Notational Practice of Complex Music

This paper suggests that rhythmic notational practice seen in complex music adhere to the principle that the number of beams/flags of any note is dependent upon the number of iterations per temporal unit. In the first in- stance this may seem obvious, since this principle forms the basis of rational rhythmic notation in music. However, with music featuring nested tuplets of two levels or more, an interesting phenomena begins to occur in which the divisions of a unit become decoupled from the expectations of rhythmic ratios, such as three in the space of the last note of a triplet. Therefore, the intent of this paper is to provide a series of proofs to show that the number of itera- tions per (divisions of) unit take precedence over the expectations of ratios when such mismatches occur.