Harmonics 128–256: Difference between revisions
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{{Infobox harmonics|128}} | |||
{{Harmonics intro|128|aka=8th octave overtone tuning; 128 tuning}} | |||
Scales can be selected as subsets of these 128 pitches, or the entire set can be used. | The tuning was developed by [[Johnny Reinhard]]. It differs from the scale only in that it has a fixed root and cannot be rotated. It consists of harmonics 128 (2<sup>7</sup>, hence 8<sup>th</sup> octave) through 255. Scales can be selected as subsets of these 128 pitches, or the entire set can be used. | ||
A key benefit of using pitches exclusively from the same harmonic series is that they share a fundamental. By using the 8<sup>th</sup> octave of a harmonic series, said fundamental will almost certainly be [https://www.merriam-webster.com/dictionary/infrasonic infrasonic], but it will still have a [[ | A key benefit of using pitches exclusively from the same harmonic series is that they share a fundamental. By using the 8<sup>th</sup> octave of a harmonic series, said fundamental will almost certainly be [https://www.merriam-webster.com/dictionary/infrasonic infrasonic], but it will still have a [[psychoacoustic]] presence. | ||
An illustratively surprising result of this higher harmonic tuning is that, since a just 4/3 does not have a power of 2 in the denominator and thus does not exist in the (octave-reduced) harmonic series, it will not be used in this tuning. Instead, when the inverse of the 3/2 ratio is needed, one may use 43/32 (511.517706¢) or 171/128 (501.423018¢). | An illustratively surprising result of this higher harmonic tuning is that, since a just [[4/3]] does not have a power of 2 in the denominator and thus does not exist in the (octave-reduced) harmonic series, it will not be used in this tuning. Instead, when the inverse of the [[3/2]] ratio is needed, one may use [[43/32]] (511.517706¢) or [[171/128]] (501.423018¢). | ||
Due to having only one prime factor (2), yet also being a higher octave of a prime mode (mode 2), it is a very strong tuning for [[primodality]], providing a large gamut of intervals without compromising their clear prime identity. | |||
[https:// | == Music == | ||
; [[Georg Friedrich Haas]] | |||
* [https://www.youtube.com/watch?v=TxGcveURI-I ''For Johnny Reinhard''] (2015) | |||
[https:// | ; [[Johnny Reinhard]] | ||
* [https://open.spotify.com/album/7jtoRTNK2Pm7vxkq5PH12b ''True''] (2014) | |||
[https:// | ; [[Glenn Branca]] | ||
* [https://www.youtube.com/watch?v=t4re9tjY5es ''Symphony #3 "Gloria"''] (1983) – actually only the 7<sup>th</sup> octave harmonics, but the same idea | |||
= | ; [[Philipp Gerschlauer]] | ||
* [https://www.youtube.com/watch?v=lGa66qHzKME ''128 notes per octave on Alto Saxophone''] (2015) | |||
[https://nuotisto.s3-eu-west-1.amazonaws.com/store/e6fc131f958d13f87f3ea56b0d57beab50473c79bbc5a705b0dd6878214a.pdf | ; [[Juhani Nuorvala]] | ||
* ''Toivo 128'' (2017) [https://soundcloud.com/juhani-nuorvala/toivo-128 recording] [https://nuotisto.s3-eu-west-1.amazonaws.com/store/e6fc131f958d13f87f3ea56b0d57beab50473c79bbc5a705b0dd6878214a.pdf score] | |||
Composers John Eaton, Anton Rovner, Peter Alexander Thoegersen, Monroe Golden, and others have also worked with 8<sup>th</sup> Octave Overtone Tuning.{{citation needed}} | |||
[https:// | == External links == | ||
* [https://stereosociety.com/20/jpg/Johnny-Reinhard/8th-Octave-Overtone-Tuning.pdf Johnny Reinhard's original paper]. | |||
* [https://www.cassgb.org/features/post/128-note-octave/ 128 NOTES PER OCTAVE ON THE SAXOPHONE: HOW I DID IT AND WHY!: Saxophonist Philipp Gerschlauer on how he went about devising a 128-note per octave fingering chart] | |||
* [https://books.google.com/books/about/8th_Octave_Overtone_Tuning_and_Bassoon_F.html?id=YE9gAQAACAAJ Johnny Reinhard - 8th Octave Overtone Tuning and Bassoon Fingerings in 128] | |||
* [https://www.kylegann.com/13th-Harmonic.html The tuning for Nursery Tunes for Demented Children by Kyle Gann] is a subset of 8th Octave Overtone Tuning. | |||
{{Navbox harmonics}} | |||
[ | [[Category:Harmonic series]] | ||
[[Category:Primodality]] | |||
[ | [[Category:Listen]] | ||
[ | |||
Latest revision as of 00:42, 11 October 2026
| Prime factorization | 27 |
| Fifth | 192/128 (701.955c) |
The harmonic segment 128::256 (also harmonics 128–256) consists of harmonics 128 through 256 (128:129:…:256) and spans one octave above the root. Used as a scale, it is also called mode 128 of the harmonic series. It is also known as 8th octave overtone tuning and 128 tuning.
The tuning was developed by Johnny Reinhard. It differs from the scale only in that it has a fixed root and cannot be rotated. It consists of harmonics 128 (27, hence 8th octave) through 255. Scales can be selected as subsets of these 128 pitches, or the entire set can be used.
A key benefit of using pitches exclusively from the same harmonic series is that they share a fundamental. By using the 8th octave of a harmonic series, said fundamental will almost certainly be infrasonic, but it will still have a psychoacoustic presence.
An illustratively surprising result of this higher harmonic tuning is that, since a just 4/3 does not have a power of 2 in the denominator and thus does not exist in the (octave-reduced) harmonic series, it will not be used in this tuning. Instead, when the inverse of the 3/2 ratio is needed, one may use 43/32 (511.517706¢) or 171/128 (501.423018¢).
Due to having only one prime factor (2), yet also being a higher octave of a prime mode (mode 2), it is a very strong tuning for primodality, providing a large gamut of intervals without compromising their clear prime identity.
Music
- For Johnny Reinhard (2015)
- True (2014)
- Symphony #3 "Gloria" (1983) – actually only the 7th octave harmonics, but the same idea
Composers John Eaton, Anton Rovner, Peter Alexander Thoegersen, Monroe Golden, and others have also worked with 8th Octave Overtone Tuning.[citation needed]
External links
- Johnny Reinhard's original paper.
- 128 NOTES PER OCTAVE ON THE SAXOPHONE: HOW I DID IT AND WHY!: Saxophonist Philipp Gerschlauer on how he went about devising a 128-note per octave fingering chart
- Johnny Reinhard - 8th Octave Overtone Tuning and Bassoon Fingerings in 128
- The tuning for Nursery Tunes for Demented Children by Kyle Gann is a subset of 8th Octave Overtone Tuning.
| 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 |