01
List enough events to find the next coincidence
Stream A marks zero, four, eight and twelve. Stream B marks zero, six and twelve. Their first shared positive position is twelve: neither four nor eight belongs to B, and six does not belong to A. Twelve is the least positive common multiple of four and six. This means both streams return to their starting alignment after twelve pulse intervals under the supplied periods and common start. It does not mean that either stream stopped between those coincidences. Each continues to mark its own regularly spaced events throughout the timeline.
02
Choose a boundary convention before counting
Describe one shared cycle using positions from zero inclusive to twelve exclusive. A contributes three events at zero, four and eight; B contributes two at zero and six. There are five stream-specific events but only four distinct onset positions: zero, four, six and eight, because the two events at zero coincide. Position twelve belongs to the next cycle under this convention. Including both zero and twelve as separate cycle starts would double-count the boundary when adjacent cycles are joined. State the interval convention beside the counts so another reader obtains the same totals.
03
Save a reusable repeating-event worksheet
The worksheet records the time unit, each stream’s period, each starting offset, the first shared positive event, the chosen cycle interval and both stream-specific and distinct onset counts. For this example, offsets are zero, periods are four and six, and the shared cycle is twelve pulses. If a stream starts at a different offset, redo the coincidence calculation rather than carrying over the common-start answer. Later musical choices can give the streams different sounds, but those choices remain separate from the event-counting result. Preserve the numbered timeline as the inspectable reference for the arrangement.