NOT.1:5.2 - Same starting times, different durations

A notation for a sequence of signals lists their starting times in units of a shared pulse. Two sequences both start signals at 0 and 2. In sequence A each signal lasts one unit; in sequence B each lasts two. The intervals are half-open: the signal is active at its start and inactive at its end.

For the question “when should each signal begin?”, the list 0, 2 suffices. For “is a signal active at time 1.5?”, it does not: the answer is no for A and yes for B. The omitted duration now changes the answer.

Try pairs of (start, duration). Sequence A becomes (0, 1), (2, 1); B becomes (0, 2), (2, 2). The reader adds duration to start and compares 1.5 with the resulting interval. This exposes the needed difference with one simple convention. A timeline with interval bars might make repeated overlap questions easier; the pair notation is easier to transmit as plain text. Their comparative value depends on the operation and access.

If a performer’s action determines the duration later, retain that unresolved value and identify which questions remain answerable. Suppose the first signal’s duration is still to be chosen between 1 and 2. Write (0, d) with d in {1, 2}, not yet chosen. In either permitted case the signal is active at 0.5; at 1.5 the answer remains unresolved. Choosing d = 2 makes the latter answer yes. The starting-time question remains answerable throughout. This continuation adds a requirement to preserve an unfinished choice, with no default that prescribes behavior the work has left open. Temporal and embodied notation design in NOT.8 develops such cases beyond this elementary timing example.