User:Unque/29edo Counterpoint Treatise: Difference between revisions
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On this page, I attempt to document in full my experience with writing counterpoint using [[29edo]] and the 29-form, with extrapolations that I've made into guidelines of a sort, which others may use as a jumping-off point for their own excursions into writing counterpoint, whether in 29edo itself or in other systems where these ideas or extrapolations therefrom may apply. These guidelines arise in large part from a combination of the writings of [[wikipedia:Johann_Joseph_Fux|Johann Fux]] and [[wikipedia:Marchetto_da_Padova|Marchetto da Padova]], analysis of the works of [[wikipedia:Johann_Sebastian_Bach|J.S. Bach]], and parameters that arose simply from trial and error in my own composition. | On this page, I attempt to document in full my experience with writing counterpoint using [[29edo]] and the 29-form, with extrapolations that I've made into guidelines of a sort, which others may use as a jumping-off point for their own excursions into writing counterpoint, whether in 29edo itself or in other systems where these ideas or extrapolations therefrom may apply. These guidelines arise in large part from a combination of the writings of [[wikipedia:Johann_Joseph_Fux|Johann Fux]] and [[wikipedia:Marchetto_da_Padova|Marchetto da Padova]], analysis of the works of [[wikipedia:Johann_Sebastian_Bach|J.S. Bach]], and parameters that arose simply from trial and error in my own composition. | ||
== Preface on Notation == | == Preface on Notation == | ||
A few notable notational features will be considered for this page. Intervals will be noted using extended diatonic notation (with ♯/♭ representing raising and lowering by a chromatic semitone, and ^/v representing raising or lowering by a diesis). Intervals included in diatonic modes will be noted with their diatonic names (where "major" and "minor" forms of an interval are respectively the wider and narrower interval that fall on a given degree), and intervals outside those modes will be denoted as "super-"/"supra-" and "sub-" forms of the closest diatonic interval. Where necessary, interval qualities may be abbreviated: m for minor, M for major, s for sub-, and S for super-/supra-. EDOstep notation (where n\29 represents n steps of 29edo, not to be confused with the JI interval n/29) may also be used for clarification when extended diatonic notation may provide difficulty to parse. | A few notable notational features will be considered for this page. Intervals will be noted using extended diatonic notation (with ♯/♭ representing raising and lowering by a chromatic semitone, and ^/v representing raising or lowering by a diesis). Intervals included in diatonic modes will be noted with their diatonic names (where "major" and "minor" forms of an interval are respectively the wider and narrower interval that fall on a given degree), and intervals outside those modes will be denoted as "super-"/"supra-" and "sub-" forms of the closest diatonic interval. Where necessary, interval qualities may be abbreviated: m for minor, M for major, s for sub-, and S for super-/supra-. EDOstep notation (where n\29 represents n steps of 29edo, not to be confused with the JI interval n/29) may also be used for clarification when extended diatonic notation may provide difficulty to parse. | ||
Interval equivalences created by 29edo will be considered equivalent here. Where multiple spellings are available in notation, sharps/flats will be prioritized over ups/downs, as it makes clear the movement by chromatic semitones; for instance, C♭ will be favored over vB. However, extended diatonic names will be favored over fifthwise names when possible, as these names are easier to parse when discussing interval sizes; for instance, "subminor third" will be favored over "doubly augmented unison" or "doubly diminished fourth," even if the interval using spellings such as C♯-F♭ or C♭-C♯ | Interval equivalences created by 29edo will be considered equivalent here. Where multiple spellings are available in notation, sharps/flats will be prioritized over ups/downs, as it makes clear the movement by chromatic semitones; for instance, C♭ will be favored over vB. However, extended diatonic names will be favored over fifthwise names when possible, as these names are easier to parse when discussing interval sizes; for instance, "supermajor second" or "subminor third" will be favored over "doubly augmented unison" or "doubly diminished fourth," even if the interval using spellings such as C♯-F♭ or C♭-C♯ | ||
== General Principles == | == General Principles == | ||
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=== Tonics and Resolution === | === Tonics and Resolution === | ||
A phrase should begin and end with all voices on the tonic, or on a perfect consonance with respect to it. At the end of a phrase, the tonic is to be approached from above or below by a conjunction (see Interval Categories). The chromatic semitone is primarily encouraged, but other resolutions are also possible. | A phrase should begin and end with all voices on the tonic, or on a perfect consonance with respect to it, unless employing a specific tonal resolution chord. At the end of a phrase, the tonic is to be approached from above or below by a conjunction (see Interval Categories). The chromatic semitone is primarily encouraged, but other resolutions are also possible. | ||
=== Interval Categories === | === Interval Categories === | ||
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#* Perfect Fourth (12\29) | #* Perfect Fourth (12\29) | ||
# '''Imperfect consonances''' are permitted as melodic steps. Between voices, imperfect consonances may be approached through any means, and as such are encouraged as the main class of interval to use in the middle of phrases. | # '''Imperfect consonances''' are permitted as melodic steps. Between voices, imperfect consonances may be approached through any means, and as such are encouraged as the main class of interval to use in the middle of phrases. | ||
#* Major Second (5\29)<sup>†</sup> | |||
#* Minor third (7\29) | #* Minor third (7\29) | ||
#* Major third (10\29) | #* Major third (10\29) | ||
# '''Cadential consonances''' are permitted as melodic steps, but should be used with reserve. Between voices, cadential consonances may be approached through any means, but they tend to resolve by contrary motion to a perfect consonance. | # '''Cadential consonances''' are permitted as melodic steps, but should be used with reserve. Between voices, cadential consonances may be approached through any means, but they tend to resolve by contrary motion to a perfect consonance. | ||
#* Subminor Third (6\29) | #* Supermajor Second / Subminor Third (6\29)<sup>†</sup> | ||
#* Supraminor Third (8\29) | #* Supraminor Third (8\29) | ||
#* Submajor Third (9\29) | #* Submajor Third (9\29) | ||
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#* Supraminor Second / Chromatic Semitone (3\29) | #* Supraminor Second / Chromatic Semitone (3\29) | ||
#* Submajor Second (4\29) | #* Submajor Second (4\29) | ||
#* Major Second (5\29) | #* Major Second (5\29)<sup>†</sup> | ||
#* Supermajor Second / Subminor Third (6\29)<sup>†</sup> | |||
#'''Dissonances''' are not permitted as melodic steps, and should generally be avoided between any two voices. | #'''Dissonances''' are not permitted as melodic steps, and should generally be avoided between any two voices. | ||
#*Augmented Third (13\29) | #*Augmented Third (13\29) | ||
#*Diminished Fifth (14\29) | #*Diminished Fifth (14\29) | ||
# The '''Diesis''' or '''Superunison''' (1\29) is permitted as a passing tone in melodies. Two voices should never be separated by the interval of a diesis except as a brief transitional position between a unison and another interval. The same guidelines apply to the Suboctave (28\29) or the Superoctave (30\29). | # The '''Diesis''' or '''Superunison''' (1\29) is permitted only as a passing tone in melodies; a voice should strongly avoid movement by a diesis on a strong beat, as the small size can destabilize the tonality. Two voices should never be separated by the interval of a diesis except as a brief transitional position between a unison and another interval. The same guidelines apply to the Suboctave (28\29) or the Superoctave (30\29). | ||
<small><sup>†</sup>Note the overlap between certain categories: the Major Second (5\29) may function either as an imperfect consonance or a conjunction; the Supermajor Second (6\29), or Subminor Third, similarly may function as either a cadential consonance or a conjunction.</small> | |||
=== Contour === | === Contour === | ||
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The voices within a fugue should form a clear hierarchy of range; one voice should remain the lowest, another the highest, and so on for any additional voices. Two adjacent voices may play a unison, but a lower voice may not reach a pitch higher than the voice above it. | The voices within a fugue should form a clear hierarchy of range; one voice should remain the lowest, another the highest, and so on for any additional voices. Two adjacent voices may play a unison, but a lower voice may not reach a pitch higher than the voice above it. | ||
The interval between two adjacent voices generally should | The interval between two adjacent voices generally should avoid exceeding a Supermajor Tenth (40\29) unless absolutely necessary to avoid dissonances or provide melodic coherence within each individual voice. | ||
=== Cadences === | === Cadences === | ||
When resolving at the end of a phrase, cadences should generally involve two or more voices moving by conjunctions in opposite directions. One or more of the voices should land on the tonic pitch, and all others should land on perfect consonances with respect to one another. | When resolving at the end of a phrase, cadences should generally involve two or more voices moving by conjunctions in opposite directions. One or more of the voices should land on the tonic pitch, and all others should land on perfect consonances with respect to one another; where there are three or more voices, specific tonal chords may apply as well. | ||
In 29edo, the intervals between two voices should generally begin on perfect consonances, move towards imperfect consonances, and finally utilize cadential consonances to create tension before resolving. The interordinal intervals (supermajor and subminor thirds and sixths) are extremely tense, and each one either exceeds or falls short of a perfect consonance by two chromatic semitones (a total of 6\29). This creates an extremely clear path to resolution via two types of movement: | In 29edo, the intervals between two voices should generally begin on perfect consonances, move towards imperfect consonances, and finally utilize cadential consonances to create tension before resolving. The interordinal intervals (supermajor and subminor thirds and sixths) are extremely tense, and each one either exceeds or falls short of a perfect consonance by two chromatic semitones (a total of 6\29). This creates an extremely clear path to resolution via two types of movement: | ||
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Due to the 29-form's inherent pull towards 3-limit structures, the diatonic scale is an integral part of its structure. The tonality of a fugue is most intuitively derived from the modes of the diatonic scale; specifically, the major and minor tonality respectively draw from the properties of the major and minor forms of the third degree of that scale. | Due to the 29-form's inherent pull towards 3-limit structures, the diatonic scale is an integral part of its structure. The tonality of a fugue is most intuitively derived from the modes of the diatonic scale; specifically, the major and minor tonality respectively draw from the properties of the major and minor forms of the third degree of that scale. | ||
No matter the tonality, perfect consonances with respect to the root take precedence over all other intervals, and should be the most emphasized intervals in a given melody. Subjects should be written primarily, if not entirely, in the diatonic scale, though the exact mode used depends on the tonality; | No matter the tonality, perfect consonances with respect to the root take precedence over all other intervals, and should be the most emphasized intervals in a given melody. Subjects should be written primarily, if not entirely, in the diatonic scale, though the exact mode used depends on the tonality; exceptions are made for the notes a chromatic semitone above or below the root, in order for the melody to form aforementioned cadences when a countermelody is added. Countermelodies and elaborations on the subject, however, should access additional tones outside of the diatonic scale to create more diverse harmonies and eventually use interordinals as final tensions to create cadences. | ||
=== Major Tonality === | === Major Tonality === | ||
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In the major tonality, expanding cadences are encouraged when resolving to fourths, and contracting cadences are encouraged when resolving to fifths. This motion ensures that the tonic pitch is approached from below rather than from above, which creates a brighter sound more indicative of a major key. | In the major tonality, expanding cadences are encouraged when resolving to fourths, and contracting cadences are encouraged when resolving to fifths. This motion ensures that the tonic pitch is approached from below rather than from above, which creates a brighter sound more indicative of a major key. | ||
When using more than two distinct voices, it is often desirable to use fuller chords for resolutions at the end of a phrase, rather than simply doubling the root or fifth across octaves. The following chords are considered for major resolutions, listed in order of consonance potential: | When using more than two distinct voices, it is often desirable to use fuller chords for resolutions at the end of a phrase, rather than simply doubling the root or fifth across octaves. Ideally, these fuller resolutions should be constructed such that the interval between any two pitches is a perfect or imperfect consonance; . The following chords are considered for major resolutions, listed in order of consonance potential: | ||
* Requiring three or more voices: | * Requiring three or more voices: | ||