The workings of a new composition: SKOLION for 6 horns in 13-limit just intonation.
This sketch starts with muted horns playing a concert F chord (written C): root as 2nd harmonic plus 3rd harmonic, 5th harmonic, 7th harmonic and 11th harmonic. This 11th harmonic becomes the 14th harmonic of a new root, the ratio 13:7. the original chord is then repeated with an 8th harmonic rather than a 7th harmonic. This 8th harmonic (written C) becomes the 11th harmonic of a new root, the ratio 16:11. Chords change in the same way throughout the excerpt. Different unmuted horn parts take turns in playing short melodies. Each section and melody is successively longer than the previous.
The recording is a bit scratchy, as it is a homespun one.
Here is the first segment in notation.
The colours help to identify the position of notes in the chord, relative to a root (or fundamental in a harmonic series). Light blue shows 3-limit intervals, such as the 3rd harmonic or 9th harmonic (perfect 5ths, 12ths and major 2nds and 9ths in chords); red shows 5-limit intervals such as the 5th harmonic (major 3rds and 10ths in chords); dark blue shows 7-limit intervals such as the 7th harmonic (minor 7ths in chords); orange shows 11-limit intervals such as the 11th harmonic (neutral 4ths and 11ths in chords); purple shows 13-limit intervals such as the 13th harmonic (neutral 6ths and 13ths in chords). [These colours are the ones Robin Hayward uses in his Tuning Vine http://www.tuningvine.com.]