Just to support the approach that the human singing voice is to be regarded as a musical instrument, I found a scientific paper about the voice as an example of the 'physics of musical instruments' (University of Regensburg).
http://www.physik.uni-regensburg.de/forschung/schwarz/Mechanik/MenschlicheStimme.pdf
Unfortunately, it's all in German, but I'll translate the introduction:
"The instrument of the voice is composed of three main components: an energy reservoir (the lungs), an oscillator (the vocal chords) and a resonating space."

Generally, I think the discussion got quite interesting, it's getting more philosophical so that the main goal is not to find a clear, final definition and "fix" it, but to get into a hermeneutic circle, in which you arrive at the same point of discussion again and again after a while, but on a slightly higher level of insight ;-)