Is the dominant tone of a major scale halfway in frequency between the tonic and octave?
If so is this why it functions as it does? ... because it's sounds less dissonant to the tonic?
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Yes, that is true†. For instance,
I don't think however that this can satisfyingly explain why a dominant acts, well, dominant.
†At least in an analytic sense. As Dave remarks, our ears actually perceive pitch rather logarithmically than linearly, and on a logarithmic scale the Ⅴ is further that half-way between the Ⅰ and its octave.
In one way you could say that a perfect fifth is halfway between root and octave. The relationship in frequency is 3:2, which is equivalent to 1.5:1. At first glance this looks like halfway. This is a very simple and consonant interval. But it doesn't quite hold. Two perfect fifths is not an octave, but a ninth! The true halfway interval is the tritone/augmented fourth/diminished fifth as two of them stacked equal an octave. Mathematically, in equal temperament the relationship of a tritone is 2^(1/2):1, or approximately 1.415:1 . Here you already see that by taking the square of it you get 2, which is the frequency relationship of an octave. No, it's not that beautiful sounding, at least not in western culture. It is what it is.
There is a sense in which the equal tempered (ET) augmented 4th or diminished 5th is the "middle" of the octave. Note how on a piano keyboard if you move up 6 semitones, and then move up 6 more, you'll get to the key that is an octave above your starting point. This has to do with the fact that we perceive pitch differences logarithmically. In a perceptual sense, the relationship between A2 and D#2 is the same as the relationship between D#2 and A3 (in equal temperament), while the the interval from A2 to E2 is perceptually distinct from the interval between E2 and A3.