Testing cognitive theories by creating a pattern-based probabilistic algorithm for melody and rhythm in jazz improvisation.

Building on previous work, which suggests that jazz improvisers insert patterns stored in procedural memory, a probabilistic model based on patterns from a corpus of Charlie Parker solos was developed and implemented. In previous analysis, patterns were detected in the corpus in significant proportions; however, the results of a parallel control situation showed minimal patterns. The control improvisation was generated by software based on grammars and contours, coincident with the cognitive position that emphasizes learned rule-based procedures in improvisation, as opposed to stored patterns. The present pattern-based improvisations, using our model, have graphs that coincide significantly with the actual human improvisation. Though briefly described earlier (Norgaard, Montiel, & Spencer, 2013), the current article expands the theoretical foundation and adds methods for evaluating our algorithm using interval distributions and alternate corpora. Specifically, we show that the algorithm is capable of generating improvisations in fiddle and classical styles, demonstrating that the pattern-based algorithm is style independent. Our model shows much promise both for future research in the cognitive underpinnings of musical improvisation as well as for the development of software based on a stylistically appropriate concatenation of actual patterns.Keywords: stochastic matrix, probability, music cognition, pattern-based software, jazz improvisationPerformance of preexisting music and musical improvisation both involve learned movements. However, during musical improvisation, the exact configuration of those movements is determined in the moment. How is this accomplished? What information is stored in the improviser's brain that enables this complex behavior? One theory posits memorized schemas form the basis for the improvised output (Pressing, 1988), while a competing theory emphasizes learned rules (Johnson-Laird, 2002). The current project further explores these questions through the implementation of a computer algorithm for improvisation based on the principle advocated by Pressing. We compare output from our model with the results of a jazz analysis study as well as with the output of a competing model that uses a rule-based algorithm to generate melodies in a jazz style. In addition, we show that our algorithm is capable of generating melodic output in other styles given a corpus in that style.Pressing's (1988) model of the cognitive processes underlying improvisation is still widely cited (Burnard, 2002; Goldman, 2012; Hargreaves, 2012; MacDonald & Wilson, 2005). Pressing divided improvisations into concatenated note groupings. Each grouping is triggered by a creative intention in the form of a mental schema that contains a cognitive image of sound and corresponding motor realization. His theory implies that these mental schemas may derive from a stored library. Therefore, should his theory be accurate, improvisations by artist-level improvisers should contain repeated melodic and rhythmic figures as the improviser repeatedly accesses the same mental schema from the stored library. Importantly, Pressing's model is based on principles gathered from an extensive review of literature from diverse fields. Therefore, his theory is not tied to a particular style of improvisation but is applicable to any novel musical output created in real-time.A competing theory of jazz improvisation emphasizes learned rules (Johnson-Laird, 2002). In support of his theoretical position, Johnson-Laird designed a rule-based algorithm that creates jazz bass lines based on contour, the underlying chord progression, and procedures related to the use of scales, chord tones, and passing tones. According to Johnson-Laird "instead of a list of fragments of rhythms, motifs, and so on, the algorithms described make use of rules" (2002, p. 440). Therefore, according to this view, there is no need for the improviser to store melodic material for later use. …