16afdo: Difference between revisions
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CompactStar (talk | contribs) Created page with "{{Infobox ADO|steps=16}} '''16ado''' is the arithmetic equal division of the octave into 16 parts of 1/16 each. Because 16 is a power of 2, 16ado corresponds to the 16..." |
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{{Infobox | {{Infobox AFDO|steps=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. | |||
The smallest [[edo]] that maintains 25% or lower relative error on all intervals of 16afdo is [[311edo]]. | |||
== Intervals == | == Intervals == | ||
{| class="wikitable center-all" | {| class="wikitable center-all" | ||
|- | |||
! # | ! # | ||
! Cents | ! Cents | ||
| Line 37: | Line 41: | ||
| 1.1875 | | 1.1875 | ||
| otonal minor third | | otonal minor third | ||
| [[File: | | [[File:Jid_19_16_pluck_adu_dr220.mp3]] | ||
|- | |- | ||
| 4 | | 4 | ||
| Line 121: | Line 125: | ||
| 1.9375 | | 1.9375 | ||
| octave-reduced 31st harmonic | | octave-reduced 31st harmonic | ||
| [[File:Jid_31_16_pluck_adu_dr220.mp3] | | [[File:Jid_31_16_pluck_adu_dr220.mp3]] | ||
|- | |- | ||
| 16 | | 16 | ||
| Line 131: | Line 135: | ||
|} | |} | ||
[[ | == Scales == | ||
{{See also| 5- to 10-tone scales from the modes of the harmonic series }} | |||
{{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}} | |||
* 16:17:20:22:24:28:15:32 [[Bryan Deister|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]] | |||
* [https://www.youtube.com/watch?v=-uolE48lmto ''Between 16th and 32nd | Harmonic Series Experiments''] | |||
; [[Bryan Deister]] | |||
* [https://www.youtube.com/watch?v=fdmunv0F9WA ''my tune 216 played on 2/16 at 216hz in 17-limit JI''] | |||
== See also == | |||
* [[8afdo]] | |||
* [[32afdo]] | |||
Latest revision as of 02:17, 14 April 2026
16afdo (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 mode 16 of the harmonic series or the Over-16 scale. Because 16 is a power of 2, 16afdo corresponds to the 16th to 32nd harmonics octave-reduced.
The smallest edo that maintains 25% or lower relative error on all intervals of 16afdo 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
|
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