Preliminary Experiments on Human Sensitivity to Rhythmic Structure in a Grammar with Recursive Self-Similarity

Processing of hierarchical structures has been proposed as a uniquely human ability, a hallmark of the linguistic system that distinguishes human language from animal communication systems (Hauser et al., 2002; Martins, 2012). Recursion is often considered the pinnacle of human-specific hierarchical structures (Hauser et al., 2002). Artificial Grammar Learning experiments have shown that adult participants are able to learn the context-free grammar AnBn, whose generation requires hierarchical rules, even without the need for semantic information (Lai and Poletiek, 2013). Parsing and generalizing grammars like AnBn requires detection that a structure, e.g., AB, is embedded between elements of another structure, e.g., A…B. Other species have not been shown unequivocally to be able to learn on the basis of the center-embedding principle required of AnBn (rather than using other strategies, Corballis, 2007; van Heijningen et al., 2009; Beckers et al., 2012; Poletiek et al., 2015; Ravignani et al., 2015), which is taken as evidence that processing of recursion is a human-specific capacity. Yet to what extent learning of an AnBn grammar can be taken as evidence for processing recursive information at all is debated. Some researchers argue that human participants could in fact use simpler strategies, such as counting and matching the number of As and Bs in a test sequence (Hochmann et al., 2008; Zimmerer et al., 2011), while others argue that despite different strategies, the same core operations are nonetheless necessary (Fitch and Friederici, 2012; Fitch, 2014). Saddy (2009) proposed that a more suitable grammar for the investigation of recursive processing may be Lindenmayer grammars, or L-systems. Uriagereka et al. (2013) have proposed that these grammars are suitable for between-species comparative work because they generate utterances that can be infinitely long and produce a “rhythm” when recognized. L-systems were first proposed by Lindenmayer to describe algae cell growth (Lindenmayer, 1968; Lindenmayer and Rozenberg, 1972) and have since been used to describe and recognize different plant structures (Samal et al., 1994). L-systems have rewrite rules that occur in parallel and have no terminal symbol, indicating that they can produce infinite sequences (Figure ​(Figure1A).1A). Because of their hierarchical structure and recursive properties, they are an interesting grammar to use in testing recursive processing. In her dissertation, Shirley (2014) began to explore the learnability of Fibonacci grammars, a subgroup of L-systems, that at each iteration produce sequences with lengths corresponding to Fibonacci numbers. She found that after a 3-min training with a Fibonacci grammar composed of syllables bi and ba, participants were able to correctly accept grammatical 10-s-long structures, and correctly reject ungrammatical ones. However, how participants processed the stimuli in Shirley's task is not clear yet. A possible rhythm-based strategy may have been used by participants to recognize a pattern in sounds generated by recursive branching, using rhythmic structure, i.e., how durational events are grouped and perceived hierarchically based on their relative accentuation. When presented with sequences of acoustic events occurring at constant time intervals (i.e., isochronous, as in Shirley, 2014), humans tend to group these events. Grouping often occurs when events are differentially accented, that is, marked by differing pitch or intensity (e.g., strong-weak-weak, Hay and Diehl, 2007). Figure 1 A derivation of the target Fibonacci grammar at the first four iterations and at the final 23rd iteration used to generate the exposure and test stimuli (A), the rewrite rules of the grammar (B), the makeup of the two foil grammars (C), and an overview ... The detection of a specific rhythmic pattern might be the mechanism participants draw upon to detect recursive structures such as those tested here. Syllables in Shirley (2014) differed by their vowel quality, with possibly some non-systematic variation in fundamental frequency and intensity. If detection strategies based on rhythmic features were used to learn Shirley's grammars, participant tested with percussion sounds (enhancing the recursive rhythmical structure of the stimuli) instead of speech syllables should show similarly high or even better performance, as the non-temporal rhythmic cues (intensity or pitch accentuation) would be enhanced, while violations in interstimulus intervals would disrupt the rhythmic detection strategy and hence grammar recognition (Shirley, 2014). Can a complex pattern, recursively and hierarchically organized according to an L-system, be learned on the basis of a rhythmical strategy? We tested this hypothesis by enhancing the rhythmic quality of the sequences by using drum sounds differing in pitch and intensity, instead of syllables. This work thus constitutes the first study on rhythm perception using L-systems1. We conducted two experiments (Figure ​(Figure1D),1D), each with two conditions (two types of foil grammars) to evaluate the learnability of the L-system grammars. Between our two experiments, we also varied instructions, to further explore whether the method of presenting the exposure stimuli had an effect on learning ability. Based on previous work by Saddy (2009) and Shirley (2014) we expected that participants would pick up on the rhythmic nature of the structures, and be able to discriminate grammatical from ungrammatical strings. Our results indicate that for the majority of our participants, rhythm alone may not be enough to learn this type of grammar; musical background, age, instruction, and the specific types of foil grammars may all be contributing factors.