User:Inthar/5L 4s: Difference between revisions
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Features of parahard semiquartal counterpoint: | Features of parahard semiquartal counterpoint: | ||
# The main difficulty is that melodic motions and timings are very unlike what we're used to in heptatonic counterpoint (stepwise motion doesn't end up where we expect it to). | # The main difficulty is that melodic motions and timings are very unlike what we're used to in heptatonic counterpoint (stepwise motion doesn't end up where we expect it to). | ||
# Fortunately, semiquartal has plenty of small steps and relatively dissonant intervals such as the | # Fortunately, semiquartal has plenty of small steps and relatively dissonant intervals such as the supermajor third, which assists with melodic movement. | ||
The notation used is conventional meantone circle-of-fifths notation plus ^/v (the small step of parahard semiquartal, 1\19 in 19edo and 1\24 in 24edo), which satisfies B^ = Cv. A semifourth can be written C-D^ or C-Ebv. | The notation used is conventional meantone circle-of-fifths notation plus ^/v (the small step of parahard semiquartal, 1\19 in 19edo and 1\24 in 24edo), which satisfies B^ = Cv. A semifourth can be written C-D^ or C-Ebv. | ||
=== Intervals === | === Intervals === | ||
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** aka minor 3rd | ** aka minor 3rd | ||
* major 3-step: 442c, dissonant (can resolve down to mosthird or up to perfect fourth) | * major 3-step: 442c, dissonant (can resolve down to mosthird or up to perfect fourth) | ||
** aka | ** aka supermajor 3rd | ||
* minor 4-step: 505c, suspended | * minor 4-step: 505c, suspended | ||
** aka perfect fourth | ** aka perfect fourth | ||
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==== Unison opening up to 4th ==== | ==== Unison opening up to 4th ==== | ||
==== How to deal with naiadics ==== | ==== How to deal with naiadics ==== | ||
===== Machaut cadences ===== | ===== Machaut cadences ===== | ||
*G^ C > G D, G^ C D^ > G D E^ | *G^ C > G D, G^ C D^ > G D E^ | ||
*A^ D > G^ D^, A^ D E^ > G^ D^ F | *A^ D > G^ D^, A^ D E^ > G^ D^ F | ||
===== | ===== Supermajor to semifourth ===== | ||
=== Parallel | === Parallel perfect 7-steps and perfect 2-steps === | ||
7-steps work best for parallel motion within the octave. Parallel 2-steps should be voiced as tenths (11-steps) or wider voicings. | |||
=== Other motions === | === Other motions === | ||
* Major to semifourth: D G^ B^ > D^ G C | * Major to semifourth: D G^ B^ > D^ G C | ||
Revision as of 19:06, 28 May 2022
This page describes my approaches to the semiquartal (5L4s) mos or generator framework, firstly a contrapuntal approach and secondly based on a fictional tradition inspired by world musics such as maqam.
Counterpoint
Features of parahard semiquartal counterpoint:
- The main difficulty is that melodic motions and timings are very unlike what we're used to in heptatonic counterpoint (stepwise motion doesn't end up where we expect it to).
- Fortunately, semiquartal has plenty of small steps and relatively dissonant intervals such as the supermajor third, which assists with melodic movement.
The notation used is conventional meantone circle-of-fifths notation plus ^/v (the small step of parahard semiquartal, 1\19 in 19edo and 1\24 in 24edo), which satisfies B^ = Cv. A semifourth can be written C-D^ or C-Ebv.
Intervals
These are all the intervals that occur in semiquartal. Cent values are in 19edo.
- minor 1-step: 63c, dissonant (tends to resolve to unison)
- major 1-step: 189c, suspended (can resolve down or up)
- perfect 2-step: 253c, consonant
- aka semifourth, ultraminor 3rd
- augmented 2-step: 379c, consonant
- aka major 3rd
- minor 3-step: 316c, consonant
- aka minor 3rd
- major 3-step: 442c, dissonant (can resolve down to mosthird or up to perfect fourth)
- aka supermajor 3rd
- minor 4-step: 505c, suspended
- aka perfect fourth
- major 4-step: 633c, dissonant (tends to resolve up to perfect fifth)
- minor 5-step (semi-)dissonant (can resolve down to perfect fourth)
- major 5-step: 693c, consonant
- aka perfect fifth
- minor 6-step: 758c, dissonant (can resolve down to perfect fifth or up to moseighth)
- aka semitenth, ultraminor 6th
- major 6-step: 884c, consonant
- aka major 6th
- minor 7-step: 821c, consonant
- aka minor 6th
- major 7-step: 947c, consonant
- aka semitwelfth, harmonic 7th
- minor 8-step: 1011c, suspended (can resolve down, less tendency to resolve up)
- major 8-step: 1137c, dissonant (tends to resolve up to octave)
- perfect 9-step: 1200, octave
Be especially careful with naiadics or semitenths in low registers.
Contrary motion
Unison opening up to 5th
Unison opening up to 4th
How to deal with naiadics
Machaut cadences
- G^ C > G D, G^ C D^ > G D E^
- A^ D > G^ D^, A^ D E^ > G^ D^ F
Supermajor to semifourth
Parallel perfect 7-steps and perfect 2-steps
7-steps work best for parallel motion within the octave. Parallel 2-steps should be voiced as tenths (11-steps) or wider voicings.
Other motions
- Major to semifourth: D G^ B^ > D^ G C
- Semiquartal dominant: G B^ D E^ > G C D^/E
Pentachords
Semiquartal enjoys pentachordality in that every mode of it consists of two conjunct or two disjunct pentachords.
2-step pentachords
- LLSS Aug-2-Step Semiquartal Pentachord
- LSLS Major Alternating "
- SLLS Large-Centered "
- LSSL Small-Centered "
- SLSL Minor Alternating "
- SSLL Dim-2-Step "
Add a fifth (major 5-step; 685.714c in 14edo, 694.737c in 19edo, 678.261c in 23edo) on top for strength. For a Locrian feel add a minor or diminished 5-step (600c in 14edo, 568.421c in 19edo, 626.087c in 23edo but 573.913c might be better) instead.