Harmonics 32–64: Difference between revisions
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{{Infobox | {{Infobox harmonics|32}} | ||
{{Harmonics intro|32}} | |||
The smallest [[edo]] that maintains 25% or lower relative error on all intervals of this scale 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 == | == 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 }} | ||
{{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}} | |||
* 32:34:36:38:40:43:44:48:52:54:56:58:60:64 ''loose approximation of [[fluid just intonation]]'' | |||
* 32:40:43:48:57:64 Arcade | |||
* 32:43:48:51:57:64 Cosmic | |||
* ''[[User:BudjarnLambeth/Some tunings for Japanese scales#Over-2]]'' (most of these are in this scale) | |||
== Music == | |||
; [[Adam Neely]] | |||
* [https://www.youtube.com/watch?v=tMSXdCWbRHw ''How to See Ghosts'' (demonstration piece)] (2018) – The piece starts at 10:17 | |||
== See also == | |||
* [[Harmonics 8–16]] | |||
* [[Harmonics 16–32]] | |||
{{Navbox harmonics}} | |||
Latest revision as of 00:37, 11 October 2026
| Prime factorization | 25 |
| Fifth | 48/32 (701.955c) |
The harmonic segment 32::64 (also harmonics 32–64) consists of harmonics 32 through 64 (32:33:…:64) and spans one octave above the root. Used as a scale, it is also called mode 32 of the harmonic series.
The smallest edo that maintains 25% or lower relative error on all intervals of this scale 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
|
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 |
- 32:34:36:38:40:43:44:48:52:54:56:58:60:64 loose approximation of fluid just intonation
- 32:40:43:48:57:64 Arcade
- 32:43:48:51:57:64 Cosmic
- User:BudjarnLambeth/Some tunings for Japanese scales#Over-2 (most of these are in this scale)
Music
- How to See Ghosts (demonstration piece) (2018) – The piece starts at 10:17
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 |