We propose a technique for exploring the abelian complexity of recurrent infinite words, focusing particularly on infinite words associated with Parry numbers. Using that technique, we give an affirmative answer to the open question posed by Richomme, Saari and Zamboni, whether the abelian complexity of the Tribonacci word attains each value in {4, 5, 6} infinitely many times. (c) 2012 Elsevier B.V. All rights reserved.