmonics 4–8: Difference between revisions

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{{Infobox AFDO|steps=4}}
{{Infobox harmonics|4}}
[[File:4ado scale.wav|thumb]]
[[File:4ado scale.wav|thumb]]


'''4afdo''' ([[AFDO|arithmetic division of the octave]]), or '''4odo''' ([[otonal division]] of the octave), divides the octave into four parts of 1/4 each. It is a superset of [[3afdo]] and a subset of [[5afdo]]. As a scale it may be known as [[Harmonic mode|mode 4 of the harmonic series]] or the [[Overtone scale #Over-n scales|Over-4]] scale. Because 4 is a power of 2, 4afdo corresponds to the 4th to 8th harmonics octave-reduced. The notes of 4afdo create a [[4:5:6:7|harmonic seventh chord]].
{{Harmonics intro|4}} The notes of this scale create a [[4:5:6:7|harmonic seventh chord]].


The smallest [[edo]]s that maintain 25% or lower relative error on all intervals of 4afdo are [[10edo]] and [[15edo]], though they are not very accurate. The next two edos, [[22edo]] and [[31edo]], are the smallest that approximate 4afdo with appreciable accuracy.
The smallest [[edo]]s that maintain 25% or lower relative error on all intervals of this scale are [[10edo]] and [[15edo]], though they are not very accurate. The next two edos, [[22edo]] and [[31edo]], are the smallest that approximate this scale with appreciable accuracy.


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

Latest revision as of 23:50, 10 October 2026

Harmonics 4–8
Prime factorization 22
Fifth 6/4 (701.955c)

The harmonics 4–8 (also harmonic series segment 4::8 or harmonic series mode 4) are a scale that consists of harmonics 4 through 8 (4:5:6:7:8) and repeats at the octave. Used as a tuning system, it is also called 4afdo. The notes of this scale create a harmonic seventh chord.

The smallest edos that maintain 25% or lower relative error on all intervals of this scale are 10edo and 15edo, though they are not very accurate. The next two edos, 22edo and 31edo, are the smallest that approximate this scale with appreciable accuracy.

Intervals

# Cents Ratio Decimal Interval name Audio
0 0 1/1 1.0000 perfect unison
1 386.3 5/4 1.2500 just major third
2 702.0 3/2 1.5000 just perfect fifth
3 968.8 7/4 1.7500 harmonic seventh
4 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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