22edo/Unque's compositional approach - Revision history

Unque at 23:34, 5 May 2026

2026-05-05T23:34:15Z

← Older revision		Revision as of 23:34, 5 May 2026
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	=== The thirds of 22edo ===		=== The thirds of 22edo ===
	22edo has two pairs of thirds: ~~a major/minor~~ pair, and ~~a supermajor/subminor pair~~; despite most often being viewed as an 11-limit system, it lacks clear representation for the neutral thirds that are characteristic of 11-limit harmony.		22edo has two pairs of thirds: one pair characteristic of the Superpyth diatonic scale, and one characteristic of Zarlino diatonic; despite most often being viewed as an 11-limit system, it lacks clear representation for the neutral thirds that are characteristic of 11-limit harmony.

	The ~~subminor~~ third at 5\22 represents 7/6 with moderate accuracy, though it is often noted to be significantly less concordant than the JI representation. Its fifth complement is the ~~supermajor~~ third at 8\22, which is an excellent representation of 9/7. This interval is perhaps better paired with 14\22 than with 13\22, as the former can be interpreted as 11/7 and thus provides the more consonant otonal 7:9:11 triad.		The superpyth minor third at 5\22 represents 7/6 with moderate accuracy, though it is often noted to be significantly less concordant than the JI representation. Its fifth complement is the superpyth major third at 8\22, which is an excellent representation of 9/7. This interval is perhaps better paired with 14\22 than with 13\22, as the former can be interpreted as 11/7 and thus provides the more consonant otonal 7:9:11 triad.

	The minor third at 6\22 is contentious in its interpretation; it is quite sharp for a minor third, though not nearly sharp enough to constitute a neutral third; by patent val, it represents 6/5 and 11/9, though in practice it does not accurately represent either of the two. Its fifth complement, the major third at 7\22, is a much clearer 5/4, having a relative error of less than 10%.		The zarlino minor third at 6\22 is contentious in its interpretation; it is quite sharp for a minor third, though not nearly sharp enough to constitute a neutral third; by patent val, it represents 6/5 and 11/9, though in practice it does not accurately represent either of the two. Its fifth complement, the zarlino major third at 7\22, is a much clearer 5/4, having a relative error of less than 10%.

	== Scales ==		== Scales ==
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	!Scales of Common Occurance		!Scales of Common Occurance
	\|-		\|-
	\|Major		\|Major (Zarlino)
	\|C maj		\|C maj
	\|C - vE - G		\|C - vE - G
Line 866:		Line 866:
	\|2L 8s; 3L 2M 2s		\|2L 8s; 3L 2M 2s
	\|-		\|-
	\|Minor		\|Minor (Zarlino)
	\|c min		\|c min
	\|C - ^E♭ - G		\|C - ^E♭ - G
Line 875:		Line 875:
	\|2L 8s; 3L 2M 2s		\|2L 8s; 3L 2M 2s
	\|-		\|-
	\|~~Supermajor~~		\|Major (Superpyth)
	\|C saj		\|C saj
	\|C - E - G		\|C - E - G
Line 884:		Line 884:
	\|5L 2s; 2L 8s		\|5L 2s; 2L 8s
	\|-		\|-
	\|~~Subminor~~		\|Minor (Superpyth)
	\|c sin		\|c sin
	\|C - E♭ - G		\|C - E♭ - G

Unque at 17:42, 1 May 2026

2026-05-01T17:42:22Z

← Older revision		Revision as of 17:42, 1 May 2026
Line 1,056:		Line 1,056:
	The C Ionian scale in Superpyth is a perfect showcase of how common-practice harmony differs from that of 22edo; specifically, quartal harmony tends to provide a more resolved sound than tertian harmony does, due to the sharp fifth exaggerating the size of the chroma. Thus, our progression can resolve quite nicely to the tonic chord, Csus4 or G<sup>4</sup>/C.		The C Ionian scale in Superpyth is a perfect showcase of how common-practice harmony differs from that of 22edo; specifically, quartal harmony tends to provide a more resolved sound than tertian harmony does, due to the sharp fifth exaggerating the size of the chroma. Thus, our progression can resolve quite nicely to the tonic chord, Csus4 or G<sup>4</sup>/C.

	A supermajor triad can be found over the fifth degree of the Ionian mode, which is much tenser than the major triad found in Meantone tunings due to the ~~major~~ seventh (the third of the V chord) being significantly sharper; this increases the strength of the pull towards the tonic, as well as destabilizes the V chord, making it clear that this is not a place of rest and thus negating the need for a dominant seventh over that chord. This allows us to restrict our progression to three-part harmony rather than switching between three- and four-part harmony as is often done in common-practice progressions.		A supermajor triad can be found over the fifth degree of the Ionian mode, which is much tenser than the major triad found in Meantone tunings due to the seventh degree (the third of the V chord) being significantly sharper; this increases the strength of the pull towards the tonic, as well as destabilizes the V chord, making it clear that this is not a place of rest and thus negating the need for a dominant seventh over that chord. This allows us to restrict our progression to three-part harmony rather than switching between three- and four-part harmony, or doubling voices as is often done in common-practice progressions.

	Note also that a ~~leading tone~~ occurs between the notes E and F; this allows us to achieve a false resolution onto the Fsus4 chord, or C<sup>4</sup>/F, in our progression by way of voice leading from a chord on E. For this example, I have chosen to use the Orwell Diminished triad over E, which provides a tense sound without sounding nasty. The Fsus4 and E<sup>ow</sup> chords also introduce B♭, which contrasts with the B♮ found in the Gsaj chord, displaying how notes pulled from outside of the ~~original~~ scale can be quite useful in writing harmonies.		Note also that a diatonic semitone occurs between the notes E and F; this allows us to achieve a false resolution onto the Fsus4 chord, or C<sup>4</sup>/F, in our progression by way of voice leading from a chord on E. For this example, I have chosen to use the Orwell Diminished triad over E, which provides a tense sound without sounding nasty. The Fsus4 and E<sup>ow</sup> chords also introduce B♭, which contrasts with the B♮ found in the Gsaj chord, displaying how notes pulled from outside of the base scale can be quite useful in writing harmonies.
	[[File:Isus4 - iiiow - IVsus4 - Vsaj.mp3\|thumb\|The Csus4 - E<sup>ow</sup> - Fsus4 - Gsaj chord progression]]		[[File:Isus4 - iiiow - IVsus4 - Vsaj.mp3\|thumb\|The Csus4 - E<sup>ow</sup> - Fsus4 - Gsaj chord progression]]
	Thus, our four-chord progression is Csus4 - E<sup>ow</sup> - Fsus4 - Gsaj. This series of chords uses a combination of voice leading, tension-and-release paradigms, and circle of fifths movement to provide a dynamic and functional harmonic progression.		Thus, our four-chord progression is Csus4 - E<sup>ow</sup> - Fsus4 - Gsaj. This series of chords uses a combination of voice leading, tension-and-release paradigms, and circle of fifths movement to provide a dynamic and functional harmonic progression.

Unque: Huge notation overhaul.

2025-09-28T18:33:50Z

Huge notation overhaul.

Show changes

Unque: Fixed some formatting, and removed joking comments leftover from when this was a user page

2025-09-23T18:36:16Z

Fixed some formatting, and removed joking comments leftover from when this was a user page

← Older revision		Revision as of 18:36, 23 September 2025
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	\| 3\22		\| 3\22
	\| 163.6		\| 163.6
	\| [[~~11/10\|~~10/9]]		\| [[10/9]]
	\| [[Porcupine]]		\| [[Porcupine]]
	\| C♯, F𝄫		\| C♯, F𝄫
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	\| 19\22		\| 19\22
	\| 1036.3		\| 1036.3
	\| [[~~20/11\|~~9/5]]		\| [[9/5]]
	\| Porcupine		\| Porcupine
	\| C♭, G𝄪		\| C♭, G𝄪
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	{\| class="wikitable sortable"		{\| class="wikitable sortable"
	\|+ style="font-size: 105%;" \|Modes of 5L~~ ~~2s		\|+ style="font-size: 105%;" \|Modes of 5L 2s
	\|-		\|-
	!Gens Up		!Gens Up
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	===5L 7s===		===5L 7s===
	The [[5L 7s]] scale is an extension of 5L~~ ~~2s created by continuing the generator sequence. Because the Circle of Fifths is bidirectional, the seven modes can be extended either by continuing the sequence upwards or downwards; those created by going up the chain are called grave modes, and those extended by going down the chain are called acute modes.		The [[5L 7s]] scale is an extension of 5L 2s created by continuing the generator sequence. Because the Circle of Fifths is bidirectional, the seven modes can be extended either by continuing the sequence upwards or downwards; those created by going up the chain are called grave modes, and those extended by going down the chain are called acute modes.
	{\| class="wikitable sortable"		{\| class="wikitable sortable"
	\|+ style="font-size: 105%;" \|Modes of 5L~~ ~~7s		\|+ style="font-size: 105%;" \|Modes of 5L 7s
	\|-		\|-
	!Gens Up		!Gens Up
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	The [[Nicetone\|3L 2M 2s]] scale is the other type of Diatonic scale represented in 22edo; this one represents the 5-limit shade of Diatonic popularized by musicians and theorists such as Ptolemy and Zarlino. It is generated by alternating intervals 6\22 and 7\22, and as such yields two different forms ("left-hand" and "right-hand") based on which generator comes first and which comes second.		The [[Nicetone\|3L 2M 2s]] scale is the other type of Diatonic scale represented in 22edo; this one represents the 5-limit shade of Diatonic popularized by musicians and theorists such as Ptolemy and Zarlino. It is generated by alternating intervals 6\22 and 7\22, and as such yields two different forms ("left-hand" and "right-hand") based on which generator comes first and which comes second.

	The 5-limit harmony of this scale is much more reminiscent of the familiar harmony used in common-practice music, so popular music translated into this scale will be much more faithful to the harmony of the original piece than it would be using 5L~~ ~~2s.		The 5-limit harmony of this scale is much more reminiscent of the familiar harmony used in common-practice music, so popular music translated into this scale will be much more faithful to the harmony of the original piece than it would be using 5L 2s.

	{\| class="wikitable sortable"		{\| class="wikitable sortable"
	\|+ style="font-size: 105%;" \|Modes of Right-hand 3L~~ ~~2M~~ ~~2s		\|+ style="font-size: 105%;" \|Modes of Right-hand 3L 2M 2s
	\|-		\|-
	!Gens Up		!Gens Up
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	{\| class="wikitable sortable"		{\| class="wikitable sortable"
	\|+ style="font-size: 105%;" \|Modes of Left-hand 3L~~ ~~2M~~ ~~2s		\|+ style="font-size: 105%;" \|Modes of Left-hand 3L 2M 2s
	\|-		\|-
	! Gens Up		! Gens Up
Line 431:		Line 431:

	===5L 2m 3s===		===5L 2m 3s===
	The [[Blackdye\|5L~~ ~~2m~~ ~~3s]] scale functions as an extension to 3L~~ ~~2M~~ ~~2s, created by adding a commatic step into each large step of that Diatonic scale. This provides the scale with three new modes in addition to the seven already present. Due to the commatic step, this scale does not distinguish the left-hand from the right-hand variants.		The [[Blackdye\|5L 2m 3s]] scale functions as an extension to 3L 2M 2s, created by adding a commatic step into each large step of that Diatonic scale. This provides the scale with three new modes in addition to the seven already present. Due to the commatic step, this scale does not distinguish the left-hand from the right-hand variants.

	While there is no singular generator sequence used to create this scale, it can be thought of as two pentatonic scales offset by a neutral second, which is coincidentally the amount by which a sharp or flat alters a note; this makes the scale easy to notate as a pentatonic scale and its sharp/flat counterpart. This splits the modes into five "grave" modes and five "acute" modes, where the grave modes place the root on the flattened pentatonic, and the acute modes place the root on the sharpened one.		While there is no singular generator sequence used to create this scale, it can be thought of as two pentatonic scales offset by a neutral second, which is coincidentally the amount by which a sharp or flat alters a note; this makes the scale easy to notate as a pentatonic scale and its sharp/flat counterpart. This splits the modes into five "grave" modes and five "acute" modes, where the grave modes place the root on the flattened pentatonic, and the acute modes place the root on the sharpened one.
	{\| class="wikitable sortable"		{\| class="wikitable sortable"
	\|+ style="font-size: 105%;" \|Modes of 5L~~ ~~2m~~ ~~3s (Grave)		\|+ style="font-size: 105%;" \|Modes of 5L 2m 3s (Grave)
	\|-		\|-
	!Gens Up		!Gens Up
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	{\| class="wikitable sortable"		{\| class="wikitable sortable"
	\|+ style="font-size: 105%;" \|Modes of 5L~~ ~~2m~~ ~~3s (Acute)		\|+ style="font-size: 105%;" \|Modes of 5L 2m 3s (Acute)
	\|-		\|-
	! Gens Up		! Gens Up
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	\| Contains the Wolf fourth (vF)		\| Contains the Wolf fourth (vF)
	\|}		\|}
	Where disambiguation is needed between the modes of 5L~~ ~~7s and 5L~~ ~~2M~~ ~~2s, the former can be described as "chromatic," and the latter as "blackdye."		Where disambiguation is needed between the modes of 5L 7s and 5L 2M 2s, the former can be described as "chromatic," and the latter as "blackdye."

	===2L 8s===		===2L 8s===
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	Erlich divides four of the five unique rotations into a 2x2 grid, categorized by how many thirds it contains (one third is "static," two is "dynamic,") and which type of third falls on the fourth degree of the scale (major or minor). The brightest mode does not appear to have been considered by Erlich, due to lacking a perfect fifth above the root.		Erlich divides four of the five unique rotations into a 2x2 grid, categorized by how many thirds it contains (one third is "static," two is "dynamic,") and which type of third falls on the fourth degree of the scale (major or minor). The brightest mode does not appear to have been considered by Erlich, due to lacking a perfect fifth above the root.
	{\| class="wikitable sortable"		{\| class="wikitable sortable"
	\|+ style="font-size: 105%;" \|Modes of 2L~~ ~~8s		\|+ style="font-size: 105%;" \|Modes of 2L 8s
	\|-		\|-
	!Gens Up		!Gens Up
Line 562:		Line 562:

	===4L 5s===		===4L 5s===
	The [[4L 5s]] scale is another quite useful scale available in 22edo ~~<s>and a perfect example of 22edo being better than 31</s>; it is~~ closely associated with [[Orwell]] temperament, and as such is best utilized alongside Orwell Chords for functional harmony (see below).		The [[4L 5s]] scale is another quite useful scale available in 22edo, closely associated with [[Orwell]] temperament, and as such is best utilized alongside Orwell Chords for functional harmony (see below).

	{\| class="wikitable sortable"		{\| class="wikitable sortable"
	\|+ style="font-size: 105%;" \|Modes of 4L~~ ~~5s		\|+ style="font-size: 105%;" \|Modes of 4L 5s
	\|-		\|-
	! Gens Up		! Gens Up
Line 956:		Line 956:

	Note also that a leading tone occurs between the notes E and F; this allows us to achieve a false resolution onto the Fsus4 chord, or C<sup>4</sup>/F, in our progression by way of voice leading from a chord on E. For this example, I have chosen to use the Orwell Diminished triad over E, which provides a tense sound without sounding nasty. The Fsus4 and E<sup>ow</sup> chords also introduce B♭, which contrasts with the B♮ found in the Gsaj chord, displaying how notes pulled from outside of the original scale can be quite useful in writing harmonies.		Note also that a leading tone occurs between the notes E and F; this allows us to achieve a false resolution onto the Fsus4 chord, or C<sup>4</sup>/F, in our progression by way of voice leading from a chord on E. For this example, I have chosen to use the Orwell Diminished triad over E, which provides a tense sound without sounding nasty. The Fsus4 and E<sup>ow</sup> chords also introduce B♭, which contrasts with the B♮ found in the Gsaj chord, displaying how notes pulled from outside of the original scale can be quite useful in writing harmonies.
	[[File:Isus4 - iiiow - IVsus4 - Vsaj.mp3\|thumb\|The Csus4 - e<sup>ow</sup> - Fsus4 - Gsaj chord progression]]		[[File:Isus4 - iiiow - IVsus4 - Vsaj.mp3\|thumb\|The Csus4 - E<sup>ow</sup> - Fsus4 - Gsaj chord progression]]
	Thus, our four-chord progression is Csus4 - e<sup>ow</sup> - Fsus4 - Gsaj. This series of chords uses a combination of voice leading, tension-and-release paradigms, and circle of fifths movement to provide a dynamic and functional harmonic progression.		Thus, our four-chord progression is Csus4 - E<sup>ow</sup> - Fsus4 - Gsaj. This series of chords uses a combination of voice leading, tension-and-release paradigms, and circle of fifths movement to provide a dynamic and functional harmonic progression.

	[[Category:Approaches to tuning systems]]		[[Category:Approaches to tuning systems]]

Lériendil: Lériendil moved page User:Unque/22edo Composition Theory to 22edo/Unque's compositional approach

2025-04-15T23:55:28Z

Lériendil moved page User:Unque/22edo Composition Theory to 22edo/Unque's compositional approach

← Older revision	Revision as of 23:55, 15 April 2025
(No difference)

Lériendil: subsumed category

2025-04-14T18:17:32Z

subsumed category

← Older revision		Revision as of 18:17, 14 April 2025
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	Thus, our four-chord progression is Csus4 - e<sup>ow</sup> - Fsus4 - Gsaj. This series of chords uses a combination of voice leading, tension-and-release paradigms, and circle of fifths movement to provide a dynamic and functional harmonic progression.		Thus, our four-chord progression is Csus4 - e<sup>ow</sup> - Fsus4 - Gsaj. This series of chords uses a combination of voice leading, tension-and-release paradigms, and circle of fifths movement to provide a dynamic and functional harmonic progression.

	~~[[Category:Method]]~~
	[[Category:Approaches to tuning systems]]		[[Category:Approaches to tuning systems]]

	== Graphs and Diagrams ==		== Graphs and Diagrams ==
	[[File:22edo Diatonic Chords.png\|frameless]]		[[File:22edo Diatonic Chords.png\|frameless]]

Unque at 22:18, 25 March 2025

2025-03-25T22:18:46Z

← Older revision		Revision as of 22:18, 25 March 2025
Line 319:		Line 319:
	\|}		\|}

			=== 3L 2M 2s ===
	===3L 2M 2s===
	The [[Nicetone\|3L 2M 2s]] scale is the other type of Diatonic scale represented in 22edo; this one represents the 5-limit shade of Diatonic popularized by musicians and theorists such as Ptolemy and Zarlino. It is generated by alternating intervals 6\22 and 7\22, and as such yields two different forms ("left-hand" and "right-hand") based on which generator comes first and which comes second.		The [[Nicetone\|3L 2M 2s]] scale is the other type of Diatonic scale represented in 22edo; this one represents the 5-limit shade of Diatonic popularized by musicians and theorists such as Ptolemy and Zarlino. It is generated by alternating intervals 6\22 and 7\22, and as such yields two different forms ("left-hand" and "right-hand") based on which generator comes first and which comes second.

Unque at 01:20, 28 February 2025

2025-02-28T01:20:48Z

← Older revision		Revision as of 01:20, 28 February 2025
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	[[Category:Method]]		[[Category:Method]]
	[[Category:Approaches to tuning systems]]		[[Category:Approaches to tuning systems]]

			== Graphs and Diagrams ==
			[[File:22edo Diatonic Chords.png\|frameless]]

Unque: Adjusted for enharmonic notes in 2L 8s

2025-02-26T16:05:08Z

Adjusted for enharmonic notes in 2L 8s

← Older revision		Revision as of 16:05, 26 February 2025
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	\|8		\|8
	\| LssssLssss		\| LssssLssss
	\| C - C♯ - E♭ - vE - F - vF♯ - ^G - G♯ - ^A - A♯ - C		\| C - C♯ - E♭ - vE - F - vF♯ - vF𝄪 - vA - ^A - ^C♭ - C
	\|Wolf Minor		\|Wolf Minor
	\| Contains the wolf fifth (^G)		\| Contains the wolf fifth (^G)
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	\|6		\|6
	\| sLssssLsss		\| sLssssLsss
	\| C - vC♯ - E♭ - vE - F - vF♯ - G - G♯ - ^A - A♯ - C		\| C - vC♯ - E♭ - vE - F - vF♯ - ^F♯ - vA - ^A - ^C♭ - C
	\|Dynamic Major		\|Dynamic Major
	\|Dual thirds are subminor and major		\|Dual thirds are subminor and major
Line 545:		Line 545:
	\|4		\|4
	\| ssLssssLss		\| ssLssssLss
	\| C - vC♯ - vE♭ - vE - F - vF♯ - G - ~~vG♯~~ - ^A - A♯ - C		\| C - vC♯ - vE♭ - vE - F - vF♯ - ^F♯ - ^A♭ - ^A - ^C♭ - C
	\| Static Major		\| Static Major
	\|Laterally symmetrical		\|Laterally symmetrical
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	\| 2		\| 2
	\| sssLssssLs		\| sssLssssLs
	\| C - vC♯ - vE♭ - ^E♭ - F - vF♯ - G - ~~vG♯~~ - A - A♯ - C		\| C - vC♯ - vE♭ - ^E♭ - F - vF♯ - ^F♯ - ^A♭ - A - ^C♭ - C
	\|Static Minor		\|Static Minor
	\|Messiaen treated this rotation as the "default"		\|Messiaen treated this rotation as the "default"
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	\|0		\|0
	\|ssssLssssL		\|ssssLssssL
	\|C - vC♯ - vE♭ - ^E♭ - vF - vF♯ - G - ~~vG♯~~ - A - ~~vA♯~~ - C		\|C - vC♯ - vE♭ - ^E♭ - vF - vF♯ - ^F♯ - ^A♭ - A - C♭ - C
	\|Dynamic Minor		\|Dynamic Minor
	\|Dual thirds are minor and supermajor		\|Dual thirds are minor and supermajor

Unque at 16:01, 26 February 2025

2025-02-26T16:01:30Z

← Older revision		Revision as of 16:01, 26 February 2025
Line 533:		Line 533:
	\|8		\|8
	\| LssssLssss		\| LssssLssss
	\| C - C♯ - ^D - D♯ - F - vF♯ - ^G - G♯ - ^A - A♯ - C		\| C - C♯ - E♭ - vE - F - vF♯ - ^G - G♯ - ^A - A♯ - C
	\|Wolf Minor		\|Wolf Minor
	\| Contains the wolf fifth (^G)		\| Contains the wolf fifth (^G)
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	\|6		\|6
	\| sLssssLsss		\| sLssssLsss
	\| C - vC♯ - ^D - D♯ - F - vF♯ - G - G♯ - ^A - A♯ - C		\| C - vC♯ - E♭ - vE - F - vF♯ - G - G♯ - ^A - A♯ - C
	\|Dynamic Major		\|Dynamic Major
	\|Dual thirds are subminor and major		\|Dual thirds are subminor and major
Line 545:		Line 545:
	\|4		\|4
	\| ssLssssLss		\| ssLssssLss
	\| C - vC♯ - D - D♯ - F - vF♯ - G - vG♯ - ^A - A♯ - C		\| C - vC♯ - vE♭ - vE - F - vF♯ - G - vG♯ - ^A - A♯ - C
	\| Static Major		\| Static Major
	\|Laterally symmetrical		\|Laterally symmetrical
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	\| 2		\| 2
	\| sssLssssLs		\| sssLssssLs
	\| C - vC♯ - D - ~~vD♯~~ - F - vF♯ - G - vG♯ - A - A♯ - C		\| C - vC♯ - vE♭ - ^E♭ - F - vF♯ - G - vG♯ - A - A♯ - C
	\|Static Minor		\|Static Minor
	\|Messiaen treated this rotation as the "default"		\|Messiaen treated this rotation as the "default"
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	\|0		\|0
	\|ssssLssssL		\|ssssLssssL
	\|C - vC♯ - D - ~~vD♯~~ - vF - vF♯ - G - vG♯ - A - vA♯ - C		\|C - vC♯ - vE♭ - ^E♭ - vF - vF♯ - G - vG♯ - A - vA♯ - C
	\|Dynamic Minor		\|Dynamic Minor
	\|Dual thirds are minor and supermajor		\|Dual thirds are minor and supermajor