Decaononic - Revision history

Overthink: /* See also */ Interval categories aren't widely used

2026-01-02T05:47:47Z

See also: Interval categories aren't widely used

← Older revision		Revision as of 05:47, 2 January 2026
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	* [[Minortone]]		* [[Minortone]]

	~~[[Category:10/9]]~~
	[[Category:Whole tone]]		[[Category:Whole tone]]

Jerdle: /* Theory */ Added another decaononic system.

2025-07-02T11:25:26Z

Theory: Added another decaononic system.

@@ Line 18: / Line 18: @@
 === Devil's dozen ===
 Devil's dozen technique is playing in [[13edo]] as if it were 12edo. Since 10/9 is closely equal to 2\13 of the octave, it can be assigned to be a 13edo whole tone. The resulting comma that is tempered out is {{monzo|-11 26 -13}} or fully 2541865828329/2500000000000 - devil's tridecalimma.
 == See also ==

CompactStar: Uh, it's not just "rather flat"

2024-02-13T02:30:42Z

Uh, it's not just "rather flat"

← Older revision		Revision as of 02:30, 13 February 2024
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	=== Whole tone scale ===		=== Whole tone scale ===
	{{Main\|10/9ths equal temperament}}		{{Main\|10/9ths equal temperament}}
	Decaononic temperaments can be represented in EDOs which compress the 12edo scale to get the major second to be equal to 10/9. In [[79edo]], for example, a whole tone itself contains a mini-12edo keymap inside it, and the final 7 notes are a truncated tetrachord. If played naively, this produces ~~a rather~~ flat fifth of 638.413c just, or 637.974c (79edo). In an effect this makes for a [[Glacial7]]-type scale.		Decaononic temperaments can be represented in EDOs which compress the 12edo scale to get the major second to be equal to 10/9. In [[79edo]], for example, a whole tone itself contains a mini-12edo keymap inside it, and the final 7 notes are a truncated tetrachord. If played naively, this produces an extremely flat fifth of 638.413c just, or 637.974c (79edo). In an effect this makes for a [[Glacial7]]-type scale.

	=== Meantone ===		=== Meantone ===

Fredg999: Categories

2023-12-12T20:14:57Z

Fredg999: Mark term as idiosyncratic, misc. edit

2023-12-12T19:12:29Z

Mark term as idiosyncratic, misc. edit

← Older revision		Revision as of 19:12, 12 December 2023
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	The '''decaononic''' technique is the way of playing and composing where a [[tone]] is considered to be equal to [[10/9]]. It is a set of temperaments that may interpret this function differently.		The '''decaononic'''{{idiosyncratic}} technique is the way of playing and composing where a [[tone]] is considered to be equal to [[10/9]]. It is a set of temperaments that may interpret this function differently.

	== Origin ==		== Origin ==
	In 5-limit just ~~intotation~~ and most of the music theory that comes with it, 10/9 is viewed as a secondary tone as opposed to [[9/8]]. In general, when the [[81/80\|difference]] between the two is eliminated, what it really means is that the "tone" is set to equal to 9/8 and the tuning completely misses 10/9. This is primarily because 9/8 and an octave are equal to a stack of two perfect fifths. 10/9 therefore in this paradigm only occurs as a side product of 9/8, and it isn't an interval of its own.		In 5-limit just intonation and most of the music theory that comes with it, 10/9 is viewed as a secondary tone as opposed to [[9/8]]. In general, when the [[81/80\|difference]] between the two is eliminated, what it really means is that the "tone" is set to equal to 9/8 and the tuning completely misses 10/9. This is primarily because 9/8 and an octave are equal to a stack of two perfect fifths. 10/9 therefore in this paradigm only occurs as a side product of 9/8, and it isn't an interval of its own.

	While there are temperaments which use 10/9 as a generator for various purposes (such as [[Porcupine]]), decaononic means that 10/9 is ''the tone,'' and 9/8 is not as emphasized.		While there are temperaments which use 10/9 as a generator for various purposes (such as [[Porcupine]]), decaononic means that 10/9 is ''the tone,'' and 9/8 is not as emphasized.

Fredg999: Etymology, misc. edits

2023-08-22T05:42:22Z

Etymology, misc. edits

← Older revision		Revision as of 05:42, 22 August 2023
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	'''~~Decaononic~~''' technique is the way of playing and composing where a ~~'''~~[[tone]]~~'''~~ is considered to be equal to ~~'''~~[[10/9]]~~'''~~.		The '''decaononic''' technique is the way of playing and composing where a [[tone]] is considered to be equal to [[10/9]]. It is a set of temperaments that may interpret this function differently.

	It is a set of temperaments that may interpret this function differently.

	== Origin ==		== Origin ==
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	== Theory ==		== Theory ==
	The name "decaononic" comes from Greek and Latin words for 10 and 9 respectively, and a letter o meaning "over", as in "[[otonal]]". In this system, one tone is set to be 10/9, about 182.4 cents, and other intervals may have multiple interpretations.		The name "decaononic", proposed by [[Eliora]], comes from Greek and Latin words for 10 and 9 respectively, and a letter o meaning "over", as in "[[otonal]]". In this system, one tone is set to be 10/9, about 182.4 cents, and other intervals may have multiple interpretations.

	=== Whole tone scale ===		=== Whole tone scale ===
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	=== Meantone ===		=== Meantone ===
	Meantone decaononic temperament assigns the perfect fifth to split the major ninth, as normal meantone would, in two. This therefore results in the fifth size of <math>\sqrt{20/9} = 1.490712...</math>, or about 691.2019 cents. The amount by which the fifth is flattened is equal to <math>\sqrt{81/80} = 1.0062...</math>, therefore this is effectively the same as ~~'''~~1/2-comma meantone~~'''~~.		Meantone decaononic temperament assigns the perfect fifth to split the major ninth, as normal meantone would, in two. This therefore results in the fifth size of <math>\sqrt{20/9} = 1.490712...</math>, or about 691.2019 cents. The amount by which the fifth is flattened is equal to <math>\sqrt{81/80} = 1.0062...</math>, therefore this is effectively the same as [[1/2 syntonic comma meantone\|1/2-comma meantone]].

	=== Devil's dozen ===		=== Devil's dozen ===

Eliora at 19:29, 13 March 2022

2022-03-13T19:29:23Z

← Older revision		Revision as of 19:29, 13 March 2022
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	[[Category:10/9]]		[[Category:10/9]]
	[[Category:Whole tone]]		[[Category:Whole tone]]
			[[Category:Terms]]

Sintel at 08:41, 24 January 2022

2022-01-24T08:41:55Z

← Older revision		Revision as of 08:41, 24 January 2022
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	=== Meantone ===		=== Meantone ===
	Meantone decaononic temperament assigns the perfect fifth to split the major ninth, as normal meantone would, in two. This therefore results in the fifth size of <math>\sqrt{20/9} = 1.490712...</math>, or about 691.2019 cents. The amount by which the fifth is flattened is equal to <math>\sqrt{81/80} = 1.~~490712~~...</math>, therefore this is effectively the same as '''1/2-comma meantone'''.		Meantone decaononic temperament assigns the perfect fifth to split the major ninth, as normal meantone would, in two. This therefore results in the fifth size of <math>\sqrt{20/9} = 1.490712...</math>, or about 691.2019 cents. The amount by which the fifth is flattened is equal to <math>\sqrt{81/80} = 1.0062...</math>, therefore this is effectively the same as '''1/2-comma meantone'''.

	=== Devil's dozen ===		=== Devil's dozen ===

Xenllium at 00:14, 27 November 2021

2021-11-27T00:14:23Z

← Older revision		Revision as of 00:14, 27 November 2021
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	It is a set of temperaments that may interpret this function differently.		It is a set of temperaments that may interpret this function differently.

	==Origin==		== Origin ==
	In 5-limit just intotation and most of the music theory that comes with it, 10/9 is viewed as a secondary tone as opposed to [[9/8]]. In general, when the [[81/80\|difference]] between the two is eliminated, what it really means is that the "tone" is set to equal to 9/8 and the tuning completely misses 10/9. This is primarily because 9/8 and an octave are equal to a stack of two perfect fifths. 10/9 therefore in this paradigm only occurs as a side product of 9/8, and it isn't an interval of its own.		In 5-limit just intotation and most of the music theory that comes with it, 10/9 is viewed as a secondary tone as opposed to [[9/8]]. In general, when the [[81/80\|difference]] between the two is eliminated, what it really means is that the "tone" is set to equal to 9/8 and the tuning completely misses 10/9. This is primarily because 9/8 and an octave are equal to a stack of two perfect fifths. 10/9 therefore in this paradigm only occurs as a side product of 9/8, and it isn't an interval of its own.

	While there are temperaments which use 10/9 as a generator for various purposes (such as [[Porcupine]]), decaononic means that 10/9 is ''the tone,'' and 9/8 is not as emphasized.		While there are temperaments which use 10/9 as a generator for various purposes (such as [[Porcupine]]), decaononic means that 10/9 is ''the tone,'' and 9/8 is not as emphasized.

	==Theory==		== Theory ==
	The name "decaononic" comes from Greek and Latin words for 10 and 9 respectively, and a letter o meaning "over", as in "[[otonal]]". In this system, one tone is set to be 10/9, about 182.4 cents, and other intervals may have multiple interpretations.		The name "decaononic" comes from Greek and Latin words for 10 and 9 respectively, and a letter o meaning "over", as in "[[otonal]]". In this system, one tone is set to be 10/9, about 182.4 cents, and other intervals may have multiple interpretations.

	=== Whole tone scale ===		=== Whole tone scale ===
	{{Main\|10/9ths equal temperament}}		{{Main\|10/9ths equal temperament}}
	Decaononic temperaments can be represented in EDOs which compress the 12edo scale to get the major second to be equal to 10/9. In [[79edo]], for example, a whole tone itself contains a mini-12edo keymap inside it, and the final 7 notes are a truncated tetrachord. If played naively, this produces a rather flat fifth of 638.413c just, or 637.974c (79edo). In an effect this makes for a [[Glacial7]]-type scale.		Decaononic temperaments can be represented in EDOs which compress the 12edo scale to get the major second to be equal to 10/9. In [[79edo]], for example, a whole tone itself contains a mini-12edo keymap inside it, and the final 7 notes are a truncated tetrachord. If played naively, this produces a rather flat fifth of 638.413c just, or 637.974c (79edo). In an effect this makes for a [[Glacial7]]-type scale.

	=== Meantone ===		=== Meantone ===
	Meantone decaononic temperament assigns the perfect fifth to split the major ninth, as normal meantone would, in two. This therefore results in the fifth size of <math>\sqrt{20/9} = 1.490712...</math>, or about 691.2019 cents. The amount by which the fifth is flattened is equal to <math>\sqrt{81/80} = 1.490712...</math>, therefore this is effectively the same as '''1/2-comma meantone'''.		Meantone decaononic temperament assigns the perfect fifth to split the major ninth, as normal meantone would, in two. This therefore results in the fifth size of <math>\sqrt{20/9} = 1.490712...</math>, or about 691.2019 cents. The amount by which the fifth is flattened is equal to <math>\sqrt{81/80} = 1.490712...</math>, therefore this is effectively the same as '''1/2-comma meantone'''.

	=== Devil's dozen ===		=== Devil's dozen ===
	Devil's dozen technique is playing in 13edo as if it were 12edo. Since 10/9 is closely equal to 2\13 of the octave, it can be assigned to be a 13edo whole tone. The resulting comma that is tempered out is [-11 26 13> or fully 2541865828329/2500000000000 - devil's tridecalimma.		Devil's dozen technique is playing in [[13edo]] as if it were 12edo. Since 10/9 is closely equal to 2\13 of the octave, it can be assigned to be a 13edo whole tone. The resulting comma that is tempered out is {{monzo\|-11 26 -13}} or fully 2541865828329/2500000000000 - devil's tridecalimma.

	==See also==		== See also ==
	* [[Minortone]]		* [[Minortone]]

			[[Category:10/9]]
			[[Category:Whole tone]]

Eliora: /* Origin */

2021-11-24T09:04:24Z

Origin

← Older revision		Revision as of 09:04, 24 November 2021
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	'''Decaononic''' technique is the way of playing and composing where a '''[[tone]]''' is considered to be equal to '''[[10/9]]'''.		'''Decaononic''' technique is the way of playing and composing where a '''[[tone]]''' is considered to be equal to '''[[10/9]]'''.

	It is a set of temperaments.		It is a set of temperaments that may interpret this function differently.

	==Origin==		==Origin==
	In most ~~musical~~ theory ~~practices, even the most ardent microtonal ones~~, 10/9 is viewed as a secondary tone as opposed to [[9/8]], ~~and~~ when the [[81/80\|difference]] between the two is eliminated, what it really means is that the "tone" is set to equal to 9/8 and the tuning completely misses 10/9.		In 5-limit just intotation and most of the music theory that comes with it, 10/9 is viewed as a secondary tone as opposed to [[9/8]]. In general, when the [[81/80\|difference]] between the two is eliminated, what it really means is that the "tone" is set to equal to 9/8 and the tuning completely misses 10/9. This is primarily because 9/8 and an octave are equal to a stack of two perfect fifths. 10/9 therefore in this paradigm only occurs as a side product of 9/8, and it isn't an interval of its own.
	~~There~~ is ~~a fair reason for this, octave with~~ 9/8 ~~consists~~ of 2 perfect fifths~~, 9/8 is a 3-limit interval, and therefore a simple interval, and in addition 9/8 is also an overtone~~. 10/9 therefore in this paradigm only occurs as a side product of 9/8, and it isn't an interval of its own.

	~~Decaononic~~ temperaments ~~do the opposite of this. Here~~, 10/9 is the ~~leading~~ tone and ~~all the other intervals are compressed to treat 10/9 as if it were~~ 9/8.		While there are temperaments which use 10/9 as a generator for various purposes (such as [[Porcupine]]), decaononic means that 10/9 is ''the tone,'' and 9/8 is not as emphasized.

	==Theory==		==Theory==
Line 13:		Line 12:
	=== Whole tone scale ===		=== Whole tone scale ===
	{{Main\|10/9ths equal temperament}}		{{Main\|10/9ths equal temperament}}
	Decaononic temperaments can be represented in EDOs which compress the 12edo scale to get the major second to be equal to 10/9. In [[79edo]], for example, a whole tone itself contains a mini-12edo keymap inside it, and the final 7 notes are a truncated tetrachord. If played naively, this produces a rather flat fifth of 638.413c just, or 637.974c (79edo).		Decaononic temperaments can be represented in EDOs which compress the 12edo scale to get the major second to be equal to 10/9. In [[79edo]], for example, a whole tone itself contains a mini-12edo keymap inside it, and the final 7 notes are a truncated tetrachord. If played naively, this produces a rather flat fifth of 638.413c just, or 637.974c (79edo). In an effect this makes for a [[Glacial7]]-type scale.
	=== Meantone ===		=== Meantone ===
	Meantone decaononic temperament assigns the perfect fifth to split the major ninth, as normal meantone would, in two. This therefore results in the fifth size of <math>\sqrt{20/9} = 1.490712...</math>, or about 691.2019 cents. The amount by which the fifth is flattened is equal to <math>\sqrt{81/80} = 1.490712...</math>, therefore this is effectively the same as '''1/2-comma meantone'''.		Meantone decaononic temperament assigns the perfect fifth to split the major ninth, as normal meantone would, in two. This therefore results in the fifth size of <math>\sqrt{20/9} = 1.490712...</math>, or about 691.2019 cents. The amount by which the fifth is flattened is equal to <math>\sqrt{81/80} = 1.490712...</math>, therefore this is effectively the same as '''1/2-comma meantone'''.

← Older revision		Revision as of 20:14, 12 December 2023
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	[[Category:10/9]]		[[Category:10/9]]
	[[Category:Whole tone]]		[[Category:Whole tone]]
	~~[[Category:Terms]]~~