How to write microtonal music
Not only does Dodeka write music in a simple and more intuitive manner, but it also offers a more compelling way to write microtonal or xenharmonic music.
While the conventional music notation is limited to a twelve-note division, Dodeka expand the musical resolution by making it possible to divide the span of an an octave into 48 small intervals, or microtones.
To capture and write notes that are outside the Western tuning and its so called twelve-tone equal temperament (12-TET), Dodeka introduces a microtonal mode, where microtones can be represented through four specific angles - 10°, 20° and 30° respectively - to indicate pitch variations.
This way, Dodeka can define four comma values, which represent 48 microtones per octave, or 48-TET. All of that, while still keeping a high degree of readability.
Angles can either be upward or downward to indicate wether the variations in frequency is slightly higher (up) or lower (down) than the initial value of the note.
The below image shows the angle variations for each position of the note in the Dodeka music notation.
What does it look like practically? Below is a transcription of several measures of Jacob's Collier a cappella version of "In the Bleak Midwinter". Even if short, this snippet provides a good example on how Dodeka notation writes microtonal compositions and microtones.
* This short example was created using June Lee's transcription. The song's full transcription is available here.
What is microtonal music?
The Encyclopaedia Britannica defines microtonal music as:
music using tones in intervals that differ from the standard semitones (half steps) of a tuning system or scale.
Similarly, for Wikipedia microtonality is:
the use in music of microtones—intervals smaller than a semitone, also called "microintervals".
To sum up, microtonal music or enharmonic music refers to all sounds and notes that are smaller than the twelve-tone system of most Western music.