32afdo: Difference between revisions
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{{Infobox AFDO|steps=32}} | {{Infobox AFDO|steps=32}} | ||
'''32afdo''' ([[AFDO|arithmetic frequency division of the octave]]), or '''32odo''' ([[otonal division]] of the octave), divides the octave into 32 parts of 1/32 each. As a scale it may be known as [[Harmonic mode|mode 32 of the harmonic series]] or the [[Overtone scale #Over-n scales|Over-32]] scale. | '''32afdo''' ([[AFDO|arithmetic frequency division of the octave]]), or '''32odo''' ([[otonal division]] of the octave), divides the octave into 32 parts of 1/32 each. It is a superset of [[31afdo]] and a subset of [[33afdo]]. As a scale it may be known as [[Harmonic mode|mode 32 of the harmonic series]] or the [[Overtone scale #Over-n scales|Over-32]] scale. | ||
The smallest [[edo]] that maintains 25% or lower relative error on all intervals of 32afdo is [[3159811edo]]. | |||
== Intervals == | == Intervals == | ||
# 33/32 | # [[33/32]] | ||
# 17/16 | # [[17/16]] | ||
# 35/32 | # [[35/32]] | ||
# 9/8 | # [[9/8]] | ||
# 37/32 | # [[37/32]] | ||
# 19/16 | # [[19/16]] | ||
# 39/32 | # [[39/32]] | ||
# 5/4 | # [[5/4]] | ||
# 41/32 | # [[41/32]] | ||
# 21/16 | # [[21/16]] | ||
# 43/32 | # [[43/32]] | ||
# 11/8 | # [[11/8]] | ||
# 45/32 | # [[45/32]] | ||
# 23/16 | # [[23/16]] | ||
# 47/32 | # [[47/32]] | ||
# 3/2 | # [[3/2]] | ||
# 49/32 | # [[49/32]] | ||
# 25/16 | # [[25/16]] | ||
# 51/32 | # [[51/32]] | ||
# 13/8 | # [[13/8]] | ||
# 53/32 | # [[53/32]] | ||
# 27/16 | # [[27/16]] | ||
# 55/32 | # [[55/32]] | ||
# 7/4 | # [[7/4]] | ||
# 57/32 | # [[57/32]] | ||
# 29/16 | # [[29/16]] | ||
# 59/32 | # [[59/32]] | ||
# 15/8 | # [[15/8]] | ||
# 61/32 | # [[61/32]] | ||
# 31/16 | # [[31/16]] | ||
# | # [[63/32]] | ||
# 2/1 | # [[2/1]] | ||
== Scales == | == Scales == | ||
{{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 }} | ||
* Arcade: 40/32 | * Arcade: {{dash|40/32, 43/32, 48/32, 57/32, 64/32|med}} | ||
* Cosmic: 43/32 | * Cosmic: {{dash|43/32, 48/32, 51/32, 57/32, 64/32|med}} | ||
* ''Loose approximation of [[fluid just intonation]]'': 17/16—9/8—19/16—5/4—43/32—11/8—3/2—13/8—27/16—7/4—29/16—15/8—2/1 | |||
== Music == | == Music == | ||
* [https://www.youtube.com/watch?v=tMSXdCWbRHw How to See Ghosts (demonstration piece)] | ; [[Adam Neely]] | ||
* [https://www.youtube.com/watch?v=tMSXdCWbRHw ''How to See Ghosts'' (demonstration piece)] (2018) – The piece starts at 10:17 | |||
Latest revision as of 03:28, 28 March 2025
32afdo (arithmetic frequency division of the octave), or 32odo (otonal division of the octave), divides the octave into 32 parts of 1/32 each. It is a superset of 31afdo and a subset of 33afdo. As a scale it may be known as mode 32 of the harmonic series or the Over-32 scale.
The smallest edo that maintains 25% or lower relative error on all intervals of 32afdo is 3159811edo.
Intervals
- 33/32
- 17/16
- 35/32
- 9/8
- 37/32
- 19/16
- 39/32
- 5/4
- 41/32
- 21/16
- 43/32
- 11/8
- 45/32
- 23/16
- 47/32
- 3/2
- 49/32
- 25/16
- 51/32
- 13/8
- 53/32
- 27/16
- 55/32
- 7/4
- 57/32
- 29/16
- 59/32
- 15/8
- 61/32
- 31/16
- 63/32
- 2/1
Scales
- Arcade: 40/32 – 43/32 – 48/32 – 57/32 – 64/32
- Cosmic: 43/32 – 48/32 – 51/32 – 57/32 – 64/32
- Loose approximation of fluid just intonation: 17/16—9/8—19/16—5/4—43/32—11/8—3/2—13/8—27/16—7/4—29/16—15/8—2/1
Music
- How to See Ghosts (demonstration piece) (2018) – The piece starts at 10:17