  We study spectral gaps of cellular differentials for finite cyclic coverings
of knot complements. Their asymptotics can be expressed in terms of
irrationality exponents associated with ratios of logarithms of algebraic
numbers determined by the first two Alexander polynomials. From this point of
view it is natural to subdivide all knots into three different types. We show
that examples of all types abound and discuss what happens for twist and torus
knots as well as knots with few crossings.
