Harmonics 8–16: Difference between revisions

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{{Infobox AFDO|steps=8}}
{{Infobox harmonics|8}}


'''8afdo''' ([[AFDO|arithmetic frequency division of the octave]]), or '''8odo''' ([[otonal division]] of the octave), divides the octave into eight parts of 1/8 each. It is a superset of [[7afdo]] and a subset of [[9afdo]]. As a scale it may be known as [[Harmonic mode|mode 8 of the harmonic series]] or the [[Overtone scale #Over-n scales|Over-8]] scale. [[Dante Rosati]] calls this the "Diatonic harmonic series scale". Because 8 is a power of 2, 8afdo corresponds to the 8th to 16th harmonics octave-reduced. 8afdo is a highly effective scale. Above its root it contains many commonly-used intervals such as [[9/8]], [[5/4]], [[3/2]], [[7/4]], [[15/8]], and [[2/1]].
{{Harmonics intro|8}} Above its root it contains many commonly-used intervals such as [[9/8]], [[5/4]], [[3/2]], [[7/4]], [[15/8]], and [[2/1]].
The [[otonal heptad]] can be obtained by removing harmonic 15.


The smallest [[edo]] that maintains 25% or lower relative error on all intervals of 8afdo is [[87edo]].
The smallest [[edo]] that maintains 25% or lower relative error on all intervals of this scale is [[87edo]].


== Intervals ==
== Intervals ==
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== Scales ==
== Scales ==
* [[Otonalpentad]]: 9/8-10/8-12/8-14/8-16/8 ''(a.k.a. springwater{{idiosyncratic}})''
{{Idiosyncratic 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.}}
* Otonalpentad with sharper third degree: 9/8-11/8-12/8-14/8-16/8
* 8:9:10:12:13:16 Metamorphic
* Otonalpentad with sharper fifth degree: 9/8-10/8-12/8-15/8-16/8
* 8:9:10:12:14:16 [[Otonalpentad]] (aka "rotated [[Harmonics 5–10]]", aka "springwater")
* 8:9:10:12:15:16 Ionosphere
* 8:9:11:12:13:16 Upwelling (clashes with some timbres, be careful with instrumentation)
* 8:9:11:12:14:16 Undercurrent
* 8:10:11:12:14:16 Ultraviolet


== Music ==
== Music ==
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* [https://www.youtube.com/watch?v=FlwN7qSGz9U ''Paracelsus for Diatonic Harmonic Guitar'']
* [https://www.youtube.com/watch?v=FlwN7qSGz9U ''Paracelsus for Diatonic Harmonic Guitar'']
* [https://www.youtube.com/watch?v=U6ElPRoIZak ''No Snow for Diatonic Harmonic Guitar'']
* [https://www.youtube.com/watch?v=U6ElPRoIZak ''No Snow for Diatonic Harmonic Guitar'']
== See also ==
* [[Harmonics 16–32]]
* [[Harmonics 32–64]]
{{Navbox harmonics}}

Latest revision as of 02:32, 11 October 2026

Harmonics 8–16
Prime factorization 23
Fifth 12/8 (701.955c)

The harmonic segment 8::16 (also harmonics 8–16) consists of harmonics 8 through 16 (8:9:…:16) and spans one octave above the root. Used as a scale, it is also called mode 8 of the harmonic series. Above its root it contains many commonly-used intervals such as 9/8, 5/4, 3/2, 7/4, 15/8, and 2/1. The otonal heptad can be obtained by removing harmonic 15.

The smallest edo that maintains 25% or lower relative error on all intervals of this scale is 87edo.

Intervals

# Cents Ratio Decimal Interval name Audio
0 0 1/1 1.0000 perfect unison
1 203.91 9/8 1.1250 whole tone
2 386.31 5/4 1.2500 just major third
3 551.32 11/8 1.3750 undecimal superfourth
4 701.96 3/2 1.5000 just perfect fifth
5 840.53 13/8 1.6250 lesser tridecimal neutral sixth
6 968.83 7/4 1.7500 harmonic seventh
7 1088.27 15/8 1.8750 just major seventh
8 1200.00 2/1 2.0000 perfect octave

Scales

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.

  • 8:9:10:12:13:16 Metamorphic
  • 8:9:10:12:14:16 Otonalpentad (aka "rotated Harmonics 5–10", aka "springwater")
  • 8:9:10:12:15:16 Ionosphere
  • 8:9:11:12:13:16 Upwelling (clashes with some timbres, be careful with instrumentation)
  • 8:9:11:12:14:16 Undercurrent
  • 8:10:11:12:14:16 Ultraviolet

Music

Dante Rosati

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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