22edo/Unque's compositional approach: Difference between revisions
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== Scales == | == Scales == | ||
=== 5L 2s === | === 5L 2s === | ||
The [[5L 2s]] scale is one of two types of Diatonic scales represented in 22edo, and represents the shade of Diatonic popularized by the Greek mathematician Archytas, which uses the 2.3.7 subgroup of Just Intonation. It is generated by the Circle of Fifths just as in common practice tunings, though the perfect fifth of 22edo is significantly sharper than any tuning attested in common practice, which makes the scale and its chords behave somewhat differently from standard Diatonic functionality. Notably, suspended chords feel less tense and more restful, while typical tertian triads tend to sound tenser and more energetic; this is the opposite of how these chords behave in Meantone tunings, and as such Western music translated into 22edo's Diatonic may sound strange if it is not adjusted to account for its unique properties. | The [[5L 2s]] scale is one of two types of Diatonic scales represented in 22edo, and represents the shade of Diatonic popularized by the Greek mathematician Archytas, which uses the 2.3.7 subgroup of Just Intonation. It is generated by the Circle of Fifths just as in common practice tunings, though the perfect fifth of 22edo is significantly sharper than any tuning attested in common practice, which makes the scale and its chords behave somewhat differently from standard Diatonic functionality. Notably, suspended chords feel less tense and more restful, while typical tertian triads tend to sound tenser and more energetic; this is the opposite of how these chords behave in Meantone tunings, and as such Western music translated into 22edo's Diatonic may sound strange if it is not adjusted to account for its unique properties. | ||
{| class="wikitable" | {| class="wikitable" | ||
|+ style="font-size: 105%;" | Modes of 5L 2s | |+ style="font-size: 105%;" | Modes of 5L 2s | ||
|- | |- | ||
! UDP | ! UDP | ||
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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" | {| class="wikitable" | ||
|+ style="font-size: 105%;" | Modes of 5L 7s | |+ style="font-size: 105%;" | Modes of 5L 7s | ||
|- | |- | ||
! UDP | ! UDP | ||
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=== 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. | ||
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" | {| class="wikitable" | ||
|+ style="font-size: 105%;" | Modes of Right-hand 3L 2M 2s | |+ style="font-size: 105%;" | Modes of Right-hand 3L 2M 2s | ||
|- | |- | ||
! UDP | ! UDP | ||
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{| class="wikitable" | {| class="wikitable" | ||
|+ style="font-size: 105%;" | Modes of Left-hand 3L 2M 2s | |+ style="font-size: 105%;" | Modes of Left-hand 3L 2M 2s | ||
|- | |- | ||
! UDP | ! UDP | ||
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|} | |} | ||
When disambiguation is needed between the modes of 5L 2s and 3L 2M 2s, the former can be described as "Superpyth" or "Archy," while the latter can be called "Nicetone" or "Zarlino" | When disambiguation is needed between the modes of 5L 2s and 3L 2M 2s, the former can be described as "Superpyth" or "Archy," while the latter can be called "Nicetone" or "Zarlino" | ||
=== 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" | {| class="wikitable" | ||
|+ style="font-size: 105%;" | Modes of 5L 2m 3s (Grave) | |+ style="font-size: 105%;" | Modes of 5L 2m 3s (Grave) | ||
|- | |- | ||
! UDP | ! UDP | ||
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{| class="wikitable" | {| class="wikitable" | ||
|+ style="font-size: 105%;" | Modes of 5L 2m 3s (Acute) | |+ style="font-size: 105%;" | Modes of 5L 2m 3s (Acute) | ||
|- | |- | ||
! UDP | ! UDP | ||
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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 === | ||
The [[2L 8s]] scale is another characteristic scale of 22edo, which was discovered independently by [[Paul Erlich]], [[Gene Ward Smith]], and [[wikipedia:Olivier_Messiaen|Olivier Messiaen]] (though the latter theorist documented [https://ianring.com/musictheory/scales/3055 the scale's analog in 12edo] rather than in 22). | The [[2L 8s]] scale is another characteristic scale of 22edo, which was discovered independently by [[Paul Erlich]], [[Gene Ward Smith]], and [[wikipedia:Olivier_Messiaen|Olivier Messiaen]] (though the latter theorist documented [https://ianring.com/musictheory/scales/3055 the scale's analog in 12edo] rather than in 22). | ||
This scale is a mode of limited transposition, which means that it has some amount of rotational symmetry. In this case, the semioctave is the axis of symmetry, and transposing a mode up by 11 steps of 22edo (or 6 steps of 12edo in the case of Messiaen's works) yields the same set of pitches as the mode on which you started. | This scale is a mode of limited transposition, which means that it has some amount of rotational symmetry. In this case, the semioctave is the axis of symmetry, and transposing a mode up by 11 steps of 22edo (or 6 steps of 12edo in the case of Messiaen's works) yields the same set of pitches as the mode on which you started. | ||
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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" | {| class="wikitable" | ||
|+ style="font-size: 105%;" | Modes of 2L 8s | |+ style="font-size: 105%;" | Modes of 2L 8s | ||
|- | |- | ||
! UDP | ! UDP | ||
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=== 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 <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). | ||
{| class="wikitable" | {| class="wikitable" | ||
|+ style="font-size: 105%;" | Modes of 4L 5s | |+ style="font-size: 105%;" | Modes of 4L 5s | ||
|- | |- | ||
! UDP | ! UDP | ||