When intelligibilities of paired speech bands do not behave the way they are supposed to.

Two rectangular 1/3-octave passbands were derived from different spectral regions of everyday sentences, with the intelligibility of one band approximately twice the others. Both passbands were then filtered to produce a series of narrower rectangular passbands. Each of the original 1/3-octave passbands in turn served as the fixed bandwidth "pedestal" and was paired with each of the series of narrower passbands of the other band. Remarkably, dual band intelligibilities were the same, regardless of which band served as pedestal, so the summed bandwidths determined intelligibility: The summed intelligibilities were irrelevant. Implications of this paradoxical "summed bandwidth rule" are discussed.