User:Inthar/5L 4s: Difference between revisions
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{{breadcrumb|5L 4s}} | |||
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, | # 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 === | ||
| Line 21: | Line 23: | ||
* 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) | ||
| Line 35: | Line 37: | ||
* 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. | ||
| Line 42: | Line 44: | ||
==== 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^ | ||
| Line 60: | Line 65: | ||
* C Fv G (Supermajor triad) | * C Fv G (Supermajor triad) | ||
* C G Bbv (Ultraminor 7th chord) | * C G Bbv (Ultraminor 7th chord) | ||
* C Fbv A (Superaugmented triad) | |||
=== Tetrads === | === Tetrads === | ||
* C Ebv Fv G | * C Ebv Fv G | ||
| Line 80: | Line 87: | ||
=== 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]] | |||
Latest revision as of 22:16, 31 January 2025
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 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).
- 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.
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: 632c, dissonant (tends to resolve up to perfect fifth)
- minor 5-step: 568c, (semi-)dissonant (can resolve down to perfect fourth)
- major 5-step: 695c, 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: 1200c, 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 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
- 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
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
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.