4afdo: Difference between revisions
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{{Infobox | {{Infobox AFDO|steps=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]]. | ||
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. | |||
== Intervals == | == Intervals == | ||
{| class="wikitable center-all" | {| class="wikitable center-all" | ||
|- | |||
! # | ! # | ||
! Cents | ! Cents | ||
| Line 37: | Line 40: | ||
| 968.8 | | 968.8 | ||
| [[7/4]] | | [[7/4]] | ||
| 1. | | 1.7500 | ||
| harmonic seventh | | harmonic seventh | ||
| [[File:Jid_7_4_pluck_adu_dr220.mp3]] | | [[File:Jid_7_4_pluck_adu_dr220.mp3]] | ||
| Line 48: | Line 51: | ||
| [[File:Jid_2_1_pluck_adu_dr220.mp3]] | | [[File:Jid_2_1_pluck_adu_dr220.mp3]] | ||
|} | |} | ||
Latest revision as of 09:58, 22 January 2026
4afdo (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 mode 4 of the harmonic series or the 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 harmonic seventh chord.
The smallest edos 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.
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 |