Armodue theory - Revision history

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VectorGraphics at 19:52, 9 April 2025

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	== Notation ==		== Notation ==
	In order to make Armodue approachable, while also making its notation distinct from Western diatonic notation, the Italian creators of the [http://armodue.com/ Armodue] system named the notes ~~numbering~~ from 1 to 9:		In order to make Armodue approachable, while also making its notation distinct from Western diatonic notation, the Italian creators of the [http://armodue.com/ Armodue] system named the notes using numbers from 1 to 9:

	1, 1#, 2, 2#, 3, 3#, 4, 5, 5#, 6, 6#, 7, 7#, 8, 8#, 9		1, 1#, 2, 2#, 3, 3#, 4, 5, 5#, 6, 6#, 7, 7#, 8, 8#, 9
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	Relative notation is simply done by specifying the number of edosteps, in order to support alternative scale constructions. For example, one refers not to the perfect fourth or fifth (at least in the specific sense of Armodue intervals) but to the intervals of 7-eka and 9-eka.		Relative notation is simply done by specifying the number of edosteps, in order to support alternative scale constructions. For example, one refers not to the perfect fourth or fifth (at least in the specific sense of Armodue intervals) but to the intervals of 7-eka and 9-eka.

	However, the interval between a note at frequency n and other at frequency 2n is called a ''tenth,'' ''decave,'' or ''decim''.		However, the interval between a note at frequency n and other at frequency 2n is called a ''tenth,'' ''decave,'' or ''decim'', as it is the tenth note of the Mavila[9] scale.

	The basic semitone of Armodue, whatever concrete temperament is used, is always called '''eka''' (from Sanskrit eka: one, unit). In the chromatic Armodue scale, one eka always corresponds to the interval between any two consecutive notes.		The basic semitone of Armodue, whatever concrete temperament is used, is always called '''eka''' (from Sanskrit eka: one, unit). In the chromatic Armodue scale, one eka always corresponds to the interval between any two consecutive notes.

	~~For composing in~~ Armodue ~~it's useful to use a ''tetragram'' (staff with~~ 4 lines):		The standard staff notation for Armodue uses 4 lines, so that 1 is always found below the first line, and 9 above the last line.

	[[file:armodue-TETR-1.jpg\|frame\|none\|© Armodue; used with permission.]]		[[file:armodue-TETR-1.jpg\|frame\|none\|© Armodue; used with permission.]]
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	The notes without accidentals form a [[Mavila\|Mavila]] [[7L_2s\|armotonic scale (7L 2s)]].		The notes without accidentals form a [[Mavila\|Mavila]] [[7L_2s\|armotonic scale (7L 2s)]].

	If for the ~~execution~~ of ~~a musical piece we need to write on two or more tetragrams~~, the notes will be written in the same way ~~for~~ every ~~tetragram~~.		This notation is similar to the KISS notation using numbers for this scale, except with the staff laid out differently (i.e. in KISS, the standard treble and bass clefs are used, and the staff has 6 lines instead of 4)

			When multiple staves are necessary, the notes will be written in the same way in every staff.

	In other words, the "1" note will be written immediately under the first line <u>in every tenth</u>.		In other words, the "1" note will be written immediately under the first line <u>in every tenth</u>.
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	The clefs 1,2,3... refers to the tenths: first, second, third...		The clefs 1,2,3... refers to the tenths: first, second, third...

	So, in the illustrated example above, the first ~~tetragram~~ (from top) refers to the 3rd tenth (central tenth, corresponding to the octave C3-C4), the second tetragram to the 5th tenth and the third to the 2nd. If we need to write simultaneously on several staves, we will draw normal braces.		So, in the illustrated example above, the first staff (from top) refers to the 3rd tenth (central tenth, corresponding to the octave C3-C4), the second tetragram to the 5th tenth and the third to the 2nd. If we need to write simultaneously on several staves, we will draw normal braces.

	~~The~~ keyboard ~~conceived by the~~ Armodue ~~authors has the same disposition~~ as ~~Goldsmith's one (except the curvature):~~		Note that you cannot connect staves like in standard notation, because the lines are offset from one decave to the next.

			This is a keyboard layout for Armodue, which can also be seen as a standard mavila keyboard layout for 16edo.

	[[file:armodue-Tastiera.jpg\|frame\|none\|© Armodue; used with permission.]]		[[file:armodue-Tastiera.jpg\|frame\|none\|© Armodue; used with permission.]]
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	[[file:Armodue_Neck.PNG\|frame\|none\|Dot-Pattern inlays, by Armodue]]		[[file:Armodue_Neck.PNG\|frame\|none\|Dot-Pattern inlays, by Armodue]]

	==Armodue ~~just intonation - connection to Lou Harrison and Andrián Pertout~~==		== Alternative Armodue tunings ==
			As the standard intervals of Armodue may be too discordant for some composers and/or listeners, here are several alternative tunings:

			=== Armodue just intonation - connection to Lou Harrison and Andrián Pertout ===
	Armodue Just Intonation is nothing else than the 16-note scale by[[Lou_Harrison\| Lou Harrison]] based on simple ratios and pure intervals. In this scale there are practically the same twelve intervals of the "natural" or "Zarlinian" scale (the semitone 16/15, the minor wholetone 10/9, the minor third 6/5, the major third 5/4, the pure forth and fifth 4/3 and 3/2, the minor sixth 8/5, the major sixth 5/3, the minor seventh that is the complement of the minor wholetone 9/5, the major seventh 15/8) in addition to the tritone and four other intervals that are based on the harmonic seventh (the ratios 8/7, 7/6, 12/7, 7/4).		Armodue Just Intonation is nothing else than the 16-note scale by[[Lou_Harrison\| Lou Harrison]] based on simple ratios and pure intervals. In this scale there are practically the same twelve intervals of the "natural" or "Zarlinian" scale (the semitone 16/15, the minor wholetone 10/9, the minor third 6/5, the major third 5/4, the pure forth and fifth 4/3 and 3/2, the minor sixth 8/5, the major sixth 5/3, the minor seventh that is the complement of the minor wholetone 9/5, the major seventh 15/8) in addition to the tritone and four other intervals that are based on the harmonic seventh (the ratios 8/7, 7/6, 12/7, 7/4).

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	==Semi-equalized Armodue==		=== Semi-equalized Armodue ===

	One step of 16edo (75 cents) is nearly equal to two steps (2\31) of [[31edo\|31edo]] (77.42 cents). If we take the latter as a base, we get semi-equalized Armodue. In this temperament there is inevitably a smaller microtone (eka between the notes '7#' and '8'). leading to the 16 note MOS Valentine[16] of [[Starling_temperaments#Valentine temperament\|valentine temperament]]. Similarly we might use three steps of [[46edo\|46edo]], 3\46, 78.26 cents, or five steps of [[77edo\|77edo]], 77.92 cents.		One step of 16edo (75 cents) is nearly equal to two steps (2\31) of [[31edo\|31edo]] (77.42 cents). If we take the latter as a base, we get semi-equalized Armodue. In this temperament there is inevitably a smaller microtone (eka between the notes '7#' and '8'). leading to the 16 note MOS Valentine[16] of [[Starling_temperaments#Valentine temperament\|valentine temperament]]. Similarly we might use three steps of [[46edo\|46edo]], 3\46, 78.26 cents, or five steps of [[77edo\|77edo]], 77.92 cents.

VectorGraphics at 00:34, 19 March 2025

2025-03-19T00:34:03Z

← Older revision		Revision as of 00:34, 19 March 2025
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	1, 1#, 2, 2#, 3, 3#, 4, 5, 5#, 6, 6#, 7, 7#, 8, 8#, 9		1, 1#, 2, 2#, 3, 3#, 4, 5, 5#, 6, 6#, 7, 7#, 8, 8#, 9

	~~Consequently~~, the interval between a note at frequency n and other at frequency 2n is called a ''tenth,'' ''decave,'' or ''decim''.		This is the recommended system for Armodue theory, though in technicality any notation system can be used.

			Relative notation is simply done by specifying the number of edosteps, in order to support alternative scale constructions. For example, one refers not to the perfect fourth or fifth (at least in the specific sense of Armodue intervals) but to the intervals of 7-eka and 9-eka.

			However, the interval between a note at frequency n and other at frequency 2n is called a ''tenth,'' ''decave,'' or ''decim''.

	The basic semitone of Armodue, whatever concrete temperament is used, is always called '''eka''' (from Sanskrit eka: one, unit). In the chromatic Armodue scale, one eka always corresponds to the interval between any two consecutive notes.		The basic semitone of Armodue, whatever concrete temperament is used, is always called '''eka''' (from Sanskrit eka: one, unit). In the chromatic Armodue scale, one eka always corresponds to the interval between any two consecutive notes.

VectorGraphics at 10:46, 17 March 2025

2025-03-17T10:46:03Z

← Older revision		Revision as of 10:46, 17 March 2025
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	''(summary translation from the Italian language site'' [http://www.armodue.com/ricerche.htm Armodue] '')''		''(summary translation from the Italian language site'' [http://www.armodue.com/ricerche.htm Armodue] '')''

	Armodue theory is a xenharmonic notation and theory system for 16-note tuning, not only in the sense of [[16edo\|16-tone equal temperament]], but also regarding half-equal tuning, [[Lou_Harrison\|Lou Harrison]]'s [[JustIntonation\|Just intonation]] 16 note scale, the natural octave division by [http://www.pertout.com/ Andrián Pertout], and the 16-to-31 [[OverToneSeries\|overtone scale]],		Armodue theory is a xenharmonic notation and theory system for 16-note tuning, not only in the sense of [[16edo\|16-tone equal temperament]], but also regarding half-equal tuning, [[Lou_Harrison\|Lou Harrison]]'s [[JustIntonation\|Just intonation]] 16 note scale, the natural octave division by [http://www.pertout.com/ Andrián Pertout], and the 16-to-31 [[OverToneSeries\|overtone scale]].

			== Notation ==
	In order to make Armodue approachable, while also making its notation distinct from Western diatonic notation, the Italian creators of the [http://armodue.com/ Armodue] system named the notes numbering from 1 to 9:		In order to make Armodue approachable, while also making its notation distinct from Western diatonic notation, the Italian creators of the [http://armodue.com/ Armodue] system named the notes numbering from 1 to 9:

VectorGraphics at 10:45, 17 March 2025

2025-03-17T10:45:33Z

← Older revision		Revision as of 10:45, 17 March 2025
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	''(summary translation from the Italian language site'' [http://www.armodue.com/ricerche.htm Armodue] '')''		''(summary translation from the Italian language site'' [http://www.armodue.com/ricerche.htm Armodue] '')''

	Armodue theory, not only in the sense of [[16edo\|16-tone equal temperament]], but also regarding half-equal tuning ~~and~~ [[Lou_Harrison\|Lou Harrison]]'s [[JustIntonation\|Just intonation]] 16 note scale, the natural octave division by [http://www.pertout.com/ Andrián Pertout], and the 16-to-31 [[OverToneSeries\|overtone scale]], ~~is a xenharmonic notation and theory system for 16-note tuning.~~		Armodue theory is a xenharmonic notation and theory system for 16-note tuning, not only in the sense of [[16edo\|16-tone equal temperament]], but also regarding half-equal tuning, [[Lou_Harrison\|Lou Harrison]]'s [[JustIntonation\|Just intonation]] 16 note scale, the natural octave division by [http://www.pertout.com/ Andrián Pertout], and the 16-to-31 [[OverToneSeries\|overtone scale]],

	In order to make Armodue approachable, while also making its notation distinct from Western diatonic notation, the Italian creators of the [http://armodue.com/ Armodue] system named the notes numbering from 1 to 9:		In order to make Armodue approachable, while also making its notation distinct from Western diatonic notation, the Italian creators of the [http://armodue.com/ Armodue] system named the notes numbering from 1 to 9:

VectorGraphics at 10:44, 17 March 2025

2025-03-17T10:44:28Z

← Older revision		Revision as of 10:44, 17 March 2025
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	''(summary translation from the Italian language site'' [http://www.armodue.com/ricerche.htm Armodue] '')''		''(summary translation from the Italian language site'' [http://www.armodue.com/ricerche.htm Armodue] '')''

	Armodue theory ~~referring~~ not only to the [[16edo\|16-tone equal temperament]], but also to half-equal and [[Lou_Harrison\|Lou Harrison]]'s [[JustIntonation\|Just intonation]] 16 note scale, the natural octave division by [http://www.pertout.com/ Andrián Pertout] and the 16-to-31 [[OverToneSeries\|overtone scale]], ~~Armodue has been proposed as~~ a ~~new~~ notation and theory system.		Armodue theory, not only in the sense of [[16edo\|16-tone equal temperament]], but also regarding half-equal tuning and [[Lou_Harrison\|Lou Harrison]]'s [[JustIntonation\|Just intonation]] 16 note scale, the natural octave division by [http://www.pertout.com/ Andrián Pertout], and the 16-to-31 [[OverToneSeries\|overtone scale]], is a xenharmonic notation and theory system for 16-note tuning.

	~~Desiring~~ to make ~~the approach to~~ Armodue ~~as easy as possible~~, ~~but conscious that they had to give new names to the notes that constitute the system~~, the Italian creators of the [http://armodue.com/ Armodue] system named ~~them~~ numbering from 1 to 9:		In order to make Armodue approachable, while also making its notation distinct from Western diatonic notation, the Italian creators of the [http://armodue.com/ Armodue] system named the notes numbering from 1 to 9:

	1, 1#, 2, 2#, 3, 3#, 4, 5, 5#, 6, 6#, 7, 7#, 8, 8#, 9		1, 1#, 2, 2#, 3, 3#, 4, 5, 5#, 6, 6#, 7, 7#, 8, 8#, 9

	Consequently, the interval between a note at frequency n and other at frequency 2n is called a ''tenth'' or ''~~decave~~''.		Consequently, the interval between a note at frequency n and other at frequency 2n is called a ''tenth,'' ''decave,'' or ''decim''.

	The basic semitone of Armodue, whatever concrete temperament is used, is always called '''eka''' (from Sanskrit eka: one, unit). In the chromatic Armodue scale, one eka always corresponds to the interval between any two consecutive notes.		The basic semitone of Armodue, whatever concrete temperament is used, is always called '''eka''' (from Sanskrit eka: one, unit). In the chromatic Armodue scale, one eka always corresponds to the interval between any two consecutive notes.
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	The notes without accidentals form a [[Mavila\|Mavila]] [[7L_2s\|~~superdiatonic~~ scale (7L 2s)]].		The notes without accidentals form a [[Mavila\|Mavila]] [[7L_2s\|armotonic scale (7L 2s)]].

	If for the execution of a musical piece we need to write on two or more tetragrams, the notes will be written in the same way for every tetragram.		If for the execution of a musical piece we need to write on two or more tetragrams, the notes will be written in the same way for every tetragram.

Lériendil: deploying new cat

2025-01-31T22:18:43Z

deploying new cat

← Older revision		Revision as of 22:18, 31 January 2025
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	[[Category:16edo]]		[[Category:16edo]]
	[[Category:~~armodue~~]]		[[Category:Armodue]]
	[[Category:~~notation~~]]		[[Category:Notation]]
	[[Category:~~valentine~~]]		[[Category:Valentine]]
			[[Category:Method]]
			[[Category:Approaches to tuning systems]]

Eliora: style and headings and an attempt at cleanup

2023-03-20T00:49:36Z

style and headings and an attempt at cleanup

← Older revision		Revision as of 00:49, 20 March 2023
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	~~__FORCETOC__~~
	~~-----~~

	~~=Armodue Theory of 16EDO=~~

	''(summary translation from the Italian language site'' [http://www.armodue.com/ricerche.htm Armodue] '')''		''(summary translation from the Italian language site'' [http://www.armodue.com/ricerche.htm Armodue] '')''

	~~Referring~~ not only to the [[16edo\|16-tone equal temperament]], but also to half-equal and [[Lou_Harrison\|Lou Harrison]]'s [[JustIntonation\|Just intonation]] 16 note scale, the natural octave division by [http://www.pertout.com/ Andrián Pertout] and the 16-to-31 [[OverToneSeries\|overtone scale]], Armodue has been proposed as a new notation and theory system.		Armodue theory referring not only to the [[16edo\|16-tone equal temperament]], but also to half-equal and [[Lou_Harrison\|Lou Harrison]]'s [[JustIntonation\|Just intonation]] 16 note scale, the natural octave division by [http://www.pertout.com/ Andrián Pertout] and the 16-to-31 [[OverToneSeries\|overtone scale]], Armodue has been proposed as a new notation and theory system.

	Desiring to make the approach to Armodue as easy as possible, but conscious that they had to give new names to the notes that constitute the system, the Italian creators of the [http://armodue.com/ Armodue] system named them numbering from 1 to 9:		Desiring to make the approach to Armodue as easy as possible, but conscious that they had to give new names to the notes that constitute the system, the Italian creators of the [http://armodue.com/ Armodue] system named them numbering from 1 to 9:
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	[[file:Armodue_Neck.PNG\|frame\|none\|Dot-Pattern inlays, by Armodue]]		[[file:Armodue_Neck.PNG\|frame\|none\|Dot-Pattern inlays, by Armodue]]

	=Armodue just intonation - connection to Lou Harrison and Andrián Pertout=		==Armodue just intonation - connection to Lou Harrison and Andrián Pertout==

	Armodue Just Intonation is nothing else than the 16-note scale by[[Lou_Harrison\| Lou Harrison]] based on simple ratios and pure intervals. In this scale there are practically the same twelve intervals of the "natural" or "Zarlinian" scale (the semitone 16/15, the minor wholetone 10/9, the minor third 6/5, the major third 5/4, the pure forth and fifth 4/3 and 3/2, the minor sixth 8/5, the major sixth 5/3, the minor seventh that is the complement of the minor wholetone 9/5, the major seventh 15/8) in addition to the tritone and four other intervals that are based on the harmonic seventh (the ratios 8/7, 7/6, 12/7, 7/4).		Armodue Just Intonation is nothing else than the 16-note scale by[[Lou_Harrison\| Lou Harrison]] based on simple ratios and pure intervals. In this scale there are practically the same twelve intervals of the "natural" or "Zarlinian" scale (the semitone 16/15, the minor wholetone 10/9, the minor third 6/5, the major third 5/4, the pure forth and fifth 4/3 and 3/2, the minor sixth 8/5, the major sixth 5/3, the minor seventh that is the complement of the minor wholetone 9/5, the major seventh 15/8) in addition to the tritone and four other intervals that are based on the harmonic seventh (the ratios 8/7, 7/6, 12/7, 7/4).
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	\|}		\|}

	=Semi-equalized Armodue=		==Semi-equalized Armodue==

	One step of 16edo (75 cents) is nearly equal to two steps (2\31) of [[31edo\|31edo]] (77.42 cents). If we take the latter as a base, we get semi-equalized Armodue. In this temperament there is inevitably a smaller microtone (eka between the notes '7#' and '8'). leading to the 16 note MOS Valentine[16] of [[Starling_temperaments#Valentine temperament\|valentine temperament]]. Similarly we might use three steps of [[46edo\|46edo]], 3\46, 78.26 cents, or five steps of [[77edo\|77edo]], 77.92 cents.		One step of 16edo (75 cents) is nearly equal to two steps (2\31) of [[31edo\|31edo]] (77.42 cents). If we take the latter as a base, we get semi-equalized Armodue. In this temperament there is inevitably a smaller microtone (eka between the notes '7#' and '8'). leading to the 16 note MOS Valentine[16] of [[Starling_temperaments#Valentine temperament\|valentine temperament]]. Similarly we might use three steps of [[46edo\|46edo]], 3\46, 78.26 cents, or five steps of [[77edo\|77edo]], 77.92 cents.

Fredg999 category edits: Removing from Category:Theory using Cat-a-lot

2023-02-20T04:04:10Z

Removing from Category:Theory using Cat-a-lot

← Older revision		Revision as of 04:04, 20 February 2023
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	[[Category:armodue]]		[[Category:armodue]]
	[[Category:notation]]		[[Category:notation]]
	~~[[Category:theory]]~~
	[[Category:valentine]]		[[Category:valentine]]