Tritriadic scale - Revision history

ArrowHead294: Formatting. Using «nowiki» tags avoids the need to use escape templates.

2024-11-24T23:38:50Z

Formatting. Using «nowiki» tags avoids the need to use escape templates.

← Older revision		Revision as of 23:38, 24 November 2024
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	A '''tritriadic scale''' is a 7-note [[just intonation]] [[scale]] generated from a chain of three ''T'':''M'':''D'' [[triad]]s whose roots are separated by the ''D''/''T'' [[interval]] (where ''T'' stands for "tonic", ''M'' for "mediant" and ''D'' for "dominant")<ref>[http://www.tonalsoft.com/enc/t/tritriadic.aspx "tritriadic"]. ''www.tonalsoft.com''. Retrieved July 24, 2021.</ref>. These three chords can be interpreted as (pseudo)subdominant, root and (pseudo)dominant. Since a tritriadic scale is generally assumed to be octave-repeating, it is obtained by [[octave reduction\|octave-reducing]] the notes from all three chords so that they fit within an octave.		A '''tritriadic scale''' is a 7-note [[just intonation]] [[scale]] generated from a chain of three ''T'':''M'':''D'' [[triad]]s whose roots are separated by the ''D''/''T'' [[interval]] (where ''T'' stands for "tonic", ''M'' for "mediant" and ''D'' for "dominant")<ref>[http://www.tonalsoft.com/enc/t/tritriadic.aspx "tritriadic"]. ''www.tonalsoft.com''. Retrieved July 24, 2021.</ref>. These three chords can be interpreted as (pseudo)subdominant, root and (pseudo)dominant. Since a tritriadic scale is generally assumed to be octave-repeating, it is obtained by [[octave reduction\|octave-reducing]] the notes from all three chords so that they fit within an octave.

	A tritriadic scale is a special case of a [[cross-set scale]]. We can express a ''T'':''M'':''D'' tritriadic scale as CrossSet({1/1, ''M''/''T'', ''D''/''T''}, {''T''/''D'', 1/1, ''D''/''T''}).		A tritriadic scale is a special case of a [[cross-set scale]]. We can express a ''T'':''M'':''D'' tritriadic scale as {{nowrap\|CrossSet({1/1, ''M''/''T'', ''D''/''T''}\|{''T''/''D'', 1/1, ''D''/''T''})}}.

	Also, this scale type is a kind of a [[generator sequence]] scale: GS(''T'':''M'':''D'')[7], or GS(''M''/''T'', ''D''/''M'')[7].		Also, this scale type is a kind of a [[generator sequence]] scale: {{nowrap\|GS(''T'':''M'':''D'')[7]\|or GS(''M''/''T'', ''D''/''M'')[7]}}.

	The concept of tritriadic scales was first developed by John Chalmers in 1986<ref>[https://xh.xentonic.org/tables-of-contents.html "Xenharmonikôn Tables of Contents"]. ''xh.xentonic.org''. Retrieved 24 July, 2021.</ref>.		The concept of tritriadic scales was first developed by John Chalmers in 1986<ref>[https://xh.xentonic.org/tables-of-contents.html "Xenharmonikôn Tables of Contents"]. ''xh.xentonic.org''. Retrieved 24 July, 2021.</ref>.

	== Example ==		== Example ==

	To build a tritriadic scale, the first step is to choose a triad. For this example, the 6:7:9 triad will be used.		To build a tritriadic scale, the first step is to choose a triad. For this example, the 6:7:9 triad will be used.

	The root chord gives the first three notes of the scale. In this example, these notes are {6/6, 7/6, 9/6}, which becomes {1/1, 7/6, 3/2} after simplification and reduction.		The root chord gives the first three notes of the scale. In this example, these notes are {{nowrap\|<nowiki>{6/6, 7/6, 9/6}</nowiki>}}, which becomes {{nowrap\|<nowiki>{1/1, 7/6, 3/2}</nowiki>}} after simplification and reduction.

	Next, to build the triad on the (pseudo)dominant, multiply all the notes from the root chord by ''D''/''T''. In this example, the dominant is 3/2, so the triad is {3/2, 21/12, 9/4}, which becomes {3/2, 7/4, 9/8} after simplification and reduction.		Next, to build the triad on the (pseudo)dominant, multiply all the notes from the root chord by ''D''/''T''. In this example, the dominant is 3/2, so the triad is {{nowrap\|<nowiki>{3/2, 21/12, 9/4}</nowiki>}}, which becomes {{nowrap\|<nowiki>{3/2, 7/4, 9/8}</nowiki>}} after simplification and reduction.

	Then, to build the triad on the (pseudo)subdominant, multiply all the notes from the root chord by ''T''/''D''. In this example, the subdominant is 2/3, so the triad is {2/3, 14/18, 1/1}, which becomes {4/3, 14/9, 1/1} after simplification and reduction.		Then, to build the triad on the (pseudo)subdominant, multiply all the notes from the root chord by ''T''/''D''. In this example, the subdominant is 2/3, so the triad is {{nowrap\|<nowiki>{2/3, 14/18, 1/1}</nowiki>}}, which becomes {{nowrap\|<nowiki>{4/3, 14/9, 1/1}</nowiki>}} after simplification and reduction.

	Finally, assemble all the notes in ascending order (without repeating the tonic and the dominant) to build the scale. The unison can be replaced by the octave for compatibility with the [[Scala]] scale file format. In this example, we get {9/8, 7/6, 4/3, 3/2, 14/9, 7/4, 2/1}, which is the [[Tritriad69]] scale.		Finally, assemble all the notes in ascending order (without repeating the tonic and the dominant) to build the scale. The unison can be replaced by the octave for compatibility with the [[Scala]] scale file format. In this example, we get {{nowrap\|<nowiki>{9/8, 7/6, 4/3, 3/2, 14/9, 7/4, 2/1}</nowiki>}}, which is the [[Tritriad69]] scale.

	== References ==		== References ==
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	== External links ==		== External links ==

	* [http://www.anaphoria.com/triscales.htm Tritriadic scale examples (with audio)]		* [http://www.anaphoria.com/triscales.htm Tritriadic scale examples (with audio)]

	[[Category:Tritriadic scales\| ]] <!-- ~~main~~ article -->		[[Category:Tritriadic scales\| ]] <!-- Main article -->
	[[Category:Just intonation]]		[[Category:Just intonation]]

Arseniiv: also related to generator-sequece scales

2024-02-17T18:39:23Z

also related to generator-sequece scales

← Older revision		Revision as of 18:39, 17 February 2024
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	A tritriadic scale is a special case of a [[cross-set scale]]. We can express a ''T'':''M'':''D'' tritriadic scale as CrossSet({1/1, ''M''/''T'', ''D''/''T''}, {''T''/''D'', 1/1, ''D''/''T''}).		A tritriadic scale is a special case of a [[cross-set scale]]. We can express a ''T'':''M'':''D'' tritriadic scale as CrossSet({1/1, ''M''/''T'', ''D''/''T''}, {''T''/''D'', 1/1, ''D''/''T''}).

			Also, this scale type is a kind of a [[generator sequence]] scale: GS(''T'':''M'':''D'')[7], or GS(''M''/''T'', ''D''/''M'')[7].

	The concept of tritriadic scales was first developed by John Chalmers in 1986<ref>[https://xh.xentonic.org/tables-of-contents.html "Xenharmonikôn Tables of Contents"]. ''xh.xentonic.org''. Retrieved 24 July, 2021.</ref>.		The concept of tritriadic scales was first developed by John Chalmers in 1986<ref>[https://xh.xentonic.org/tables-of-contents.html "Xenharmonikôn Tables of Contents"]. ''xh.xentonic.org''. Retrieved 24 July, 2021.</ref>.

Akselai: add cross-set scale

2024-01-22T19:14:49Z

add cross-set scale

← Older revision		Revision as of 19:14, 22 January 2024
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	A '''tritriadic scale''' is a 7-note [[just intonation]] [[scale]] generated from a chain of three ''T'':''M'':''D'' [[triad]]s whose roots are separated by the ''D''/''T'' [[interval]] (where ''T'' stands for "tonic", ''M'' for "mediant" and ''D'' for "dominant")<ref>[http://www.tonalsoft.com/enc/t/tritriadic.aspx "tritriadic"]. ''www.tonalsoft.com''. Retrieved July 24, 2021.</ref>. These three chords can be interpreted as (pseudo)subdominant, root and (pseudo)dominant. Since a tritriadic scale is generally assumed to be octave-repeating, it is obtained by [[octave reduction\|octave-reducing]] the notes from all three chords so that they fit within an octave.		A '''tritriadic scale''' is a 7-note [[just intonation]] [[scale]] generated from a chain of three ''T'':''M'':''D'' [[triad]]s whose roots are separated by the ''D''/''T'' [[interval]] (where ''T'' stands for "tonic", ''M'' for "mediant" and ''D'' for "dominant")<ref>[http://www.tonalsoft.com/enc/t/tritriadic.aspx "tritriadic"]. ''www.tonalsoft.com''. Retrieved July 24, 2021.</ref>. These three chords can be interpreted as (pseudo)subdominant, root and (pseudo)dominant. Since a tritriadic scale is generally assumed to be octave-repeating, it is obtained by [[octave reduction\|octave-reducing]] the notes from all three chords so that they fit within an octave.

			A tritriadic scale is a special case of a [[cross-set scale]]. We can express a ''T'':''M'':''D'' tritriadic scale as CrossSet({1/1, ''M''/''T'', ''D''/''T''}, {''T''/''D'', 1/1, ''D''/''T''}).

	The concept of tritriadic scales was first developed by John Chalmers in 1986<ref>[https://xh.xentonic.org/tables-of-contents.html "Xenharmonikôn Tables of Contents"]. ''xh.xentonic.org''. Retrieved 24 July, 2021.</ref>.		The concept of tritriadic scales was first developed by John Chalmers in 1986<ref>[https://xh.xentonic.org/tables-of-contents.html "Xenharmonikôn Tables of Contents"]. ''xh.xentonic.org''. Retrieved 24 July, 2021.</ref>.

Fredg999: Categories

2021-08-14T18:36:37Z

Fredg999: Added references section (omitted in the initial version)

2021-07-24T05:21:01Z

Added references section (omitted in the initial version)

← Older revision		Revision as of 05:21, 24 July 2021
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	Finally, assemble all the notes in ascending order (without repeating the tonic and the dominant) to build the scale. The unison can be replaced by the octave for compatibility with the [[Scala]] scale file format. In this example, we get {9/8, 7/6, 4/3, 3/2, 14/9, 7/4, 2/1}, which is the [[Tritriad69]] scale.		Finally, assemble all the notes in ascending order (without repeating the tonic and the dominant) to build the scale. The unison can be replaced by the octave for compatibility with the [[Scala]] scale file format. In this example, we get {9/8, 7/6, 4/3, 3/2, 14/9, 7/4, 2/1}, which is the [[Tritriad69]] scale.

			== References ==
			<references />

	== External links ==		== External links ==

Fredg999: Introduction + Example

2021-07-24T05:18:48Z

Introduction + Example

New page

A '''tritriadic scale''' is a 7-note [[just intonation]] [[scale]] generated from a chain of three ''T'':''M'':''D'' [[triad]]s whose roots are separated by the ''D''/''T'' [[interval]] (where ''T'' stands for "tonic", ''M'' for "mediant" and ''D'' for "dominant")<ref>[http://www.tonalsoft.com/enc/t/tritriadic.aspx "tritriadic"]. ''www.tonalsoft.com''. Retrieved July 24, 2021.</ref>. These three chords can be interpreted as (pseudo)subdominant, root and (pseudo)dominant. Since a tritriadic scale is generally assumed to be octave-repeating, it is obtained by [[octave reduction|octave-reducing]] the notes from all three chords so that they fit within an octave.

The concept of tritriadic scales was first developed by John Chalmers in 1986<ref>[https://xh.xentonic.org/tables-of-contents.html "Xenharmonikôn Tables of Contents"]. ''xh.xentonic.org''. Retrieved 24 July, 2021.</ref>.

== Example ==

To build a tritriadic scale, the first step is to choose a triad. For this example, the 6:7:9 triad will be used.

The root chord gives the first three notes of the scale. In this example, these notes are {6/6, 7/6, 9/6}, which becomes {1/1, 7/6, 3/2} after simplification and reduction.

Next, to build the triad on the (pseudo)dominant, multiply all the notes from the root chord by ''D''/''T''. In this example, the dominant is 3/2, so the triad is {3/2, 21/12, 9/4}, which becomes {3/2, 7/4, 9/8} after simplification and reduction.

Then, to build the triad on the (pseudo)subdominant, multiply all the notes from the root chord by ''T''/''D''. In this example, the subdominant is 2/3, so the triad is {2/3, 14/18, 1/1}, which becomes {4/3, 14/9, 1/1} after simplification and reduction.

Finally, assemble all the notes in ascending order (without repeating the tonic and the dominant) to build the scale. The unison can be replaced by the octave for compatibility with the [[Scala]] scale file format. In this example, we get {9/8, 7/6, 4/3, 3/2, 14/9, 7/4, 2/1}, which is the [[Tritriad69]] scale.

== External links ==

* [http://www.anaphoria.com/triscales.htm Tritriadic scale examples (with audio)]

[[Category:Scale]]
[[Category:Just intonation]]

← Older revision		Revision as of 18:36, 14 August 2021
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	* [http://www.anaphoria.com/triscales.htm Tritriadic scale examples (with audio)]		* [http://www.anaphoria.com/triscales.htm Tritriadic scale examples (with audio)]

	[[Category:~~Scale~~]]		[[Category:Tritriadic scales\| ]] <!-- main article -->
	[[Category:Just intonation]]		[[Category:Just intonation]]