User:VectorGraphics/Quaternity musical traditions
In Vector's sci-fi world Quaternity, different alien cultures have developed distinct musical and harmonic traditions, as follows:
Morov
Morov is an astronomy-focused culture of sidessors, a species that calls the TRAPPIST-1 system its home.
This served as an astrological justification for just intonation, and resulted in the construction of a harmonic system based on 5/3, 8/5, 3/2, and 4/3, the ratios by which the orbits of TRAPPIST-1's planets relate to each other (due to the compactness of the system, they were able to determine that Ntiscifer, or Ntishifrr, their home planet, was indeed a planet orbiting the star, as well as how fast it was doing so), and their octave complements 5/4 and 6/5. These octave complements were viewed as the descending intervals 3/5 and 5/8, octave-reduced. The intervals were named after the planets whose ratios they represented, as follows:
| Ratio | WBN | Cents | Name | Orbital ratio | Orbital ratio (IRL planet names) |
|---|---|---|---|---|---|
| 5/3 | major sixth | 884 | Kirrudo | Kirruts-Dofrr | c-d |
| 8/5 | minor sixth | 814 | Barinkirr | Barin-Kirruts | b-c |
| 4/3 | perfect fourth | 498 | Hamennigai | Hamennifrr-Gairon | f-g |
| 3/2 | perfect fifth | 702 | Dontishi | Dofrr-Ntishifrr | d-e |
| 3/5 | minor third | -884 (316) | Dokirruts | Dofrr-Kirruts | d-c |
| 5/8 | major third | -814 (386) | Kirrubar | Kirruts-Barin | c-b |
The scale that is used is based on stacking each of these intervals sequentially, resulting in 7 notes collapsing to 4 scale degrees of 1/1-9/8-3/2-15/8. This creates some new intervals between some of the notes - as a rule, for ascending intervals, the innermost planet is listed first, and for descending intervals, the innermost planet is listed last. All of the following intervals are octave-reduced (note that 5/4 and 8/5 have different names in different contexts):
| Ratio (Octave-reduced) | WBN | Cents (Octave-reduced) | Name | Orbital ratio | Orbital ratio (IRL planet names) |
|---|---|---|---|---|---|
| 15/8 | major seventh | 1088 | Kirruham | Kirruts-Hamennifrr | c-f |
| 16/15 | minor second | 112 | Hamennikirr | Hamennifrr-Kirruts | f-c |
| 9/8 | major second | 204 | Doham | Dofrr-Hamennifrr | d-f |
| 16/9 | minor seventh | 996 | Hamennido | Hamennifrr-Dofrr | f-d |
| 5/4 | major third | 386 | Kirruntishi | Kirruts-Ntishifrr | c-e |
| 8/5 | minor sixth | 814 | Ntishikirr | Ntishifrr-Kirruts | e-c |
Two main modes of the scale were in use: the Ntiscifer mode, starting on the note equivalent to Ntiscifer's orbit, and the Hothifer (Hothifrr) mode, starting on the note equivalent to Hothifer's orbit. Musically, these are equivalent to starting on the first and fifth of the scale (generating 1/1-9/8-3/2-15/8 and 1/1-5/4-4/3-3/2 respectively). The Ntiscifer mode became the default due to generating more consonant intervals including the 4:5:6 harmonic series fragment
As music became more free and expressive due to expanding cultural contact, 7-well temperament (similar to the Western diatonic scale) came into use, with intervals generally about 0c 180c 370c 510c 690c 870c 1060c 1200c (approximations).
Ultimately, due to music theory becoming less associated with the actual just ratios and more with the scales themselves, a 7edo system was chosen,
Ollati
Another culture of sidessors on Ntiscifer.
The pre-Ollati peoples prior to the eruption utilized well temperament systems designed simply to divide the octave rather than approximate JI, though using JI as an aid to tune their instruments. The number of notes in question was 16, because a) early divisions were harmonic series fragments, which used 16 notes, b) 16 more equally spaced notes lined up vaguely with important intervals such as 5/4 and 3/2, and c) the base of their counting system was 16. The regular temperament corresponding to 16edo is named Ntiscifer for this reason.
(WIP)