Asymmetry in scales enhances learning of new musical structures

Convergent evolution in a large cross-cultural database of musical scales

Scales, sets of discrete pitches that form the basis of melodies, are thought to be one of the most universal hallmarks of music. But we know relatively little about cross-cultural diversity of scales or how they evolved. To remedy this, we assemble a cross-cultural database (Database of Musical Scales: DaMuSc) of scale data, collected over the past century by various ethnomusicologists. Statistical analyses of the data highlight that certain intervals (e.g., the octave, fifth, second) are used frequently across cultures. Despite some diversity among scales, it is the similarities across societies which are most striking: step intervals are restricted to 100-400 cents; most scales are found close to equidistant 5- and 7-note scales. We discuss potential mechanisms of variation and selection in the evolution of scales, and how the assembled data may be used to examine the root causes of convergent evolution.

The effects of rhythmic structure on tapping accuracy

Prior investigations of simple rhythms in familiar time signatures have shown the importance of several mechanisms; notably, those related to metricization and grouping. But there has been limited study of complex rhythms, including those in unfamiliar time signatures, such as are found outside mainstream Western music. Here, we investigate how the structures of 91 rhythms with nonisochronous onsets (mostly complex, several in unfamiliar time signatures) influence the accuracy, velocity, and timing of taps made by participants attempting to synchronize with these onsets. The onsets were piano-tone cues sounded at a well-formed subset of isochronous cymbal pulses; the latter occurring every 234 ms. We modelled tapping at both the rhythm level and the pulse level; the latter provides insight into how rhythmic structure makes some cues easier to tap and why incorrect (uncued) taps may occur. In our models, we use a wide variety of quantifications of rhythmic features, several of which are novel and many of which are indicative of underlying mechanisms, strategies, or heuristics. The results show that, for these tricky rhythms, taps are disrupted by unfamiliar period lengths and are guided by crude encodings of each rhythm: the density of rhythmic cues, their circular mean and variance, and recognizing common small patterns and the approximate positions of groups of cues. These lossy encodings are often counterproductive for discriminating between cued and uncued pulses and are quite different to mechanisms-such as metricization and emphasizing group boundaries-thought to guide tapping behaviours in learned and familiar rhythms.

Asymmetry in scales enhances learning of new musical structures

Despite the remarkable variability music displays across cultures, certain recurrent musical features motivate the hypothesis that fundamental cognitive principles constrain the way music is produced. One such feature concerns the structure of musical scales. The vast majority of musical cultures use scales that are not uniformly symmetric-that is, scales that contain notes spread unevenly across the octave. Here we present evidence that the structure of musical scales has a substantial impact on how listeners learn new musical systems. Three experiments were conducted to test the hypothesis that nonuniformity facilitates the processing of melodies. Novel melodic stimuli were composed based on artificial grammars using scales with different levels of symmetry. Experiment 1 tested the acquisition of tonal hierarchies and melodic regularities on three different 12-tone equal-tempered scales using a finite-state grammar. Experiments 2 and 3 used more flexible Markov-chain grammars and were designed to generalize the effect to 14-tone and 16-tone equal-tempered scales. The results showed that performance was significantly enhanced by scale structures that specified the tonal space by providing unique intervallic relations between notes. These results suggest that the learning of novel musical systems is modulated by the symmetry of scales, which in turn may explain the prevalence of nonuniform scales across musical cultures.