Some ancient texts I ran into once long ago asserted that a minimum of about 8 cycles was necessary, with pure tones electrically produced, for most people to discern a pitch for a sound. Embedded in a melody, or as part of a chord, a shorter sound may be detected as "present" and the expected pitch will be supplied by the standard "awesome brainpower" of the average listener.

For musical instruments, it's incredibly difficult to produce a short sound that starts - continues - and ends at a single pitch. The usual presence of many harmonic overtones also confuddles the issue. The human listener, being not constrained to judge what actually is present may hear what is not (that awesome brain power again).

An "exact" answer would be extremely difficult to produce without rigorous specification of the instrument(s), weather, terrain, enemy forces and their disposition, troops at hand, reserves available, ammunition load, reliablilty of resupply channels, and whether you feel lucky. Then the answer would only be good for the few microseconds until the situation changes, and somebody would still argue with you.

John