Harmonics 2–4: Difference between revisions

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{{Infobox ADO|steps=2}}
{{Infobox harmonics|2}}
'''2ado''' ([[ADO|arithmetic division of the octave]]), or '''2-ODO''' ([[otonal division]] of the octave), if the attempt is made to use it as an actual scale, would divide the [[octave]] into two arithmetically equal parts, and may also be known as [[Harmonic mode|mode 2 of the harmonic series]] or the [[Overtone_scale#Over-n_scales|Over-2]] scale. The only non-trivial interval is the just perfect fifth [[3/2]], since 3/2 is arithmetically halfway between 1/1 and 2/1.
{{Harmonics intro|2}} It is equivalent to Subharmonics 2–4, and to the [[1L 1s|monowood]] [[mos scale]] tuned to the just perfect fifth or just perfect fourth. The only non-trivial intervals are the just perfect fifth [[3/2]], since 3/2 is arithmetically halfway between 1/1 and 2/1, and its [[octave complement]] [[4/3]].


== Intervals ==
== Intervals ==
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[[Category:ADO]]
{{Navbox harmonics}}

Latest revision as of 23:38, 10 October 2026

Harmonics 2–4
Prime factorization 2 (prime)
Fifth 3/2 (701.955c)

The harmonics 2–4 (also harmonic series segment 2::4 or harmonic series mode 2) are a scale that consists of harmonics 2 through 4 (2:3:4) and repeats at the octave. Used as a tuning system, it is also called 2afdo. It is equivalent to Subharmonics 2–4, and to the monowood mos scale tuned to the just perfect fifth or just perfect fourth. The only non-trivial intervals are the just perfect fifth 3/2, since 3/2 is arithmetically halfway between 1/1 and 2/1, and its octave complement 4/3.

Intervals

# Cents Ratio Decimal Interval name Audio
0 0.0 1/1 1.0000 perfect unison
1 702.0 3/2 1.5000 just perfect fifth
2 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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