128afdo - Revision history

Sintel: Well-tuned piano is in a basic 2.3.7 limit scale. Not relevant here

2025-08-08T19:59:49Z

Well-tuned piano is in a basic 2.3.7 limit scale. Not relevant here

← Older revision		Revision as of 19:59, 8 August 2025
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	; [[Georg Friedrich Haas]]		; [[Georg Friedrich Haas]]
	* [https://www.youtube.com/watch?v=TxGcveURI-I ''For Johnny Reinhard''] (2015)		* [https://www.youtube.com/watch?v=TxGcveURI-I ''For Johnny Reinhard''] (2015)

	~~; [[La Monte Young]]~~
	* [https://www.nicovideo.jp/watch/sm7119661 ''The Well-Tuned Piano''] (1964) – actually up to the 11<sup>th</sup> octave harmonics, but the same idea

	; [[Johnny Reinhard]]		; [[Johnny Reinhard]]

Cmloegcmluin: /* Music */

2025-03-07T06:33:09Z

Music

← Older revision		Revision as of 06:33, 7 March 2025
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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 -->~~		; [[La Monte Young]]
			* [https://www.nicovideo.jp/watch/sm7119661 ''The Well-Tuned Piano''] (1964) – actually up to the 11<sup>th</sup> octave harmonics, but the same idea

			; [[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 ==

Sintel: mode 80 -> mode 128

2025-03-06T21:51:43Z

mode 80 -> mode 128

← Older revision		Revision as of 21:51, 6 March 2025
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	{{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.		'''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.

	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 '''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.

FloraC: Rework intro and music sections

2025-02-23T11:44:03Z

Rework intro and music sections

← Older revision		Revision as of 11:44, 23 February 2025
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	{{Infobox AFDO\|steps=128}}The '''8<sup>th</sup> Octave Overtone Tuning''', sometimes known as '''128 Tuning''', is a tuning developed by [[Johnny Reinhard\|Johnny Reinhard]]. It is equivalent to '''[[AFDO\|128afdo]]''', except that it has a fixed root and cannot be rotated.		{{Infobox AFDO\|steps=128}}

	~~It consists of harmonics~~ of the [[~~OverToneSeries\|harmonic series~~]], ~~numbers~~ 128 ~~(2<sup>7<~~/~~sup>, hence 8<sup>th</sup> octave) through 255~~. It is an [[~~Overtone_scale#Over-1_scales\|Over-1 scale~~]]~~, specifically~~ [[~~Harmonic_mode~~\|mode ~~128]]~~ of the harmonic series.		'''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 [[~~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¢).
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	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.

	== ~~Reading~~ ==		== 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://~~stereosociety~~.com/~~20/jpg/Johnny-Reinhard/8th-Octave-Overtone-Tuning.pdf Johnny Reinhard~~'~~s original paper~~].		; [[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.~~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~~]		; [[Philipp Gerschlauer]]
			* [https://www.youtube.com/watch?v=lGa66qHzKME ''128 notes per octave on Alto Saxophone'']

	[~~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~~]		; [[Juhani Nuorvala]]
			* [https://nuotisto.s3-eu-west-1.amazonaws.com/store/e6fc131f958d13f87f3ea56b0d57beab50473c79bbc5a705b0dd6878214a.pdf ''Toivo 128''] (2017) – bassoon solo accompanied by a soundtrack (score only)
	~~== See also ==~~

	~~[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.~~

	~~== Scores ==~~

	[https://nuotisto.s3-eu-west-1.amazonaws.com/store/e6fc131f958d13f87f3ea56b0d57beab50473c79bbc5a705b0dd6878214a.pdf ~~Juhani Nuorvala -~~ Toivo 128]

	~~== Listening ==~~		Composers John Eaton, Rovner, Thoegersen, 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:Primodality]]		[[Category:Primodality]]
	[[Category:Listen]]		[[Category:Listen]]

BudjarnLambeth: Change requested by User:Holger Stoltenberg

2025-01-16T02:00:46Z

Change requested by User:Holger Stoltenberg

← Older revision		Revision as of 02:00, 16 January 2025
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	{{Infobox AFDO\|steps=128}}The '''8<sup>th</sup> Octave Overtone Tuning''', sometimes known as '''128 Tuning''', is a tuning developed by [[Johnny Reinhard\|Johnny Reinhard]]. It is equivalent to '''[[AFDO\|128afdo]]''', except that it has a fixed root and cannot be rotated.		{{Infobox AFDO\|steps=128}}The '''8<sup>th</sup> Octave Overtone Tuning''', sometimes known as '''128 Tuning''', is a tuning developed by [[Johnny Reinhard\|Johnny Reinhard]]. It is equivalent to '''[[AFDO\|128afdo]]''', except that it has a fixed root and cannot be rotated.

	It consists of harmonics of the [[OverToneSeries\|harmonic series]], numbers 128 (2<sup>8</sup>, hence 8<sup>th</sup> octave) through 255. It is an [[Overtone_scale#Over-1_scales\|Over-1 scale]], specifically [[Harmonic_mode\|mode 128]] of the harmonic series.		It consists of harmonics of the [[OverToneSeries\|harmonic series]], numbers 128 (2<sup>7</sup>, hence 8<sup>th</sup> octave) through 255. It is an [[Overtone_scale#Over-1_scales\|Over-1 scale]], specifically [[Harmonic_mode\|mode 128]] of the harmonic series.

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

BudjarnLambeth at 03:28, 14 January 2025

2025-01-14T03:28:56Z

← Older revision		Revision as of 03:28, 14 January 2025
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	{{Infobox AFDO\|steps=128}}The '''8<sup>th</sup> Octave Overtone Tuning''', sometimes known as '''128 Tuning''', is a tuning developed by [[Johnny Reinhard\|Johnny Reinhard]]. It is equivalent to '''128afdo''', except that it has a fixed root and cannot be rotated.		{{Infobox AFDO\|steps=128}}The '''8<sup>th</sup> Octave Overtone Tuning''', sometimes known as '''128 Tuning''', is a tuning developed by [[Johnny Reinhard\|Johnny Reinhard]]. It is equivalent to '''[[AFDO\|128afdo]]''', except that it has a fixed root and cannot be rotated.

	It consists of harmonics of the [[OverToneSeries\|harmonic series]], numbers 128 (2<sup>8</sup>, hence 8<sup>th</sup> octave) through 255. It is an [[Overtone_scale#Over-1_scales\|Over-1 scale]], specifically [[Harmonic_mode\|mode 128]] of the harmonic series.		It consists of harmonics of the [[OverToneSeries\|harmonic series]], numbers 128 (2<sup>8</sup>, hence 8<sup>th</sup> octave) through 255. It is an [[Overtone_scale#Over-1_scales\|Over-1 scale]], specifically [[Harmonic_mode\|mode 128]] of the harmonic series.

BudjarnLambeth: Tease out the differences between 128 Tuning and 128afdo

2025-01-14T03:25:16Z

Tease out the differences between 128 Tuning and 128afdo

← Older revision		Revision as of 03:25, 14 January 2025
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	{{Infobox AFDO\|steps=128}}The '''8<sup>th</sup> Octave Overtone Tuning''', sometimes known as '''128 Tuning~~''' or '''128afdo~~''', is a tuning developed by [[Johnny Reinhard\|Johnny Reinhard]].		{{Infobox AFDO\|steps=128}}The '''8<sup>th</sup> Octave Overtone Tuning''', sometimes known as '''128 Tuning''', is a tuning developed by [[Johnny Reinhard\|Johnny Reinhard]]. It is equivalent to '''128afdo''', except that it has a fixed root and cannot be rotated.

	It consists of harmonics of the [[OverToneSeries\|harmonic series]], numbers 128 (2<sup>8</sup>, hence 8<sup>th</sup> octave) through 255. It is an [[Overtone_scale#Over-1_scales\|Over-1 scale]], specifically [[Harmonic_mode\|mode 128]] of the harmonic series.		It consists of harmonics of the [[OverToneSeries\|harmonic series]], numbers 128 (2<sup>8</sup>, hence 8<sup>th</sup> octave) through 255. It is an [[Overtone_scale#Over-1_scales\|Over-1 scale]], specifically [[Harmonic_mode\|mode 128]] of the harmonic series.

BudjarnLambeth: capitalisation

2024-02-26T07:33:59Z

capitalisation

← Older revision		Revision as of 07:33, 26 February 2024
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	{{Infobox AFDO\|steps=128}}The '''8<sup>th</sup> Octave Overtone Tuning''', sometimes known as '''128 Tuning''' or '''128afdo''', is a tuning developed by [[Johnny Reinhard\|Johnny Reinhard]].		{{Infobox AFDO\|steps=128}}The '''8<sup>th</sup> Octave Overtone Tuning''', sometimes known as '''128 Tuning''' or '''128afdo''', is a tuning developed by [[Johnny Reinhard\|Johnny Reinhard]].

	It consists of harmonics of the [[OverToneSeries\|harmonic series]], numbers 128 (2<sup>8</sup>, hence 8<sup>th</sup> octave) through 255. It is an [[Overtone_scale#Over-1_scales\|Over-1 scale]], specifically [[Harmonic_mode\|~~Mode~~ 128]] of the harmonic series.		It consists of harmonics of the [[OverToneSeries\|harmonic series]], numbers 128 (2<sup>8</sup>, hence 8<sup>th</sup> octave) through 255. It is an [[Overtone_scale#Over-1_scales\|Over-1 scale]], specifically [[Harmonic_mode\|mode 128]] of the harmonic series.

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

BudjarnLambeth: Mentioned its value in primodal music

2024-02-26T07:33:14Z

Mentioned its value in primodal music

← Older revision		Revision as of 07:33, 26 February 2024
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	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.

	== Reading ==		== Reading ==
Line 41:		Line 43:
	Composers John Eaton, Rovner, Thoegersen, Golden, and others have also worked with 8<sup>th</sup> 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:Primodality]]
	[[Category:Listen]]		[[Category:Listen]]

BudjarnLambeth: Added infobox

2024-02-26T04:02:28Z

Added infobox

← Older revision		Revision as of 04:02, 26 February 2024
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	The '''8<sup>th</sup> Octave Overtone Tuning''', sometimes known as '''128 Tuning''' or '''128afdo''', is a tuning developed by [[Johnny Reinhard\|Johnny Reinhard]].		{{Infobox AFDO\|steps=128}}The '''8<sup>th</sup> Octave Overtone Tuning''', sometimes known as '''128 Tuning''' or '''128afdo''', is a tuning developed by [[Johnny Reinhard\|Johnny Reinhard]].

	It consists of harmonics of the [[OverToneSeries\|harmonic series]], numbers 128 (2<sup>8</sup>, hence 8<sup>th</sup> octave) through 255. It is an [[Overtone_scale#Over-1_scales\|Over-1 scale]], specifically [[Harmonic_mode\|Mode 128]] of the harmonic series.		It consists of harmonics of the [[OverToneSeries\|harmonic series]], numbers 128 (2<sup>8</sup>, hence 8<sup>th</sup> octave) through 255. It is an [[Overtone_scale#Over-1_scales\|Over-1 scale]], specifically [[Harmonic_mode\|Mode 128]] of the harmonic series.