Introduction
Many studies (Krumhansl & Castellano, 1983; Shepard & Jordan, 1984) have demonstrated that musical schemata in long-term memory influence the way musical events are encoded and memorized. Such cognitive schemata correspond to the knowledge acquired from repeated exposure to musical pieces belonging to a given culture. Indeed, simple exposure to tonal music would be sufficient for a listener to acquire implicit knowledge concerning the regularities of this musical system (Tillmann, Bharucha & Bigand, 2000). Implicit learning allows us to acquire highly complex information without conscious and controlled processing. Listeners generate expectations about what incoming events are likely to be encountered and when they are likely to do so. The way these expectations are more or less fulfilled by the composer contributes to the perception of musical expression (Meyer, 1956; Jackendoff, 1991). One way of generating these expectations consists of varying and developing thematic materials. In Western music, development and variation are usually primed by the exposition of the themes, but they can also prime the exposition of the themes in their literal form. The memory for these related auditory events based on a certain degree of similarity between various aspects of the materials and structure guides listeners' attention and contributes to the cognitive integration of the piece.
According to Gernsbacher (1990), development and variation in music may act in a similar way to language by contributing to the integration of all the sections of a discourse into a whole. In their text comprehension model, Kintsch & Van Dijk (1975, 1978) demonstrated that memory traces of stimuli are achieved by focusing attention on a selection of key elements of the perceived structure. In music, such key elements could correspond to what McAdams (1989) called form-bearing dimensions. They refer to certain categories of auditory attributes such as rhythm, duration, pitch, and timbre to which listeners are sensitive and from which they can distinguish different levels of relations among musical events. It has been pointed out by McAdams & Matzkin (2003) that the most crucial link between two different musical patterns is the degree of similarity (i.e. a theme followed by its variation). Thus, the comprehension of musical form would depend on the perception of invariant cues between musical events. A number of studies have addressed the question of similarity in music (Dowling, 1972; Krumhansl, Sandell & Sergeant, 1987; Pitt & Monahan, 1987; Bartlett & Dowling, 1988; Matzkin, 2001; McAdams & Matzkin, 2003), and demonstrated that listeners are able to extract prominent cues from the musical surface in order to get a coherent representation of the musical structure.
Recent work by Deliège (2001) concerned the implicit memorization of prominent cues from music. She developed the notion of imprint formation to designate the processes involved in music perception and more specifically to describe the perceptual consequence of the insistent use of the same cue in more or less varied forms within a given musical piece. According to her, variations of a given musical cue would not be memorized in all their diversity and complexity. Memorization is based on the simplification and reduction of inputs to integrate them into a network of knowledge. Given this rule of information coding in memory, the concept of imprint implies the retention of critical information about a collection of more or less similar presentations of a given cue. This notion of imprint is based on the model of prototype according to which a number of items possess a set of properties originating from a basic model. The formation of an imprint would largely depend on the features memorized from previous listening. It would be determined by the content of the schematic knowledge in implicit memory. As outlined in Berz (1995), tonal structure is certainly an organizational element that influences the memorization of musical events. Some researchers have argued that the memorization of a simple tonal melody merely involves the elaboration of a mental model in which few cues from the musical surface are needed (cf. Sloboda & Parker, 1985). In other words, for a tonal piece, the automatic activation of musical structure kept in memory would suffice to convey relevant cues for recognition. A number of studies used melodic contour and pitch height as the most prominent cues for the processing of musical information. For instance, Dowling & Fujitani (1981) demonstrated that contour information was relatively easy to encode. Dewitt & Crowder (1986) revealed that contour and intervallic content could be easily retained over time.
With an unconventional musical structure, it seems more difficult for listeners to situate musical information within some kind of previously memorized organizational framework. Without previous knowledge of a new musical structure, more surface features would probably be needed to identify similarities between two musical events. In other words, memorization of atonal musical sequences probably first requires the encoding of musical surface features rather than the internal representations of a learned stylistic norm. Concerning the surface features of atonal music, listeners' abilities to encode and memorize them have been clearly demonstrated (Deliège, 1989, 2001). Moreover, Lerdahl (1989) argued that listeners should be able both to encode surface characteristics of atonal music and to elaborate more abstract representations of its structure. One can hypothesize that surface features would require the processing of sound events, while the elaboration of abstract representations would require the integration of the relation between musical events and the hierarchical structure of the piece.
In a study intended to investigate memorization ability for surface features and the more abstract representation of these features in atonal music, Krumhansl (1991) assessed the effect of pitch change on musically trained listeners' recognition memory for different sequences from a contemporary piece by O. Messiaen. Her goal was to test recognition memory performance with an unfamiliar musical style for which listeners did not possess schematic knowledge. In this study, the second half of the piece was transformed in different ways in order to change the pitch independently of other musical dimensions in the piece. Some transformations were constructed to preserve the melodic contour and the rhythmic framework, whereas others modified the specific coupling between values of pitch, duration, and dynamics. The task consisted of presenting the original first half of the piece followed either by one of the several transformations of materials from the first part (transformed version) or by original excerpts from the first (original old version) or second (original new version) parts of the piece. For each pair of sequences (original plus one of the transformed or old/new original versions), listeners were asked to judge whether or not the latter sequence came from the original part of the piece. The repeated listening effect of the original part of the piece on recognition performance was also investigated. Krumhansl (1991) supposed that (a) if the original old version was accurately recognized, this should indicate that listeners memorized the surface features of music; (b) if the original new version was well recognized it should signify that listeners were able to elaborate and memorize a more abstract representation of surface features in order to generalize them to another part of the piece. Finally, she hypothesized that the recognition performance for the different modifications of the piece's pitch structure should indicate the listener's sensitivity to different kinds of surface regularities. First of all, her findings revealed that repeated exposure to the original first part of the piece had no effect on memory performance, suggesting that the recognition process was not based on memory trace reinforcement, but rather on a rapid comparison between perceived immediate musical cues. The results also clearly showed that listeners both encode and abstract the surface features of the music. Furthermore, transformations preserving the correlation between pitch height and duration of the original versions were highly recognized, whereas those not respecting this relation were not recognized as belonging to the original version. This suggests that the pitch-height/duration relation, and more generally the melodic contour, constitute a salient feature for extracting similarity cues. In order to test the influence of previous musical knowledge on memory recognition processing, Krumhansl (1991) carried out the same task with professional musicians to whom the musical structure of the piece was described. Interestingly, findings revealed that recognition performance was strongly similar to that observed for nonprofessional listeners unfamiliar with the piece's structure. Such results surprisingly reveal that familiarity with the structure of the piece does not change the musical criteria used to judge similarity between musical sequences. More generally, these data demonstrate that listeners possess a long-term memory capacity to encode, maintain, and elaborate abstract representations of surface features within a musical piece, whatever the level of familiarity with its structure.
In the present study, the recognition of perceptual invariance between original and transformed versions from The Angel of Death by Roger Reynolds was studied through implicit memorization of similarity relations. This study specifically concerns the elaboration of implicit musical association between excerpts from an unconventional style of music. We assume that similarity relationships between thematic cells and their transformations create associative links between different sections of the piece. Our aim was to investigate whether these links result in memory priming and refreshing effects.
The specificity of the relation between themes and variations in The Angel of Death is that some variations in the electroacoustic part of the piece consist of a systematic segmentation of original thematic materials according to a particular transformation algorithm. The composer has created two kinds of algorithms: SPIRLZ and SPLITZ. Both transformations, illustrated in Figure 1, keep the nature of original sound material but impose different changes on their temporal structure. Memory for similarity cues between themes and their electroacoustic transformations certainly requires the ability to abstract common characteristics shared between them.
In the SPIRLZ algorithm, the material is considered as a series of contiguous segments. The algorithm rearranges these segments in time, starting somewhere in the middle and then progressively concatenating segments taken alternately from before and after those already used. It performs this operation in several cycles and the size of the segments and the starting segment can be changed to create an accelerating or decelerating impression. The composer conceives of the operation as a sort of spiraling through the original material.
The SPLITZ algorithm is a transformation that also consists of a segmentation of the original excerpt. The even- and odd-numbered segments are separated spatially (into right and left channels in our case) and the odd ones are played in chronological order, while the even ones are played in reverse order. Different amplitude envelopes are also applied to the even and odd segments. The relative durations of the segments are defined according to a number series derived from one of those used in The Angel of Death. This transformation gives the impression of a very irregular sound with many silences from which a multiply reflecting hall-mirror impression can result.
According to the composer, both algorithms cut the original excerpts into constituent segments in order to rearrange them in a particular way that modulates their original structure. This modulation affects the time domain of the musical structure by imposing a new formal idea on the original source. Through such transformations, the composer algorithmically applied fragmenting identities to original excerpts from the thematic materials of the piece, similarly to transformations applied in the making of the computer layer of the piece at a later stage in the compositional process.
With such materials, the question is whether the similarity of the materials in the themes and variations creates implicit knowledge about their relationships. First, we wondered if listening to the original themes could facilitate recognition of their algorithmically transformed versions. To test this question, we first carried out a priming experiment. Two other experiments were conducted in order to test the refreshing effect (re-exposition) of the transformed versions on their subsequent recognition.
