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{{Infobox | {{Infobox AFDO|steps=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]]. | |||
The smallest [[edo]] that maintains 25% or lower relative error on all intervals of 8afdo is [[87edo]]. | |||
== Intervals == | == Intervals == | ||
{| class="wikitable center-all" | {| class="wikitable center-all" | ||
| Line 6: | Line 10: | ||
! Cents | ! Cents | ||
! Ratio | ! Ratio | ||
! Decimal | |||
! Interval name | ! Interval name | ||
! Audio | ! Audio | ||
| Line 12: | Line 17: | ||
| 0 | | 0 | ||
| [[1/1]] | | [[1/1]] | ||
| 1.0000 | |||
| perfect unison | | perfect unison | ||
| | | | ||
|- | |- | ||
| 1 | | 1 | ||
| 203. | | 203.91 | ||
| [[9/8]] | | [[9/8]] | ||
| | | 1.1250 | ||
| whole tone | |||
| [[File:Jid_9_8_pluck_adu_dr220.mp3]] | | [[File:Jid_9_8_pluck_adu_dr220.mp3]] | ||
|- | |- | ||
| 2 | | 2 | ||
| 386. | | 386.31 | ||
| [[5/4]] | | [[5/4]] | ||
| 1.2500 | |||
| just major third | | just major third | ||
| [[File:Jid_5_4_pluck_adu_dr220.mp3]] | | [[File:Jid_5_4_pluck_adu_dr220.mp3]] | ||
|- | |- | ||
| 3 | | 3 | ||
| 551. | | 551.32 | ||
| [[11/8]] | | [[11/8]] | ||
| 1.3750 | |||
| undecimal superfourth | | undecimal superfourth | ||
| [[File:Jid_11_8_pluck_adu_dr220.mp3]] | | [[File:Jid_11_8_pluck_adu_dr220.mp3]] | ||
|- | |- | ||
| 4 | | 4 | ||
| | | 701.96 | ||
| [[3/2]] | | [[3/2]] | ||
| 1.5000 | |||
| just perfect fifth | | just perfect fifth | ||
| [[File:Jid_3_2_pluck_adu_dr220.mp3]] | | [[File:Jid_3_2_pluck_adu_dr220.mp3]] | ||
|- | |- | ||
| 5 | | 5 | ||
| 840. | | 840.53 | ||
| [[13/8]] | | [[13/8]] | ||
| 1.6250 | |||
| lesser tridecimal neutral sixth | | lesser tridecimal neutral sixth | ||
| [[File:Jid_13_8_pluck_adu_dr220.mp3]] | | [[File:Jid_13_8_pluck_adu_dr220.mp3]] | ||
|- | |- | ||
| 6 | | 6 | ||
| 968. | | 968.83 | ||
| [[7/4]] | | [[7/4]] | ||
| 1.7500 | |||
| harmonic seventh | | harmonic seventh | ||
| [[File:Jid_7_4_pluck_adu_dr220.mp3]] | | [[File:Jid_7_4_pluck_adu_dr220.mp3]] | ||
|- | |- | ||
| 7 | | 7 | ||
| 1088. | | 1088.27 | ||
| [[15/8]] | | [[15/8]] | ||
| 1.8750 | |||
| just major seventh | | just major seventh | ||
| [[File:Jid_15_8_pluck_adu_dr220.mp3]] | | [[File:Jid_15_8_pluck_adu_dr220.mp3]] | ||
|- | |- | ||
| 8 | | 8 | ||
| 1200. | | 1200.00 | ||
| [[2/1]] | | [[2/1]] | ||
| 2.0000 | |||
| perfect octave | | perfect octave | ||
| [[File:Jid_2_1_pluck_adu_dr220.mp3]] | | [[File:Jid_2_1_pluck_adu_dr220.mp3]] | ||
|} | |} | ||
[[ | == Scales == | ||
{{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.}} | |||
* 8:9:10:12:13:16 Metamorphic | |||
* 8:9:10:12:14:16 [[Otonalpentad]] (aka "rotated [[5afdo]]", 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]] | |||
* [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''] | |||
== See also == | |||
* [[16afdo]] | |||
* [[32afdo]] | |||
Latest revision as of 14:38, 23 April 2026
8afdo (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 mode 8 of the harmonic series or the 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.
The smallest edo that maintains 25% or lower relative error on all intervals of 8afdo 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 5afdo", 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