16afdo: Difference between revisions
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{{Infobox AFDO|steps=16}} | {{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. 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. | '''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 135: | Line 138: | ||
{{See also| 5- to 10-tone scales from the modes of the harmonic series }} | {{See also| 5- to 10-tone scales from the modes of the harmonic series }} | ||
* Mechanical: 19/ | * [[1-3-7-9 hexany]] | ||
* Moonbeam: 18/ | * Deister Tune 216: 17/16–5/4–11/8–3/2–7/4–15/8–32/16 | ||
* Volcanic: 17/ | * Mechanical: 19/16–20/16–24/16–28/16–32/16 | ||
* Moonbeam: 18/16–19/16–24/16–30/16–32/16 | |||
* Volcanic: 17/16–20/16–24/16–28/16–32/16 | |||
== Music == | == Music == | ||
* [https:// | ; [[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''] | |||
Latest revision as of 10:40, 10 August 2025
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
- 1-3-7-9 hexany
- Deister Tune 216: 17/16–5/4–11/8–3/2–7/4–15/8–32/16
- Mechanical: 19/16–20/16–24/16–28/16–32/16
- Moonbeam: 18/16–19/16–24/16–30/16–32/16
- Volcanic: 17/16–20/16–24/16–28/16–32/16