User:Unque/29edo Counterpoint Treatise: Difference between revisions
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'''Note: This page is currently under construction, and will be subject to major expansion in the near future. Come back soon!''' | '''Note: This page is currently under construction, and will be subject to major expansion in the near future. Come back soon!''' | ||
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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. | 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♯ | ||
== General Principles == | == General Principles == | ||
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Note also that all four types of interordinal intervals have at least one type of resolution available. As such, the tension between two voices can be determined plainly by the type of cadence and the quality of the resolution, and conversely, the resolution can be determined plainly by the type of cadence and the quality of the tension. | Note also that all four types of interordinal intervals have at least one type of resolution available. As such, the tension between two voices can be determined plainly by the type of cadence and the quality of the resolution, and conversely, the resolution can be determined plainly by the type of cadence and the quality of the tension. | ||
{| class="wikitable" | {| class="wikitable" | ||
|+Determining | |+Determining cadential intervals for known resolutions | ||
!Cadence Type | !Cadence Type | ||
!Unison | !Unison | ||
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|} | |} | ||
{| class="wikitable" | {| class="wikitable" | ||
|+Determining resolutions for known | |+Determining resolutions for known cadential intervals | ||
!Cadence Type | !Cadence Type | ||
!Subminor Third | !Subminor Third | ||
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** 1 - P4 - P5 - M6 | ** 1 - P4 - P5 - M6 | ||
** 1 - M2 - P5 - M6 | ** 1 - M2 - P5 - M6 | ||
[[File:3-voice Contracting Cadence.png|thumb|An example of a three-voice cadence. Notice how the lower two voices create | [[File:3-voice Contracting Cadence.png|thumb|An example of a three-voice cadence. Notice how the lower two voices create an expanding cadence into the perfect fourth, while the highest voice moves in parallel with the middle voice.]] | ||
Inversions of these chords may apply; for instance, M3 - P5 - P8 is considered to have the same consonance potential as 1 - M3 - P5. It should be noted, however, that the highest and lowest voice will be the most prominent in a given chord, and it is thus encouraged that those voices play the root or fifth of the key in resolutions when possible. | Inversions of these chords may apply; for instance, M3 - P5 - P8 is considered to have the same consonance potential as 1 - M3 - P5. It should be noted, however, that the highest and lowest voice will be the most prominent in a given chord, and it is thus encouraged that those voices play the root or fifth of the key in resolutions when possible. | ||
Tensions towards these resolutions can be made by combining types of expanding and contracting cadences; for instance, the chord 1 - M3 - P5 may be approached by a tension | Tensions towards these resolutions can be made by combining types of expanding and contracting cadences; for instance, the chord 1 - M3 - P5 may be approached by a tension such as SM7 - m3 - sm6, where each voice in the tension differs from its resolution by one chroma. | ||
Finally, and perhaps most importantly, resolutions with lower consonance potential should be avoided as the final resolution of the piece, but are encouraged to be employed at the end of a phrase before a transition to another section. | Finally, and perhaps most importantly, resolutions with lower consonance potential should be avoided as the final resolution of the piece, but are encouraged to be employed at the end of a phrase before a transition to another section. | ||
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==== Minor Modes ==== | ==== Minor Modes ==== | ||
Three diatonic modes contain minor triads over the root: Dorian, Aeolian, and Phrygian. Just like with the major modes, each of these modes has its own distinct sound that can provide different pros and cons for writing | Three diatonic modes contain minor triads over the root: Dorian, Aeolian, and Phrygian. Just like with the major modes, each of these modes has its own distinct sound that can provide different pros and cons for writing fugue subjects. | ||
The Dorian mode's major sixth degree is exceptionally useful as a lead into the diminished octave / submajor seventh, being four steps away rather than the awkward seven-step lurch that would occur in the other modes. The diminished octave is one of the most important types of leading intervals into the root, because it is included in four of the seven perfect types of cadences. This feature alone makes Dorian one of the most desirable minor modes for counterpoint writing, since the other modes must either employ a minor third step size, add more non-diatonic intervals to the subject to bypass this step size, or find another method of resolution. | The Dorian mode's major sixth degree is exceptionally useful as a lead into the diminished octave / submajor seventh, being four steps away rather than the awkward seven-step lurch that would occur in the other modes. The diminished octave is one of the most important types of leading intervals into the root, because it is included in four of the seven perfect types of cadences. This feature alone makes Dorian one of the most desirable minor modes for counterpoint writing, since the other modes must either employ a minor third step size, add more non-diatonic intervals to the subject to bypass this step size, or find another method of resolution. | ||