Two issues concerning tonal hierarchies: comment on Castellano, Bharucha, and Krumhansl.

First, because tonal hierarchies exist in the music of long-established traditions, we may assume that they confer certain processing advantages. Such hierarchies capitalize on certain properties of the pitch memory system that do not require a tonal setting for demonstration. Furthermore, they facilitate the generation of hierarchical representations of sequential patterns of pitches, and such representations enable considerable parsimony of encoding. Second, the listener's establishment of a tonal hierarchy involves a process of key attribution. This process draws not only on the identities of the notes presented but also draws on their orderings. Certain sequential grouping factors are involved here that can also be shown to exist outside a tonal setting. We are therefore dealing with an elaborate bootstrapping operation, through which both a key and a sequential representation are arrived at by the listener.