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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 parahard semiquartal 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).
# 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 naiadic, 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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** 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 semisixth, naiadic, ultramajor 3rd
** aka supermajor 3rd
* minor 4-step: 505c, suspended
* minor 4-step: 505c, suspended
** aka perfect fourth
** aka perfect fourth
* major 4-step: 633c, dissonant (tends to resolve up to perfect fifth)
* 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: 693c, consonant
* 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: 1200, octave
* 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 naiadics ====
==== How to deal with supermajor thirds ====
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.
===== 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^
*A^ D > G^ D^, A^ D E^ > G^ D^ F
*A^ D > G^ D^, A^ D E^ > G^ D^ F


===== Naiadic to semifourth =====
===== Supermajor to semifourth =====


=== Parallel moseighths and mosthirds ===
=== 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
* Semiquartal dominant: G B^ D E^ > G C D^/E
* Semiquartal dominant: G B^ D E^ > G C D^/E


== Melodic approaches: A concultural tradition ==
== Chords ==
=== In-universe background ===
=== Triads ===
Modern Bjeheond (''bay-HUND'') is a small subtropical continent (about the size of Australia). Two Bjeheondian languages function as working languages: Tergetian, a language in the Lakovic family which was originally spoken in the continent Talma to the north, and Literary Netagin, a language isolate based on triconsonantal roots. The two languages are thought to have influenced each other pre-historically, before Proto-Tergetians settled in Talma. The two main countries are the Republic of Bjeheond, a former colony of the Tergetian Empire, and Tumhan, the homeland of the Netagin people. Tergetian and (vernacular varieties of) Netagin are both widely spoken.
* C Ebv G (Ultraminor triad)
 
* C Fv G (Supermajor triad)
Bjeheondian music is mainly based on Netagin music, which is based on two main scales: (1) the equi-heptatonic scale, or (2) ''hanier''s, which are scales similar to the semiquartal scale, the nine-note scale LLSLSLSLS which is an extension of the familiar pentatonic scale. This section mainly deals with the use of the semiquartal scale in Netagin music. Netagin music is usually taught to foreigners based on [[14edo]], and modern produced Netagin music use this tuning, as well as other semiquartal edos.
* C G Bbv (Ultraminor 7th chord)
 
* C Fbv A (Superaugmented triad)
Liturgical chanting is not fixed to a particular tuning and may use traditional microtonal inflections or fine-tuned intervals.
 
A Netagin ''hanier'' /hɐ'nɪɾ/ (literally 'stepping') consists of a nine-note scale plus a choice of which subsets to emphasize, either a set of two ''pezům'' /pɛ'zum/ (pentachords, lit. 'set of five') or a framework based on a ''buri'' /by'ɾi/ (lit. 'sprint'), a pentatonic subset. Different styles encourage different subset use.
 
=== Pentachordal ===
In theory, the six possible ''pezům''s, or pentachords, with large (2\14) and small (1\14) steps that build up a scale are:
# ''pezům Qykabavin'' /ʔɨkəbɐ'vin/: LLSS
# ''pezům Lannin'' /lɐn'nin/: LSLS (The modern ''Lannie'' mode of the semiquartal scale is made of two ''pezům Lannin''.)
# ''pezům Qahdiebin'' /ʔəɦdɪ'bin/: LSSL
# ''pezům Zierokin'' /zɪro'kin/: SLLS (The modern ''Zierokie'' mode begins with a ''pezům Zierokin''.)
# ''pezům Vašmin'' /vɐʃ'min/: SLSL (The modern ''Vašmie'' mode is made of two ''pezům Vašmin''.)
# ''pezům Nobbaxin'' /nobbɐ'xin/: SSLL
In practice, usually only the first five are used. The two ''pezům''s may be disjunct (separated by a major second), or conjunct (either spanning a minor seventh above the root or the major second above the root).
 
The top note of a ''pezům'' functions similarly to the ''ghammāz'' in Arabic ''ajnās''.
 
A style that emphasizes ''pezům''s is preferred in folk music (to emphasizing ''pezům''s).
 
=== Pentatonic ===
=== Mode names ===
Semiquartal modal harmony is a more modern construct and is a staple of modern Netagin popular music, such as rock, metal and electronic music. (Music imported from Tergetian culture was originally not based on mosses or modes, but on JI; but some modern theories developed in Bjeheond have emphasized various mosses).
 
Modes of the 9-note scale are called ''hačama'' (sg. ''hačame'', lit. facial expression). These are distinct from the traditional ''hanier''s.


* 8|0: LLsLsLsLs ''Cimmaqie'' (Tsimmaïan ''tsim-ə-EE-ən'')
=== Tetrads ===
* 7|1: LsLLsLsLs ''Tavůlie'' (Tavulian)
* C Ebv Fv G
* 6|2: LsLsLLsLs ''Lannie'' (Lannian)
* C Ebv F G
* 5|3: LsLsLsLLs ''Bonžie'' (Bonzhian)
* C Fv G Av
* 4|4: LsLsLsLsL ''Čitupie'' (Chitupian)
* C Ebv G Av
* 3|5: sLLsLsLsL ''Zierokie'' (Zierokian)
* C Gbv Bb (Locrian 7th): approximates 5:7:9 in 33edo semiquartal
* 2|6: sLsLLsLsL ''Vašmie'' (Vashmian)
== Pentachords ==
* 1|7: sLsLsLLsL ''Pahnačie'' (Pahnachian)
Semiquartal enjoys pentachordality in that every mode of it consists of two conjunct or two disjunct pentachords.
* 0|8: sLsLsLsLL ''Qyporie'' (Iporian)
=== 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 "


One can think of 5L 4s modes as being built from two pentachords (division of the perfect fourth into four intervals) plus a whole tone. The possible pentachords are LsLs, sLLs, and sLsL. (In this fictional culture, these pentachords are called ''Lannin'', ''Zierokin'', and ''Vašmin'', respectively, and is part of a larger system of pentachords based around the semifourth.)
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.


TODO: Does having native mode names make sense?
=== Neutralized pentachords (in 19edo and 28edo) ===
=== Enharmonic pentachords (in 23edo) ===
[[Category:Semiquartal]]
[[Category:Method]]
[[Category:Approaches to tuning systems]]
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