Harmonics 16–32: Difference between revisions

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{{Infobox AFDO|steps=16}}
{{Infobox harmonics|16}}


'''16afdo''' ([[AFDO|arithmetic frequency division of the octave]]), or '''16-ODO''' ([[otonal division]] of the octave), divides the octave into 16 parts of 1/16 each. It is a superset of [[15afdo]] and a subset of [[17afdo]]. As a scale it may be known as [[Harmonic mode|mode 16 of the harmonic series]] or the [[Overtone scale #Over-n scales|Over-16]] scale. Because 16 is a power of 2, 16afdo corresponds to the 16th to 32nd harmonics octave-reduced.
{{Harmonics intro|16}}


The smallest [[edo]] that maintains 25% or lower relative error on all intervals of 16afdo is [[311edo]].
The smallest [[edo]] that maintains 25% or lower relative error on all intervals of this scale is [[311edo]].


== Intervals ==
== Intervals ==
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| 1.8125
| 1.8125
| octave-reduced 29th harmonic
| octave-reduced 29th harmonic
| [[File:Jid_7_4_pluck_adu_dr220.mp3]]
|
|-
|-
| 14
| 14
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== See also ==
== See also ==
* [[8afdo]]
* [[Harmonics 8–16]]
* [[32afdo]]
* [[Harmonics 32–64]]
 
{{Navbox harmonics}}

Latest revision as of 00:10, 11 October 2026

Harmonics 16–32
Prime factorization 24
Fifth 24/16 (701.955c)

The harmonic segment 16::32 (also harmonics 16–32) consists of harmonics 16 through 32 (16:17:…:32) and spans one octave above the root. Used as a scale, it is also called mode 16 of the harmonic series. The inverse consists of subharmonics 16–32.

The smallest edo that maintains 25% or lower relative error on all intervals of this scale is 311edo.

Intervals

# Cents Ratio Decimal Interval name Audio
0 0 1/1 1.0000 perfect unison
1 104.96 17/16 1.0625 large septendecimal semitone
2 203.91 9/8 1.1250 whole tone
3 297.51 19/16 1.1875 otonal minor third
4 386.31 5/4 1.2500 just major third
5 470.78 21/16 1.3125 septimal subfourth
6 551.32 11/8 1.3750 undecimal superfourth
7 628.27 23/16 1.4375 octave-reduced 23rd harmonic
8 701.96 3/2 1.5000 just perfect fifth
9 772.63 25/16 1.5625 classic(al) augmented fifth
10 840.53 13/8 1.6250 lesser tridecimal neutral sixth
11 905.87 27/16 1.6875 Pythagorean major sixth
12 968.83 7/4 1.7500 harmonic seventh
13 1029.58 29/16 1.8125 octave-reduced 29th harmonic
14 1088.27 15/8 1.8750 just major seventh
15 1145.04 31/16 1.9375 octave-reduced 31st harmonic
16 1200.00 2/1 2.0000 perfect octave

Scales

See also: 5- to 10-tone scales from the modes of the harmonic series
This article or section contains multiple idiosyncratic terms. Such terms are used by only a few people and are not regularly used within the community.

Terms: Most of these names were coined, and are solely used, by Budjarn Lambeth - however he was only the first to name many of these scales, others have probably already used them before him

  • 16:17:20:22:24:28:15:32 Deister Tune 216
  • 16:17:20:24:28:32 Volcanic
  • 16:18:19:24:28:32 Moonbeam
  • 16:18:21:24:26:28:32 Canopy
  • 16:19:20:24:28:32 Mechanical

Music

Ambient Esoterica
Bryan Deister

See also

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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