In Hindemith's book The craft of musical composition. Book 1, Theoretical part, he says that (p. 97)
The lower tone of a third or a seventh (in the absence of any better interval) is the root of the chord.
If the chord contains two or more equal intervals, and those are the best intervals, the root of the lower one is the root of the chord.
However, immediately later he states that (p. 101):
Among the chords which have no tritone, there are two of which the interpretation depends on context, and which in consequence have no root, but only a root representative: the augmented triad and the chord composed of two superposed fourths.
Now, if we were to go by the criterions of p.97, wouldn't this mean, for example, the root of the augmented triad is its lowest tone? And therefore it does have a root, contradicting what's stated in p.101?
What is meant by "the interpretation depends on context"? Is it the case that in consideration of the root, one needs to check all possible transpositions (i.e. changing which octave each tone are in) of the tomes in the chord? And if the root determined from one transposition differs from that determined from another, as is the case for the augmented triad, the root of the chord cannot be determined? Or is it meant somewhat another way?