User:Inthar/5L 4s: Difference between revisions
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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. | 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 == | == Counterpoint == | ||
Features of | Features of hard-of-basic (basic to superhard) 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 supermajor third, which assists with melodic movement. | # Fortunately, semiquartal has plenty of small steps and relatively dissonant intervals such as the supermajor third, which assists with melodic movement. | ||
# 5L 4s counterpoint is also easier than in mosses such as 5L 3s and 4L 3s which do not have perfect fifths, in that consonance of basic triads is stable under inverting or revoicing. | |||
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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* minor 4-step: 505c, suspended | * minor 4-step: 505c, suspended | ||
** aka perfect fourth | ** aka perfect fourth | ||
* major 4-step: | * major 4-step: 632c, dissonant (tends to resolve up to perfect fifth) | ||
* minor 5-step (semi-)dissonant (can resolve down to perfect fourth) | * minor 5-step: 568c, (semi-)dissonant (can resolve down to perfect fourth) | ||
* major 5-step: | * major 5-step: 695c, consonant | ||
** aka perfect fifth | ** aka perfect fifth | ||
* minor 6-step: 758c, dissonant (can resolve down to perfect fifth or up to moseighth) | * minor 6-step: 758c, dissonant (can resolve down to perfect fifth or up to moseighth) | ||
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* minor 8-step: 1011c, suspended (can resolve down, less tendency to resolve up) | * minor 8-step: 1011c, suspended (can resolve down, less tendency to resolve up) | ||
* major 8-step: 1137c, dissonant (tends to resolve up to octave) | * major 8-step: 1137c, dissonant (tends to resolve up to octave) | ||
* perfect 9-step: | * perfect 9-step: 1200c, octave | ||
Be especially careful with naiadics or semitenths in low registers. | Be especially careful with naiadics or semitenths in low registers. | ||
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==== Unison opening up to 5th ==== | ==== Unison opening up to 5th ==== | ||
==== Unison opening up to 4th ==== | ==== Unison opening up to 4th ==== | ||
==== How to deal with | ==== How to deal with supermajor thirds ==== | ||
===== Stepwise motions ===== | |||
Descending stepwise motion spanning supermajor thirds (major 3-steps) are effective small resting points. ''Ascending'' stepwise motion is less stable unless you can make the context stabilize the supermajor third above the basepoint (e.g. as the tonic, or part of a supermajor triad sonority). | |||
===== Machaut cadences ===== | ===== Machaut cadences ===== | ||
*G^ C > G D, G^ C D^ > G D E^ | *G^ C > G D, G^ C D^ > G D E^ | ||
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* Semiquartal dominant: G B^ D E^ > G C D^/E | * Semiquartal dominant: G B^ D E^ > G C D^/E | ||
== Chords == | |||
=== Triads === | |||
* C Ebv G (Ultraminor triad) | |||
* C Fv G (Supermajor triad) | |||
* C G Bbv (Ultraminor 7th chord) | |||
* C Fbv A (Superaugmented triad) | |||
=== Tetrads === | |||
* C Ebv Fv G | |||
* C Ebv F G | |||
* C Fv G Av | |||
* C Ebv G Av | |||
* C Gbv Bb (Locrian 7th): approximates 5:7:9 in 33edo semiquartal | |||
== Pentachords == | == Pentachords == | ||
Semiquartal enjoys pentachordality in that every mode of it consists of two conjunct or two disjunct pentachords. | Semiquartal enjoys pentachordality in that every mode of it consists of two conjunct or two disjunct pentachords. | ||
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=== Neutralized pentachords (in 19edo and 28edo) === | === Neutralized pentachords (in 19edo and 28edo) === | ||
=== Enharmonic pentachords (in 23edo) === | === Enharmonic pentachords (in 23edo) === | ||
[[Category:Semiquartal]] | |||
[[Category:Method]] | |||
[[Category:Approaches to tuning systems]] | |||