Cognitive representation of “musical fractals”: Processing hierarchy and recursion in the auditory domain

Abstract

The human ability to process hierarchical structures has been a longstanding research topic. However, the nature of the cognitive machinery underlying this faculty remains controversial. Recursion, the ability to embed structures within structures of the same kind, has been proposed as a key component of our ability to parse and generate complex hierarchies. Here, we investigated the cognitive representation of both recursive and iterative processes in the auditory domain. The experiment used a two-alternative forced-choice paradigm: participants were exposed to three-step processes in which pure-tone sequences were built either through recursive or iterative processes, and had to choose the correct completion. Foils were constructed according to generative processes that did not match the previous steps. Both musicians and non-musicians were able to represent recursion in the auditory domain, although musicians performed better. We also observed that general ‘musical’ aptitudes played a role in both recursion and iteration, although the influence of musical training was somehow independent from melodic memory. Moreover, unlike iteration, recursion in audition was well correlated with its non-auditory (recursive) analogues in the visual and action sequencing domains. These results suggest that the cognitive machinery involved in establishing recursive representations is domain-general, even though this machinery requires access to information resulting from domain-specific processes.

Recursion in action: An fMRI study on the generation of new hierarchical levels in motor sequences

“…These recursive principles can be described with a recursive notation α à α [αα], as in Lindenmayer systems (Lindenmayer, 1968). This kind of rewrite rules have been used to describe visual (Martins, Martins, & Fitch, 2016), melodic (Martins, Gingras, Puig-Waldmueller, & Fitch, 2017), and rhythmic fractals (Geambasu, Ravignani, & Levelt, 2016). To control for general task-effects involving visual-motor planning, working memory and movement sequence execution, our approach included a third rule-Repetition-in which complete motor sequences had to be repeated, without necessity to add any items or levels.…”

The right inferior frontal gyrus processes nested non-local dependencies in music

“…Previous studies on processing hierarchical structures in music argued that humans can differentiate between auditory tone sequences generated according to a hierarchical recursive rule and an iterative rule 12 , show priming effects in integrating harmonic contextual information 13 , 14 , and discriminate between grammatical and ungrammatical transformations in serialist music 15 , 16 . Moreover, harmonically irregular chords within a chord sequence were shown to elicit an early right anterior negativity (ERAN) in event-related brain potentials (ERPs) (using EEG 11 , 17 , 18 and MEG for the magnetic equivalent 19 ), which can already be observed in infants 20 , and in a musical scale previously unheard by participants 21 .…”

Language Evolution in Biolinguistics from a Multi-Factor Perspective

“…Martins and his colleagues have shown that recursion is available in the visuo-spatial domain [23] and that its use does not require language resources. Later, they [24] further study musical signals of recursion reflected in musicians and non-musicians in the auditory domain, which manifests recursion can be processed in the non-linguistic auditory domain, but that the capacity to form recursive representations strongly correlates with the same ability in the visual and action sequencing domains. In the evolutionary period, only human is a perfect specie to successively compete the whole process.…”