ABSTRACT
Syncopation is the spice of rhythm. It adds surprise to an otherwise bland rhythm. We can easily feel when a rhythm has syncopation, but translating that feeling to mathematical terms, my general goal with all musical properties explored in this book is easier said than done. A prerequisite for making progress in this direction is a precise constructive denition. Consider how some dictionaries explain what syncopation is. e New Oxford American Dictionary denes a syncopated rhythm as one in which the “beats or accents” are displaced “so that strong beats become weak beats and vice versa.” From the mathematical point of view, this denition is not very satisfactory because the notions of “strong” and “weak” beats have not been dened. e Oxford Grove Music Online Dictionary denes syncopation as: “e regular shi ing of each beat in a measured pattern by the same amount ahead of or behind its normal position in that pattern.” is denition also lacks mathematical rigor because the notion of “normal” has not been specied. e Harvard Dictionary of Music denes syncopation as “A momentary contradiction of the prevailing meter.”* is denition assumes we know what meter is, but more problematically, how do we interpret the words “momentary” and “prevailing?” As a nal example, consider the lesser-known on-line Virginia Tech Multimedia Music Dictionary; it denes syncopation as the “deliberate upsetting of the meter or pulse of a composition by means of a temporary shi ing of the accent to a weak beat or an o-beat.” Does this mean that if the shi ing of the weak beat is not deliberate, there is no syncopation? Furthermore, what is the dierence between a weak beat and an o-beat?
