User:Unque/Chord interlacing (scale building method) - Revision history

Unque at 05:53, 18 November 2024

2024-11-18T05:53:53Z

← Older revision		Revision as of 05:53, 18 November 2024
Line 8:		Line 8:

	== Ancient Greek Genera ==		== Ancient Greek Genera ==
	The Ancient Greek genera can be interpreted as Chord Interlace scales. A five-limit shade of the Genus Diatonic, for instance, can be created using the chord ~~[[Tel:~~10/9 - 5/4 - 4/3~~\|10/9 - 5/4 - 4/3]]~~ (with step sizes ~~[[Tel:10/9 - 9/8 - 16\|~~10/9 - 9/8 - 16]]/15), and a seven-limit shade can be created with the chord 8/7 - 9/7 - 4/3 (with step sizes 8/7 - 9/8 - 28/27). Scales of the other genera can be similarly created by interlacing the [[Tetrachord\|tetrachords]] thereof.		The Ancient Greek genera can be interpreted as Chord Interlace scales. A five-limit shade of the Genus Diatonic, for instance, can be created using the chord 10/9 - 5/4 - 4/3 (with step sizes 10/9 - 9/8 - 16/15), and a seven-limit shade can be created with the chord 8/7 - 9/7 - 4/3 (with step sizes 8/7 - 9/8 - 28/27). Scales of the other genera can be similarly created by interlacing the [[Tetrachord\|tetrachords]] thereof.

	The modern equal-tempered tunings of the [[5L 2s\|Diatonic]] scale can be similarly created using the [[12edo\|12-EDO]] chord 2 - 4 - 5, with step sizes 2 - 2 - 1; this can also be extended to other tunings thereof, such as [[17edo\|17-EDO]] (with the chord 3 - 6 - 7), [[19edo\|19-EDO]] (with the chord 3 - 6 - 8), [[31edo\|31-EDO]] (with the chord 5 - 10 - 13), and any other desired shade of the diatonic scale.		The modern equal-tempered tunings of the [[5L 2s\|Diatonic]] scale can be similarly created using the [[12edo\|12-EDO]] chord 2 - 4 - 5, with step sizes 2 - 2 - 1; this can also be extended to other tunings thereof, such as [[17edo\|17-EDO]] (with the chord 3 - 6 - 7), [[19edo\|19-EDO]] (with the chord 3 - 6 - 8), [[31edo\|31-EDO]] (with the chord 5 - 10 - 13), and any other desired shade of the diatonic scale.

	== Maqamat and Ajnas ==		== Maqamat and Ajnas ==
	The Arabic Maqamat are built using chords called Ajnas. For instance, Maqam Rast is created using two Ajnas Rast (though the Perfect Fifth is typically considered to be contained in the lower tetrachord, making Jins Upper Rast distinct from Lower Rast). If we take an approximation of the four-note Jins Rast, such as the 9:~~10:11~~:12 ~~tetrachord~~, we can use a Chord Interlace scale to create a reasonable approximation of Maqam Rast. This can also be done for other Maqamat whose Jins are identical or nearly so, such as 'Ajam and Hijazkar.		The Arabic Maqamat are built using chords called Ajnas. For instance, Maqam Rast is created using two Ajnas Rast (though the Perfect Fifth is typically considered to be contained in the lower tetrachord, making Jins Upper Rast distinct from Lower Rast). If we take an approximation of the four-note Jins Rast, such as the 9::12 harmonic segment, we can use a Chord Interlace scale to create a reasonable approximation of Maqam Rast. This can also be done for other Maqamat whose Jins are identical or nearly so, such as 'Ajam and Hijazkar.

	Keep in mind that while the generated scales might sound similar to the traditional maqamat, this method of approximation is extremely crude, and a very poor representation of the actual traditions.		Keep in mind that while the generated scales might sound similar to the traditional maqamat, this method of approximation is extremely crude, and a very poor representation of the actual traditions.

Moremajorthanmajor: /* Maqamat and Ajnas */

2024-11-18T00:40:10Z

Maqamat and Ajnas

← Older revision		Revision as of 00:40, 18 November 2024
Line 3:		Line 3:
	== Scale Formation ==		== Scale Formation ==
	[[File:Mode 7 Interlace.png\|thumb\|An example of a Chord Interlace scale, built using the harmonic segment 7::10. Note how the first instance of the chord (shown in red) begins on the root pitch, and the other instance (shown in blue) ends on the octave.]]		[[File:Mode 7 Interlace.png\|thumb\|An example of a Chord Interlace scale, built using the harmonic segment 7::10. Note how the first instance of the chord (shown in red) begins on the root pitch, and the other instance (shown in blue) ends on the octave.]]
	Building a scale via chord interlacing requires only a single chord; this chord can be in pure JI or it can be tempered. Two instances of this chord are arranged such that one instance begins on the root pitch, and the other terminates on the period (usually an octave, though other periods are possible).		Building a scale via chord interlacing requires only a single chord; this chord can be in pure JI or it can be tempered. Two instances of this chord are arranged such that one instance begins on the root pitch, and the other terminates on the period (usually an octave, though other periods are possible).

	Chord Interlace scales are so named due to the interlacing of the notes that the scale provides if the chord terminates higher than half of the period; for instance, 5/3 is more than half of an octave, so a chord that terminates on 5/3 will interlace with its counterpart. Note that, in spite of the name, not all chords will interlace when constructing a scale in this manner.		Chord Interlace scales are so named due to the interlacing of the notes that the scale provides if the chord terminates higher than half of the period; for instance, 5/3 is more than half of an octave, so a chord that terminates on 5/3 will interlace with its counterpart. Note that, in spite of the name, not all chords will interlace when constructing a scale in this manner.

	== Ancient Greek Genera ==		== Ancient Greek Genera ==
	The Ancient Greek genera can be interpreted as Chord Interlace scales. A five-limit shade of the Genus Diatonic, for instance, can be created using the chord 10/9 - 5/4 - 4/3 (with step sizes 10/9 - 9/8 - 16/15), and a seven-limit shade can be created with the chord 8/7 - 9/7 - 4/3 (with step sizes 8/7 - 9/8 - 28/27). Scales of the other genera can be similarly created by interlacing the [[Tetrachord\|tetrachords]] thereof.		The Ancient Greek genera can be interpreted as Chord Interlace scales. A five-limit shade of the Genus Diatonic, for instance, can be created using the chord [[Tel:10/9 - 5/4 - 4/3\|10/9 - 5/4 - 4/3]] (with step sizes [[Tel:10/9 - 9/8 - 16\|10/9 - 9/8 - 16]]/15), and a seven-limit shade can be created with the chord 8/7 - 9/7 - 4/3 (with step sizes 8/7 - 9/8 - 28/27). Scales of the other genera can be similarly created by interlacing the [[Tetrachord\|tetrachords]] thereof.

	The modern equal-tempered tunings of the [[5L 2s\|Diatonic]] scale can be similarly created using the [[12edo\|12-EDO]] chord 2 - 4 - 5, with step sizes 2 - 2 - 1; this can also be extended to other tunings thereof, such as [[17edo\|17-EDO]] (with the chord 3 - 6 - 7), [[19edo\|19-EDO]] (with the chord 3 - 6 - 8), [[31edo\|31-EDO]] (with the chord 5 - 10 - 13), and any other desired shade of the diatonic scale.		The modern equal-tempered tunings of the [[5L 2s\|Diatonic]] scale can be similarly created using the [[12edo\|12-EDO]] chord 2 - 4 - 5, with step sizes 2 - 2 - 1; this can also be extended to other tunings thereof, such as [[17edo\|17-EDO]] (with the chord 3 - 6 - 7), [[19edo\|19-EDO]] (with the chord 3 - 6 - 8), [[31edo\|31-EDO]] (with the chord 5 - 10 - 13), and any other desired shade of the diatonic scale.

	== Maqamat and Ajnas ==		== Maqamat and Ajnas ==
	The Arabic Maqamat are built using chords called Ajnas. For instance, Maqam Rast is created using two Ajnas Rast (though the Perfect Fifth is typically considered to be contained in the lower tetrachord, making Jins Upper Rast distinct from Lower Rast). If we take an approximation of the four-note Jins Rast, such as the 9::12 tetrachord, we can use a Chord Interlace scale to create a reasonable approximation of Maqam Rast. This can also be done for other Maqamat whose Jins are identical or nearly so, such as 'Ajam and Hijazkar.		The Arabic Maqamat are built using chords called Ajnas. For instance, Maqam Rast is created using two Ajnas Rast (though the Perfect Fifth is typically considered to be contained in the lower tetrachord, making Jins Upper Rast distinct from Lower Rast). If we take an approximation of the four-note Jins Rast, such as the 9:10:11:12 tetrachord, we can use a Chord Interlace scale to create a reasonable approximation of Maqam Rast. This can also be done for other Maqamat whose Jins are identical or nearly so, such as 'Ajam and Hijazkar.

	Keep in mind that while the generated scales might sound similar to the traditional maqamat, this method of approximation is extremely crude, and a very poor representation of the actual traditions.		Keep in mind that while the generated scales might sound similar to the traditional maqamat, this method of approximation is extremely crude, and a very poor representation of the actual traditions.

	== Other Applications ==		== Other Applications ==
	Chord interlace scales can provide a useful structure for any JI or tempered scale. Any and all chords can be used to generate such a scale - this includes [[Harmonic series segment\|overtone segments]], undertone segments, [[generator]] patterns, [[Delta-rational chord\|DR chords]], or any other arbitrarily-chosen chords the composer may want to use.		Chord interlace scales can provide a useful structure for any JI or tempered scale. Any and all chords can be used to generate such a scale - this includes [[Harmonic series segment\|overtone segments]], undertone segments, [[generator]] patterns, [[Delta-rational chord\|DR chords]], or any other arbitrarily-chosen chords the composer may want to use.

Unque at 18:41, 29 September 2024

2024-09-29T18:41:31Z

← Older revision		Revision as of 18:41, 29 September 2024
Line 13:		Line 13:

	== Maqamat and Ajnas ==		== Maqamat and Ajnas ==
	The Arabic Maqamat are built using chords called Ajnas. For instance, Maqam Rast is created using two ~~copies of Jins~~ Rast~~<!-- There are two forms of Jins Rast, often~~ considered to be ~~separate Ajnas;~~ the ~~difference between the two is the presence or absence of the Perfect Fifth. -->~~. If we take an approximation of ~~this~~ Rast ~~chord~~, such as the 9::12 tetrachord, we can use a Chord Interlace scale to create a reasonable approximation of Maqam Rast. This can also be done for other Maqamat whose Jins are identical or nearly so, such as 'Ajam and Hijazkar.		The Arabic Maqamat are built using chords called Ajnas. For instance, Maqam Rast is created using two Ajnas Rast (though the Perfect Fifth is typically considered to be contained in the lower tetrachord, making Jins Upper Rast distinct from Lower Rast). If we take an approximation of the four-note Jins Rast, such as the 9::12 tetrachord, we can use a Chord Interlace scale to create a reasonable approximation of Maqam Rast. This can also be done for other Maqamat whose Jins are identical or nearly so, such as 'Ajam and Hijazkar.

	Keep in mind that while the generated scales might sound similar to the traditional maqamat, this method of approximation is extremely crude, and a very poor representation of the actual traditions.		Keep in mind that while the generated scales might sound similar to the traditional maqamat, this method of approximation is extremely crude, and a very poor representation of the actual traditions.

Unque at 18:36, 29 September 2024

2024-09-29T18:36:08Z

← Older revision		Revision as of 18:36, 29 September 2024
Line 11:		Line 11:

	The modern equal-tempered tunings of the [[5L 2s\|Diatonic]] scale can be similarly created using the [[12edo\|12-EDO]] chord 2 - 4 - 5, with step sizes 2 - 2 - 1; this can also be extended to other tunings thereof, such as [[17edo\|17-EDO]] (with the chord 3 - 6 - 7), [[19edo\|19-EDO]] (with the chord 3 - 6 - 8), [[31edo\|31-EDO]] (with the chord 5 - 10 - 13), and any other desired shade of the diatonic scale.		The modern equal-tempered tunings of the [[5L 2s\|Diatonic]] scale can be similarly created using the [[12edo\|12-EDO]] chord 2 - 4 - 5, with step sizes 2 - 2 - 1; this can also be extended to other tunings thereof, such as [[17edo\|17-EDO]] (with the chord 3 - 6 - 7), [[19edo\|19-EDO]] (with the chord 3 - 6 - 8), [[31edo\|31-EDO]] (with the chord 5 - 10 - 13), and any other desired shade of the diatonic scale.

			== Maqamat and Ajnas ==
			The Arabic Maqamat are built using chords called Ajnas. For instance, Maqam Rast is created using two copies of Jins Rast<!-- There are two forms of Jins Rast, often considered to be separate Ajnas; the difference between the two is the presence or absence of the Perfect Fifth. -->. If we take an approximation of this Rast chord, such as the 9::12 tetrachord, we can use a Chord Interlace scale to create a reasonable approximation of Maqam Rast. This can also be done for other Maqamat whose Jins are identical or nearly so, such as 'Ajam and Hijazkar.

			Keep in mind that while the generated scales might sound similar to the traditional maqamat, this method of approximation is extremely crude, and a very poor representation of the actual traditions.

	== Other Applications ==		== Other Applications ==
	Chord Interlace scales can be used to approximate other musical traditions, such as the Arabic Ajnas and Maqamat. If we interpret [https://maqamworld.com/en/jins/upper_rast.php Jins Rast] as a 9::12 tetrachord, for instance, then the Chord Interlace scale built from this tetrachord provides a convincing [https://maqamworld.com/en/maqam/rast.php Maqam Rast].		Chord interlace scales can provide a useful structure for any JI or tempered scale. Any and all chords can be used to generate such a scale - this includes [[Harmonic series segment\|overtone segments]], undertone segments, [[generator]] patterns, [[Delta-rational chord\|DR chords]], or any other arbitrarily-chosen chords the composer may want to use.

	~~Additionally, chord~~ interlace scales can provide a useful structure for a JI or tempered scale. Any and all chords can be used to generate such a scale - this includes [[Harmonic series segment\|overtone segments]], undertone segments, [[generator]] patterns, [[Delta-rational chord\|DR chords]], or any other arbitrarily-chosen chords the composer may want to use.

Unque at 22:33, 18 September 2024

2024-09-18T22:33:33Z

← Older revision		Revision as of 22:33, 18 September 2024
Line 10:		Line 10:
	The Ancient Greek genera can be interpreted as Chord Interlace scales. A five-limit shade of the Genus Diatonic, for instance, can be created using the chord 10/9 - 5/4 - 4/3 (with step sizes 10/9 - 9/8 - 16/15), and a seven-limit shade can be created with the chord 8/7 - 9/7 - 4/3 (with step sizes 8/7 - 9/8 - 28/27). Scales of the other genera can be similarly created by interlacing the [[Tetrachord\|tetrachords]] thereof.		The Ancient Greek genera can be interpreted as Chord Interlace scales. A five-limit shade of the Genus Diatonic, for instance, can be created using the chord 10/9 - 5/4 - 4/3 (with step sizes 10/9 - 9/8 - 16/15), and a seven-limit shade can be created with the chord 8/7 - 9/7 - 4/3 (with step sizes 8/7 - 9/8 - 28/27). Scales of the other genera can be similarly created by interlacing the [[Tetrachord\|tetrachords]] thereof.

	~~Similarly, the~~ modern equal-tempered ~~tuning~~ of the [[5L 2s\|Diatonic]] scale can be created ~~with~~ the [[12edo\|12-EDO]] chord 2 - 4 - 5, with step sizes 2 - 2 - 1.		The modern equal-tempered tunings of the [[5L 2s\|Diatonic]] scale can be similarly created using the [[12edo\|12-EDO]] chord 2 - 4 - 5, with step sizes 2 - 2 - 1; this can also be extended to other tunings thereof, such as [[17edo\|17-EDO]] (with the chord 3 - 6 - 7), [[19edo\|19-EDO]] (with the chord 3 - 6 - 8), [[31edo\|31-EDO]] (with the chord 5 - 10 - 13), and any other desired shade of the diatonic scale.

	== Other Applications ==		== Other Applications ==
	Chord Interlace scales can be used to approximate other musical traditions, such as the Arabic Ajnas and Maqamat. If we interpret [https://maqamworld.com/en/jins/upper_rast.php Jins Rast] as a 9::12 tetrachord, for instance, then the Chord Interlace scale built from this tetrachord provides a convincing [https://maqamworld.com/en/maqam/rast.php Maqam Rast].		Chord Interlace scales can be used to approximate other musical traditions, such as the Arabic Ajnas and Maqamat. If we interpret [https://maqamworld.com/en/jins/upper_rast.php Jins Rast] as a 9::12 tetrachord, for instance, then the Chord Interlace scale built from this tetrachord provides a convincing [https://maqamworld.com/en/maqam/rast.php Maqam Rast].

	Additionally, chord interlace scales can provide a useful structure for a JI or tempered scale. Any and all chords can be used to generate ~~the~~ scale - this includes [[Harmonic series segment\|overtone segments]], undertone segments, generator patterns, [[Delta-rational chord\|DR chords]], or any other arbitrarily-chosen chords the composer may want to use.		Additionally, chord interlace scales can provide a useful structure for a JI or tempered scale. Any and all chords can be used to generate such a scale - this includes [[Harmonic series segment\|overtone segments]], undertone segments, [[generator]] patterns, [[Delta-rational chord\|DR chords]], or any other arbitrarily-chosen chords the composer may want to use.

Unque: Created page with "Chord Interlacing is a method of building scales out of a chord. == Scale Formation == File:Mode 7 Interlace.png|thumb|An example of a Chord Interlace scale, built using th..."

2024-09-17T05:32:59Z

Created page with "Chord Interlacing is a method of building scales out of a chord. == Scale Formation == File:Mode 7 Interlace.png|thumb|An example of a Chord Interlace scale, built using th..."

New page

Chord Interlacing is a method of building scales out of a chord.

== Scale Formation ==
[[File:Mode 7 Interlace.png|thumb|An example of a Chord Interlace scale, built using the harmonic segment 7::10. Note how the first instance of the chord (shown in red) begins on the root pitch, and the other instance (shown in blue) ends on the octave.]]
Building a scale via chord interlacing requires only a single chord; this chord can be in pure JI or it can be tempered. Two instances of this chord are arranged such that one instance begins on the root pitch, and the other terminates on the period (usually an octave, though other periods are possible).

Chord Interlace scales are so named due to the interlacing of the notes that the scale provides if the chord terminates higher than half of the period; for instance, 5/3 is more than half of an octave, so a chord that terminates on 5/3 will interlace with its counterpart. Note that, in spite of the name, not all chords will interlace when constructing a scale in this manner.

== Ancient Greek Genera ==
The Ancient Greek genera can be interpreted as Chord Interlace scales. A five-limit shade of the Genus Diatonic, for instance, can be created using the chord 10/9 - 5/4 - 4/3 (with step sizes 10/9 - 9/8 - 16/15), and a seven-limit shade can be created with the chord 8/7 - 9/7 - 4/3 (with step sizes 8/7 - 9/8 - 28/27). Scales of the other genera can be similarly created by interlacing the [[Tetrachord|tetrachords]] thereof.

Similarly, the modern equal-tempered tuning of the [[5L 2s|Diatonic]] scale can be created with the [[12edo|12-EDO]] chord 2 - 4 - 5, with step sizes 2 - 2 - 1.

== Other Applications ==
Chord Interlace scales can be used to approximate other musical traditions, such as the Arabic Ajnas and Maqamat. If we interpret [https://maqamworld.com/en/jins/upper_rast.php Jins Rast] as a 9::12 tetrachord, for instance, then the Chord Interlace scale built from this tetrachord provides a convincing [https://maqamworld.com/en/maqam/rast.php Maqam Rast].

Additionally, chord interlace scales can provide a useful structure for a JI or tempered scale. Any and all chords can be used to generate the scale - this includes [[Harmonic series segment|overtone segments]], undertone segments, generator patterns, [[Delta-rational chord|DR chords]], or any other arbitrarily-chosen chords the composer may want to use.