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Well-tuned piano is in a basic 2.3.7 limit scale. Not relevant here
 
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The 8<sup>th</sup> Octave Overtone Tuning, sometimes known as 128 Tuning, is a tuning developed by [[Johnny Reinhard|Johnny Reinhard]].
{{Infobox AFDO|steps=128}}


It consists of harmonics of the [[OverToneSeries|harmonic series]], numbers 128 (2<sup>8</sup>, hence 8<sup>th</sup> octave) through 255.
'''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.


Scales can be selected as subsets of these 128 pitches, or the entire set can be used.
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.


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 [[wikipedia:Psychoacoustics|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.


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¢).  


== Reading ==
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://stereosociety.com/20/jpg/Johnny-Reinhard/8th-Octave-Overtone-Tuning.pdf Johnny Reinhard's original paper].
== Music ==
; [[Georg Friedrich Haas]]
* [https://www.youtube.com/watch?v=TxGcveURI-I ''For Johnny Reinhard''] (2015)


[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]
; [[Johnny Reinhard]]
* [https://open.spotify.com/album/7jtoRTNK2Pm7vxkq5PH12b ''True''] (2014)


[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]
; [[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


== See also ==
; [[Philipp Gerschlauer]]
* [https://www.youtube.com/watch?v=lGa66qHzKME ''128 notes per octave on Alto Saxophone''] (2015)


[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.
; [[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]
== Scores ==
 
[https://nuotisto.s3-eu-west-1.amazonaws.com/store/e6fc131f958d13f87f3ea56b0d57beab50473c79bbc5a705b0dd6878214a.pdf Juhani Nuorvala - Toivo 128]
   
   
== Listening ==
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://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]
 
[https://johnnyreinhard.bandcamp.com/track/toivo-128-by-juhani-nuorvala-for-bassoon-and-pre-recording Juhani Nuorvala - Toivo 128 for bassoon and pre-recording]
 
[https://www.youtube.com/watch?v=sfWV4rNB6KE Well Tuned Piano] (actually up to the 11th octave harmonics, but same idea)
 
[https://www.youtube.com/watch?v=t4re9tjY5es Symphony #3 “Gloria”] (actually only the 7th octave harmonics, but the same idea)
 
[https://store.cdbaby.com/cd/johnnyreinhard1 Johnny Reinhard - True]


[https://www.youtube.com/watch?v=lGa66qHzKME 128 notes per octave on Alto Saxophone - Philipp Gerschlauer]
== 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.


Composers John Eaton, Rovner, Thoegersen, Golden, and others have also worked with 8<sup>th</sup> Octave Overtone Tuning.
[[Category:Harmonic series]]
[[Category:Harmonic series]]
[[Category:AFDO]]
[[Category:Primodality]]
[[Category:Listen]]
[[Category:Listen]]
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