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This page describes my approaches to the [[semiquartal]] (5L4s) mos, 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 ==

=== ~~Harmony~~ ===

Features of hard-of-basic (basic to superhard) semiquartal counterpoint:

== ~~Melodic approaches: A concultural tradition~~ ==

# 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).

=== ~~In-universe background~~ ===

# Fortunately, semiquartal has plenty of small steps and relatively dissonant intervals such as the supermajor third, which assists with melodic movement.

~~Modern Bjeheond~~ (''~~bay-HUND~~'') is ~~a small subtropical continent~~ (~~about the size of Australia)~~. ~~Two Bjeheondian languages have official status: Tergetian, a language in the Lakovic family~~. ~~The two main countries are~~ the ~~Republic~~ of ~~Bjeheond,~~ a ~~former colony of the Windermere Empire, and Tumhan, the homeland of the Netagin people~~. ~~Tergetian~~, ~~which was originally spoken on the continent Talma to the north~~, ~~and Netagin, a language isolate, are both widely spoken. The two languages are thought to have influenced each other pre-historically, before Proto-Tergetians settled in Talma.~~

# 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

~~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 221212121 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.

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

~~Liturgical chanting is not fixed to a particular tuning~~ and ~~may use traditional microtonal inflections~~ or ~~fine-tuned intervals~~.

=== 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

A 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'zuəm/ (pentachords, lit. 'set of five') or a framework based on a ''buri'' /by'ɾi/ (lit. 'sprint'), a pentatonic subset where 1\19 is not used as a step. Different styles encourage different subset use.

== Chords ==

== ~~Inthar's mode names~~ ==

=== Triads ===

~~The following names are taken from a fictional semiquartal-based musical culture.~~

* C Ebv G (Ultraminor triad)

* ~~8|0: LLsLsLsLs Tsimmaïan~~ (~~tsim-ə-EE-ən~~)

* C Fv G (Supermajor triad)

* ~~7|1: LsLLsLsLs Tavulian~~

* C G Bbv (Ultraminor 7th chord)

* ~~6|2: LsLsLLsLs Lannian~~

* C Fbv A (Superaugmented triad)

* ~~5|3: LsLsLsLLs Bonzhian~~

* 4|4: LsLsLsLsL Tjatupian (~~chə-TOO-piən~~)

* 3|5: sLLsLsLsL Zierokian

* 2|6: sLsLLsLsL Vashmian

* 1|7: sLsLsLLsL Pahnachian

* 0|8: sLsLsLsLL Iporian

~~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~~.)

=== 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 "

~~TODO: Does having native mode names make sense?~~

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.

=== ~~Pentachordal~~ ===

=== Neutralized pentachords (in 19edo and 28edo) ===

=== ~~Pentatonic~~ ===

=== Enharmonic pentachords (in 23edo) ===

[[Category:Semiquartal]]

[[Category:Method]]

[[Category:Approaches to tuning systems]]

@@ Line 1: / Line 1: @@
-This page describes my approaches to the [[semiquartal]] (5L4s) mos, firstly a contrapuntal approach and secondly based on a fictional tradition inspired by world musics such as maqam.
+{{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.
 == Counterpoint ==
-=== Harmony ===
+Features of hard-of-basic (basic to superhard) semiquartal counterpoint:
-== Melodic approaches: A concultural tradition ==
+# 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).
-=== In-universe background ===
+# Fortunately, semiquartal has plenty of small steps and relatively dissonant intervals such as the supermajor third, which assists with melodic movement.
-Modern Bjeheond (''bay-HUND'') is a small subtropical continent (about the size of Australia). Two Bjeheondian languages have official status: Tergetian, a language in the Lakovic family. The two main countries are the Republic of Bjeheond, a former colony of the Windermere Empire, and Tumhan, the homeland of the Netagin people. Tergetian, which was originally spoken on the continent Talma to the north, and Netagin, a language isolate, are both widely spoken. The two languages are thought to have influenced each other pre-historically, before Proto-Tergetians settled in Talma.
+# 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
-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 221212121 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.
+===== Supermajor to semifourth =====
-Liturgical chanting is not fixed to a particular tuning and may use traditional microtonal inflections or fine-tuned intervals.
+=== Parallel perfect 7-steps and perfect 2-steps ===
+-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
-A 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'zuəm/ (pentachords, lit. 'set of five') or a framework based on a ''buri'' /by'ɾi/ (lit. 'sprint'), a pentatonic subset where 1\19 is not used as a step. Different styles encourage different subset use.
+== Chords ==
-== Inthar's mode names ==
+=== Triads ===
-The following names are taken from a fictional semiquartal-based musical culture.
+* C Ebv G (Ultraminor triad)
-* 8|0: LLsLsLsLs Tsimmaïan (tsim-ə-EE-ən)
+* C Fv G (Supermajor triad)
-* 7|1: LsLLsLsLs Tavulian
+* C G Bbv (Ultraminor 7th chord)
-* 6|2: LsLsLLsLs Lannian
+* C Fbv A (Superaugmented triad)
-* 5|3: LsLsLsLLs Bonzhian
-* 4|4: LsLsLsLsL Tjatupian (chə-TOO-piən)
-* 3|5: sLLsLsLsL Zierokian
-* 2|6: sLsLLsLsL Vashmian
-* 1|7: sLsLsLLsL Pahnachian
-* 0|8: sLsLsLsLL Iporian
-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.)
+=== 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 "
-TODO: Does having native mode names make sense?
+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.
-=== Pentachordal ===
+=== Neutralized pentachords (in 19edo and 28edo) ===
-=== Pentatonic ===
+=== Enharmonic pentachords (in 23edo) ===
+[[Category:Semiquartal]]
+[[Category:Method]]
+[[Category:Approaches to tuning systems]]