The following series of note durations are the basis for my series of compositions called Lines. I have intentionally excluded the use of time signatures in all of these works because of the multiple subdivisions that can be implied throughout when using each of these single-bar phrases (3/2, 6/4, 12/8, 24/16, etc…).
Single-bar duration sets can be described by using the aligning row and column. For example, 12 x 3 describes twelve eighth-notes grouped in three or 16 x 4 is sixteen dotted eighth-notes grouped in four. The below example represents the grid view of these duration line sets.
Duration lines are used compositionally to create polyrhythmic dissonance/consonance and can be used mathematically to build structure.