User:Inthar/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.

Counterpoint

Features of parahard semiquartal counterpoint:

1. 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).
2. Fortunately, semiquartal has plenty of small steps and relatively dissonant intervals such as the naiadic, 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 semisixth, naiadic, ultramajor 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

How to deal with naiadics

Let's be honest, I'm no Zhea and I think naiadics are straight-up dissonances. This dissonance is, however, a useful property since these are relatively easy to resolve.

Machaut cadences

• G^ C > G D, G^ C D^ > G D E^
• A^ D > G^ D^, A^ D E^ > G^ D^ F

Other motions

• Major to semifourth: D G^ B^ > D^ G C
• Semiquartal dominant: G B^ D E^ > G C D^/E

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 on top for strength. For a Locrian feel add a minor 5-step (600c in 14edo, 568.421c in 19edo, 626.087c in 23edo) instead.