This article shows that specific properties of long-distance phonotactic patterns derived from consonantal harmony patterns (Hansson 2001, Rose and Walker 2004) follow from a learner that generalizes only on the basis of the order of sounds, not the distance between them. The proposed learner is simple, efficient, and provably correct, and does not require an a priori notion of tier or projection (contra the model in Hayes and Wilson 2008); nor does it rely on the additional structure provided by Optimality Theory grammars (Prince and Smolensky 1993, 2004) or grammars in the principles-and-parameters framework (Chomsky 1981, Dresher and Kaye 1990, Gibson and Wexler 1994). Not only does the noncounting nature of nonlocal dependencies automatically follow from the way the learner generalizes, it also explains the absence of blocking patterns from the typology. Finally, the learner lends support to the idea that long-distance phonotactic patterns are phenomenologically distinct from spreading patterns, contra the hypothesis of Strict Locality (Gafos 1999, et seq.).