ABSTRACT
In much traditional, classical, and contemporary music around the world, one hears a distinctive and characteristic rhythm that appears to be an essential feature of the music, that stands out above the other rhythms, and that repeats throughout most if not the entire piece. Sometimes this essential feature will be merely an isochronous pulsation without any recognizable periodicity. At other times, the music will be characterized by unique periodic patterns. ese special rhythms are generally called timelines.* Timelines should be distinguished from the more general term rhythmic ostinatos. A rhythmic ostinato (from the word obstinate) refers to a rhythm or phrase that is continually repeated during a musical piece. Timelines, on the other hand, are more particular ostinatos that are easily recognized and remembered, play a distinguished role in the music, and also serve the functions of conductor and regulator, by signaling to other musicians the fundamental cyclic structure of the piece. us, timelines act as an orienting device that facilitates musicians to stay together and helps soloists navigate the rhythmic landscape oered by the other instruments. Indeed, Royal Hartigan considers timelines akin to the “heartbeat” of the music.† Wendell Logan refers to the timeline as a life-line.‡ Since timelines repeat over and over in a cyclic manner, they are periodic, and thus it is natural to represent them on a circle.§ Figure 3.1 illustrates two examples of well-known timelines: one is very short consisting of three onsets in a cycle of eight pulses, and the other is relatively long, made
up of 24 onsets in a cycle of 36 pulses. e onsets (or sounded pulses) are shown as black-lled circles and the silent pulses as white-lled circles. It is assumed throughout the text that a rhythm starts at the pulse labeled zero, and that time ows in a clockwise direction.
