> 2. The fact that we see big "bumps" in the frequency spectrum at
> specific frequency ratios is a necessary consequence of the acoustics of
> the human vocal apparatus. Any sound-making "tube" will generate
> overtones, at the fifth and the octave in particular. This only shows
> that the human voice must abide by the laws of acoustics, just as any
> sound-making apparatus does.
This gets it just about right. I would add only that it's also possible that people *prefer* to hear intervals that coincide with the natural harmonic intervals (fifth, fourth, third, sixth etc.) simply because they're more subjectively pleasing. To the best of my knowledge most musical scales world-wide seem to be built on (sometimes extended from) these intervals, though the human voice and many other instruments are capable of continuous variation in pitch and are not physically constrained to discrete pitches defined by the natural intervals (as are, say, organ pipes and horns).
The problem with the Neuroscience people's article is that they're unaware of the history. If I'm decoding their rather opaque prose correctly, they appear to believe that the twelve-part division of the octave is somehow given and primary, and then cultures "select" subsets of these to make their musical scales.
This is exactly backwards. The natural intervals come first, then pentatonic seems to be next, then the diatonic scales and modes (seven notes per octave, the white keys of the piano), then non-tempered "ficta" (the black keys of the piano, but unequally spaced in pitch between the neighboring white keys), and finally -- and only in Western music in the last couple of centuries -- the familiar chromatic scale of twelve equally spaced semitones.
This scale is derived historically from the natural intervals, but it has so far left them behind that it contains almost no acoustically pure intervals -- and on the piano, none at all; even the octaves are out of tune, due to the inharmonicity of thick wires.
Good singers, interestingly, tend to drift back to singing pure intervals both melodically and harmonically, unless there's a piano around to bludgeon them back into the Industrial Revolution standard railway gauge of equal temperament.
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Michael Smith mjs at smithbowen.net http://stopmebeforeivoteagain.org