As any scholar might guess, duration is simply the length of time a sound or tone is sustained. The sonic history of a sound is described in terms of its ADSR envelope , i.e., its attack, decay, sustain and release. Amazingly, if a tone's attack and release are obscured, e.g.,, via using the volume slider on a synth, you may be surprised to discover how difficult it is to identify the timbre being played. The harmonic series is a naturally-occurring phenomenon that is truly an acoustical, as well as a mathematical, marvel. Any time a pitch is sounded, we are actually hearing a composite sound which consists of that particular fundamental pitch plus its many partials or harmonics .
Partials are typically inaudible to the human ear, but they do exist.
The ear identifies the fundamental as the specific pitch in that it is the loudest. An interesting experiment is to highlight partials via sympathetic vibration on a good acoustic piano. Lightly depress a key representing a partial for a given fundamental. Continue to depress that key. Now, firmly play the fundamental note and quickly release it.