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 "

A concultural tradition

In-universe background

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.

Bjeheondian music is mainly based on Netagin music, which is based on two main scales: (1) the equi-heptatonic scale, or (2) haniers, 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.

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 pezůms, or pentachords, with large (2\14) and small (1\14) semiquartal steps that build up a scale are:

1. LLSS Augmented-2-Step Semiquartal Pentachord: pezům Kabavin /kəbɐ'vin/
2. LSLS Major Alternating Semiquartal Pentachord: pezům Lannin /lɐn'nin/ (The modern Lannie mode of the semiquartal scale is made of two pezům Lannin.)
3. LSSL Small-Centered Semiquartal Pentachord: pezům Kesnin /kɛs'nin/
4. SLLS Large-Centered Semiquartal Pentachord: pezům Zierokin /zɪro'kin/ (The modern Zierokie mode begins with a pezům Zierokin.)
5. SLSL Minor Alternating Semiquartal Pentachord: pezům Vašmin /vɐʃ'min/ (The modern Vašmie mode is made of two pezům Vašmin.)
6. SSLL Diminished-2-Step Semiquartal Pentachord: pezům Nobbaxin /nobbɐ'xin/

In practice, usually only the first five are used. The two pezůms 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, if the pezům is in the bottom, may actually be a fifth above the root. This note at the top functions similarly to the ghammāz in Arabic ajnās.

A style that emphasizes pezůms is preferred in folk music (to emphasizing pezůms).

Pentatonic

Buris are mainly used in liturgical chanting.

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 /ɦətʃɐˈma/ (sg. hačame /ɦətʃɐˈmɛ/, lit. facial expression). These are distinct from the traditional haniers.

• 8|0: LLsLsLsLs Cimmaqie /tsimə'ʔɪ/ (Tsimmaïan tsim-ə-EE-ən)
• 7|1: LsLLsLsLs Tavůlie /təvu'lɪ/ (Tavulian)
• 6|2: LsLsLLsLs Lannie /lɐn'nɪ/ (Lannian)
• 5|3: LsLsLsLLs Bonžie /bon'ʒɪ/ (Bonzhian)
• 4|4: LsLsLsLsL Čitupie /tʃity'pɪ/ (Chitupian)
• 3|5: sLLsLsLsL Zierokie /zɪro'kɪ/ (Zierokian)
• 2|6: sLsLLsLsL Vašmie /vɐʃ'mɪ/ (Vashmian)
• 1|7: sLsLsLLsL Pahnačie /pəɦnɐ'tʃɪ/ (Pahnachian)
• 0|8: sLsLsLsLL Qyporie /ʔɨpo'rɪ/ (Iporian)

The Lannie, Zierokin and Vašmin modes are named after the Lannin, Zierokin, and Vašmin pentachords, respectively.

TODO: Does having native mode names make sense?

Use of 28edo

In modern times 28edo is also used, often for its diasem scale with step ratio 4:3:1.