Harmonics 8–16: Difference between revisions
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{{Infobox | {{Infobox harmonics|8}} | ||
{{Harmonics intro|8}} 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 [[otonal heptad]] can be obtained by removing harmonic 15. | |||
The smallest [[edo]] that maintains 25% or lower relative error on all intervals of this scale is [[87edo]]. | |||
== Intervals == | == Intervals == | ||
{| class="wikitable center-all" | {| class="wikitable center-all" | ||
| Line 18: | Line 23: | ||
|- | |- | ||
| 1 | | 1 | ||
| 203. | | 203.91 | ||
| [[9/8]] | | [[9/8]] | ||
| 1.1250 | | 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 | | 1.2500 | ||
| Line 32: | Line 37: | ||
|- | |- | ||
| 3 | | 3 | ||
| 551. | | 551.32 | ||
| [[11/8]] | | [[11/8]] | ||
| 1.3750 | | 1.3750 | ||
| Line 39: | Line 44: | ||
|- | |- | ||
| 4 | | 4 | ||
| | | 701.96 | ||
| [[3/2]] | | [[3/2]] | ||
| 1.5000 | | 1.5000 | ||
| Line 46: | Line 51: | ||
|- | |- | ||
| 5 | | 5 | ||
| 840. | | 840.53 | ||
| [[13/8]] | | [[13/8]] | ||
| 1.6250 | | 1.6250 | ||
| Line 53: | Line 58: | ||
|- | |- | ||
| 6 | | 6 | ||
| 968. | | 968.83 | ||
| [[7/4]] | | [[7/4]] | ||
| 1.7500 | | 1.7500 | ||
| Line 60: | Line 65: | ||
|- | |- | ||
| 7 | | 7 | ||
| 1088. | | 1088.27 | ||
| [[15/8]] | | [[15/8]] | ||
| 1.8750 | | 1.8750 | ||
| Line 67: | Line 72: | ||
|- | |- | ||
| 8 | | 8 | ||
| 1200. | | 1200.00 | ||
| [[2/1]] | | [[2/1]] | ||
| 2.0000 | | 2.0000 | ||
| Line 74: | Line 79: | ||
|} | |} | ||
[[ | == 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 [[Harmonics 5–10]]", 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 == | |||
* [[Harmonics 16–32]] | |||
* [[Harmonics 32–64]] | |||
{{Navbox harmonics}} | |||
Latest revision as of 02:32, 11 October 2026
| Prime factorization | 23 |
| Fifth | 12/8 (701.955c) |
The harmonic segment 8::16 (also harmonics 8–16) consists of harmonics 8 through 16 (8:9:…:16) and spans one octave above the root. Used as a scale, it is also called mode 8 of the harmonic series. 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 otonal heptad can be obtained by removing harmonic 15.
The smallest edo that maintains 25% or lower relative error on all intervals of this scale 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 Harmonics 5–10", 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
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 |