Information-Theoretic Measures Predict the Human Judgment of Rhythm Complexity

Perceptual Complexity as Normalized Shannon Entropy

Complexity is one of the most important variables in how the brain performs decision making based on esthetic values. Multiple definitions of perceptual complexity have been proposed, with one of the most fruitful being the Normalized Shannon Entropy one. However, the Normalized Shannon Entropy definition has theoretical gaps that we address in this article. Focusing on visual perception, we first address whether normalization fully corrects for the effects of measurement resolution on entropy. The answer is negative, but the remaining effects are minor, and we propose alternate definitions of complexity, correcting this problem. Related to resolution, we discuss the ideal spatial range in the computation of spatial complexity. The results show that this range must be small but not too small. Furthermore, it is suggested by the analysis of this range that perceptual spatial complexity is based solely on translational isometry. Finally, we study how the complexities of distinct visual variables interact. We argue that the complexities of the variables of interest to the brain's visual system may not interact linearly because of interclass correlation. But the interaction would be linear if the brain weighed complexities as in Kempthorne's λ-Bayes-based compromise problem. We finish by listing several experimental tests of these theoretical ideas on complexity.

Singing Ability Assessment: Development and validation of a singing test based on item response theory and a general open-source software environment for singing data

We describe the development of the Singing Ability Assessment (SAA) open-source test environment. The SAA captures and scores different aspects of human singing ability and melodic memory in the context of item response theory. Taking perspectives from both melodic recall and singing accuracy literature, we present results from two online experiments (N = 247; N = 910). On-the-fly audio transcription is produced via a probabilistic algorithm and scored via latent variable approaches. Measures of the ability to sing long notes indicate a three-dimensional principal components analysis solution representing pitch accuracy, pitch volatility and changes in pitch stability (proportion variance explained: 35%; 33%; 32%). For melody singing, a mixed-effects model uses features of melodic structure (e.g., tonality, melody length) to predict overall sung melodic recall performance via a composite score [R2c = .42; R2m = .16]. Additionally, two separate mixed-effects models were constructed to explain performance in singing back melodies in a rhythmic [R2c = .42; R2m = .13] and an arhythmic [R2c = .38; R2m = .11] condition. Results showed that the yielded SAA melodic scores are significantly associated with previously described measures of singing accuracy, the long note singing accuracy measures, demographic variables, and features of participants' hardware setup. Consequently, we release five R packages which facilitate deploying melodic stimuli online and in laboratory contexts, constructing audio production tests, transcribing audio in the R environment, and deploying the test elements and their supporting models. These are published as open-source, easy to access, and flexible to adapt.

A predictive coding approach to modelling the perceived complexity of popular music drum patterns

This study presents a method to estimate the complexity of popular music drum patterns based on a core idea from predictive coding. Specifically, it postulates that the complexity of a drum pattern depends on the quantity of surprisal it causes in the listener. Surprisal, according to predictive coding theory, is a numerical measure that takes large values when the perceiver's internal model of the surrounding world fails to predict the actual stream of sensory data (i.e. when the perception surprises the perceiver), and low values if model predictions and sensory data agree. The proposed new method first approximates a listener's internal model of a popular music drum pattern (using ideas on enculturation and a Bayesian learning process). It then quantifies the listener's surprisal evaluating the discrepancies between the predictions of the internal model and the actual drum pattern. It finally estimates drum pattern complexity from surprisal. The method was optimised and tested using a set of forty popular music drum patterns, for which empirical perceived complexity measurements are available. The new method provided complexity estimates that had a good fit with the empirical measurements ( R 2 = . 852 ). The method was implemented as an R script that can be used to estimate the complexity of popular music drum patterns in the future. Simulations indicate that we can expect the method to predict perceived complexity with a good fit ( R 2 ≥ . 709 ) in 99% of drum pattern sets randomly drawn from the Western popular music repertoire. These results suggest that surprisal indeed captures essential aspects of complexity, and that it may serve as a basis for a general theory of perceived complexity.

Symbolic dynamics of music from Europe and Japan

After a brief introduction to the theory underlying block-entropy and its relation to the dynamics of complex systems as well as certain information theory aspects, we study musical texts coming from two distinct musical traditions, Japanese and Western European, encoded via symbolic dynamics. We quantify their information content, also known as the degree of "non-randomness" which essentially defines the complexity of the text. We analyze the departure of "total randomness" to the constraints underlying the dynamics of the symbol generating process. Following Shannon on his attribution of these constraints as the key factors of the emergence of complexity, we observe that it can be accurately assessed by the texts' block-entropy vs block-length scaling laws.

A Comparison of Human and Computational Melody Prediction Through Familiarity and Expertise

Melody prediction is an important aspect of music listening. The success of prediction, i.e., whether the next note played in a song is the same as the one predicted by the listener, depends on various factors. In the paper, we present two studies, where we assess how music familiarity and music expertise influence melody prediction in human listeners, and, expressed in appropriate data/algorithmic ways, computational models. To gather data on human listeners, we designed a melody prediction user study, where familiarity was controlled by two different music collections, while expertise was assessed by adapting the Music Sophistication Index instrument to Slovenian language. In the second study, we evaluated the melody prediction accuracy of computational melody prediction models. We evaluated two models, the SymCHM and the Implication-Realization model, which differ substantially in how they approach melody prediction. Our results show that both music familiarity and expertise affect the prediction accuracy of human listeners, as well as of computational models.

Time for Change: Implementation of Aksentijevic-Gibson Complexity in Psychology

Given that complexity is critical for psychological processing, it is somewhat surprising that the field was dominated for a long time by probabilistic methods that focus on the quantitative aspects of the source/output. Although the more recent approaches based on the Minimum Description Length principle have produced interesting and useful models of psychological complexity, they have not directly defined the meaning and quantitative unit of complexity measurement. Contrasted to these mathematical approaches are various ad hoc measures based on different aspects of structure, which can work well but suffer from the same problem. The present manuscript is composed of two self-sufficient, yet related sections. In Section 1, we describe a complexity measure for binary strings which satisfies both these conditions (Aksentijevic–Gibson complexity; AG). We test the measure on a number of classic studies employing both short and long strings and draw attention to an important feature—a complexity profile—that could be of interest in modelling the psychological processing of structure as well as analysis of strings of any length. In Section 2 we discuss different factors affecting the complexity of visual form and showcase a 2D generalization of AG complexity. In addition, we provide algorithms in R that compute the AG complexity for binary strings and matrices and demonstrate their effectiveness on examples involving complexity judgments, symmetry perception, perceptual grouping, entropy, and elementary cellular automata. Finally, we enclose a repository of codes, data and stimuli for our example in order to facilitate experimentation and application of the measure in sciences outside psychology.

The brain tracks auditory rhythm predictability independent of selective attention

The brain responds to violations of expected rhythms, due to extraction- and prediction of the temporal structure in auditory input. Yet, it is unknown how probability of rhythm violations affects the overall rhythm predictability. Another unresolved question is whether predictive processes are independent of attention processes. In this study, EEG was recorded while subjects listened to rhythmic sequences. Predictability was manipulated by changing the stimulus-onset-asynchrony (SOA deviants) for given tones in the rhythm. When SOA deviants were inserted rarely, predictability remained high, whereas predictability was lower with more frequent SOA deviants. Dichotic tone-presentation allowed for independent manipulation of attention, as specific tones of the rhythm were presented to separate ears. Attention was manipulated by instructing subjects to attend to tones in one ear only, while keeping the rhythmic structure of tones constant. The analyses of event-related potentials revealed an attenuated N1 for tones when rhythm predictability was high, while the N1 was enhanced by attention to tones. Bayesian statistics revealed no interaction between predictability and attention. A right-lateralization of attention effects, but not predictability effects, suggested potentially different cortical processes. This is the first study to show that probability of rhythm violation influences rhythm predictability, independent of attention.