  The distance of an operation from being associative can be "measured" by its
associative spectrum, an appropriate sequence of positive integers. Associative
spectra were introduced in a publication by B. Cs\'ak\'any and T. Waldhauser in
2000 for binary operations (see arXiv:1102.2124). We generalize this concept to
p-ary operations, interpret associative spectra in terms of equational
theories, and use this interpretation to find a characterization of fine
spectra, to construct polynomial associative spectra, and to show that there
are continuously many different spectra. Furthermore, an equivalent
representation of bracketings is studied.
