My take on the subject is that there are two other important factors to the timbre of an instrument:
– ADSR envelope curve (Attack-Decay-Sustain-Release)
The envelope curve mainly depends on the physical attributes and construction of the instrument, but it can be greatly influenced by the player through articulation (how you attack the sound, what you do during the emission, how you close it), and it has a great impact on timbre perception.
Resonance is the sympathetic vibration of other bodies. We have resonance within the instrument (again, construction and materials) but unsurprisingly there is some mouth and head resonance even when playing the melodica (as it happens with any other wind instrument and with voices). In general, resonance affects volume but, being at different frequencies, it can substantially change the harmonic spectrum thus changing the timbre.
Both factors are, to a certain extent, in the “hands” of the player and would account for what Daren wrote:
– a steady and consistent air flow
– resonance (through body relaxation, different mouth shapes, etc.)
– articulation control (different tongue and key attacks, control during the sound life, control over the closing of the sound)
These two factors clearly influence the harmonic spectrum thus making the use of an oscilloscope somehow limited and less reliable. Actually, being a large part of the timbre influenced by the player, I find it almost impossible to have an “objective” timbre analysis, unless we restrain the context (i.e. one single note mechanically produced), but I guess that wouldn’t tell us much 🙂