Harmonics 128–256: Difference between revisions

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{{Infobox AFDO|steps=128}}
{{Infobox harmonics|128}}


'''128afdo''' ([[AFDO|arithmetic frequency division of the octave]]), or '''128odo''' ([[otonal division]] of the octave), divides the octave into 128 parts of 1/128 each. It is a superset of [[127afdo]] and a subset of [[129afdo]]. As a scale it may be known as [[harmonic mode|mode 128 of the harmonic series]] or the [[overtone scale #Over-n scales|Over-128]] scale.
{{Harmonics intro|128|aka=8th octave overtone tuning; 128 tuning}}


The '''8<sup>th</sup> Octave Overtone Tuning''', sometimes known as '''128 Tuning''', is a tuning developed by [[Johnny Reinhard]]. It is equivalent to 128afdo, except that it has a fixed root and cannot be rotated. It consists of harmonics of the [[harmonic series]], numbers 128 (2<sup>7</sup>, hence 8<sup>th</sup> octave) through 255. It is an Over-1 scale, specifically mode 128 of the harmonic series. 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 [[psychoacoustic]] presence.
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.
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== Music ==
== Music ==
* [https://johnnyreinhard.bandcamp.com/track/most-recent-for-johnny-reinhard-by-georg-friedrich-haas-for-solo-bassoon-in-128-tuning Georg Friedrich Haas - FOR JOHNNY REINHARD for bassoon in 128]{{dead link}}
; [[Georg Friedrich Haas]]
* [https://johnnyreinhard.bandcamp.com/track/toivo-128-by-juhani-nuorvala-for-bassoon-and-pre-recording Juhani Nuorvala - Toivo 128 for bassoon and pre-recording]{{dead link}}
* [https://www.youtube.com/watch?v=TxGcveURI-I ''For Johnny Reinhard''] (2015)
* [https://www.youtube.com/watch?v=sfWV4rNB6KE Well Tuned Piano]{{dead link}} (actually up to the 11th octave harmonics, but same idea)
 
* [https://store.cdbaby.com/cd/johnnyreinhard1 Johnny Reinhard - True]{{forbidden}} <!-- subscription required -->
; [[Johnny Reinhard]]
* [https://open.spotify.com/album/7jtoRTNK2Pm7vxkq5PH12b ''True''] (2014)


; [[Glenn Branca]]
; [[Glenn Branca]]
* [https://www.youtube.com/watch?v=t4re9tjY5es ''Symphony #3 "Gloria"''] (1983) – actually only the 7th octave harmonics, but the same idea
* [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]]
; [[Philipp Gerschlauer]]
* [https://www.youtube.com/watch?v=lGa66qHzKME ''128 notes per octave on Alto Saxophone'']
* [https://www.youtube.com/watch?v=lGa66qHzKME ''128 notes per octave on Alto Saxophone''] (2015)


; [[Juhani Nuorvala]]
; [[Juhani Nuorvala]]
* [https://nuotisto.s3-eu-west-1.amazonaws.com/store/e6fc131f958d13f87f3ea56b0d57beab50473c79bbc5a705b0dd6878214a.pdf ''Toivo 128''] (2017) – bassoon solo accompanied by a soundtrack (score only)
* ''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, Rovner, Thoegersen, Golden, and others have also worked with 8<sup>th</sup> Octave Overtone Tuning{{citation needed}}.
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}}


== External links ==
== External links ==
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* [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://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.
* [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:Harmonic series]]
[[Category:Primodality]]
[[Category:Primodality]]
[[Category:Listen]]
[[Category:Listen]]

Latest revision as of 00:42, 11 October 2026

Harmonics 128–256
Prime factorization 27
Fifth 192/128 (701.955c)

The harmonics 128–256 (also harmonic series segment 128::256 or harmonic series mode 128) are a scale that consists of harmonics 128 through 256 (128:129:…:256) and repeats at the octave. Used as a tuning system, it is also called 128afdo. 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

Georg Friedrich Haas
Johnny Reinhard
Glenn Branca
Philipp Gerschlauer
Juhani Nuorvala

Composers John Eaton, Anton Rovner, Peter Alexander Thoegersen, Monroe Golden, and others have also worked with 8th Octave Overtone Tuning.[citation needed]

External links

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
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