Functional harmony is an integral part of many repertoires in the Western musical practices, including both diatonic and extended tonality. In the latter context, music-theoretical accounts suggest that the three octatonic equivalence classes (OECs) consisting of pitch-classes related by stacked minor-third intervals may be associated with tonic (T), dominant (D), and subdominant (S) functions. Whether this theoretical description of music is also relevant to the perception of music has not yet been tested empirically. In this study, 100 participants familiar with Western repertoires were presented with jazz chord progressions containing chord substitutions. When each stimulus had been played, participants predicted how many more chords they would have expected to hear before the progression could reach a plausible conclusion. We computed the similarity of responses for pairs of stimuli containing different harmonic substitutions and modeled such similarity values based on different measures of harmonic relatedness between substitutions. Data show that the OEC membership of substitutions strongly predicts the similarity of participants' completion ratings. Bayesian mixed-effects modeling of similarity values further showed a categorical distinction between D and S as functional categories, on one hand, and T, on the other hand. The data also appear to reflect the prevalent influence of rock and pop repertoires on the participants, encouraging further research into the influence of stylistic diversity and musical expertise. Overall, results contribute to the characterization of listeners' implicit knowledge of the principles of harmonic structure in extended tonality and support the relevance of OECs not only as descriptors of extended-tonal compositional practices but also parsimonious predictors of perceived functionality.