  We find the general five-dimensional, supersymmetric black ring solutions in
M-theory based upon a circular ring, but with arbitrary, fluctuating charge
distributions around the ring. The solutions have three arbitrary charge
distribution functions, but their asymptotic charges and angular momenta only
depend upon the total charges on the ring. The arbitrary density fluctuations
thus represent "hair." By varying the charge distributions one can continuously
change the entropy of these black rings; to our knowledge this is the first
solution in which the entropy depends on classical moduli. We also show that
there is a family of solutions, with two arbitrary functions, for which the
horizon remains rotationally invariant, and yet the complete solution breaks
rotational symmetry. If the horizon area is set to zero then one obtains
families of supertube solutions. We find that our general solutions are
governed by three harmonic functions that may be thought of as classical
excitations of a string. The horizon area provides a natural Lorentz metric on
these excitations, and the constancy of the rotational invariance of the
horizon imposes a set of Virasoro constraints.
