128afdo: Difference between revisions
Jump to navigation
Jump to search
m Change requested by User:Holger Stoltenberg |
Rework intro and music sections |
||
| Line 1: | Line 1: | ||
{{Infobox AFDO|steps=128}} | {{Infobox AFDO|steps=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 80 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 [[ | 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¢). | ||
| Line 11: | Line 11: | ||
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. | 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 == | ||
* [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}} | |||
* [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=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 --> | |||
[https:// | ; [[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. | ; [[Philipp Gerschlauer]] | ||
* [https://www.youtube.com/watch?v=lGa66qHzKME ''128 notes per octave on Alto Saxophone''] | |||
[ | ; [[Juhani Nuorvala]] | ||
* [https://nuotisto.s3-eu-west-1.amazonaws.com/store/e6fc131f958d13f87f3ea56b0d57beab50473c79bbc5a705b0dd6878214a.pdf ''Toivo 128''] (2017) – bassoon solo accompanied by a soundtrack (score only) | |||
[https://nuotisto.s3-eu-west-1.amazonaws.com/store/e6fc131f958d13f87f3ea56b0d57beab50473c79bbc5a705b0dd6878214a.pdf | |||
Composers John Eaton, Rovner, Thoegersen, Golden, and others have also worked with 8<sup>th</sup> Octave Overtone Tuning{{citation needed}}. | |||
[https://www. | == 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. | |||
[[Category:Harmonic series]] | [[Category:Harmonic series]] | ||
[[Category:Primodality]] | [[Category:Primodality]] | ||
[[Category:Listen]] | [[Category:Listen]] | ||
Revision as of 11:44, 23 February 2025
128afdo (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 mode 80 of the harmonic series or the Over-128 scale.
The 8th 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 (27, hence 8th 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 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 - FOR JOHNNY REINHARD for bassoon in 128[dead link]
- Juhani Nuorvala - Toivo 128 for bassoon and pre-recording[dead link]
- Well Tuned Piano[dead link] (actually up to the 11th octave harmonics, but same idea)
- Johnny Reinhard - True[forbidden]
- Symphony #3 "Gloria" (1983) – actually only the 7th octave harmonics, but the same idea
- Toivo 128 (2017) – bassoon solo accompanied by a soundtrack (score only)
Composers John Eaton, Rovner, Thoegersen, 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.