Search Results (2)

Deciphering the structural hierarchy of musical compositions is indispensable for a range of music analysis applications, encompassing feature extraction, data compression, interpretation, and visualization. In this paper, we introduce a quantitative model grounded in fractal theory to evaluate the significance of individual notes within a musical piece. To analyze the quantized note importance, we adopt a rhythm-based approach and propose a series of detection operators informed by fundamental rhythmic combinations. Employing the Mamba model, we carry out recursive detection operations that offer a hierarchic understanding of musical structures. By organizing the composition into a tree data structure, we achieve an ordered layer traversal that highlights the music piece’s multi-dimensional features. Musical compositions often exhibit intrinsic symmetry in their temporal organization, manifested through repetition, variation, and self-similar patterns across scales. Among these symmetry properties, fractality stands out as a prominent characteristic, reflecting recursive structures both rhythmically and melodically. Our model effectively captures this property, providing insights into the fractal-like regularities within music. It also proves effective in musical phrase boundary detection tasks, enhancing the clarity and visualization of musical information. The findings illustrate the model’s potential to advance the quantitative analysis of music hierarchy, promoting novel methodologies in musicological research. Full article

Nature has inspired music since the dawn of humankind and has contributed to the creation and development of music as an art form. However, attempts to use the science of nature (i.e., quantitative ecology) to inform music as a broader art-science system is comparatively underdeveloped. In this paper an approach from biodiversity assessments is borrowed to quantify structural diversity in music scores. The approach is analogous in its nature and considers notations with distinct pitches and duration as equivalents of species in ecosystems, measures within a score as equivalents of ecosystems, and the sum of measures (i.e., the entire score) as a landscape in which ecosystems are embedded. Structural diversity can be calculated at the level of measures (“alpha diversity”) and the entire score (“gamma diversity”). An additional metric can be derived that quantifies the structural differentiation between measures in a score (“beta diversity”). The approach is demonstrated using music scores that vary in complexity. The method seems particularly suitable for hypothesis testing to objectively identify many of the intricate phenomena in music. For instance, questions related to the variability within and between musical genres or among individual composers can be addressed. Another potential application is an assessment of ontogenetic structural variability in the works of composers during their lifetime. Such information can then be contrasted with other cultural, psychological, and historical variables, among others. This study shows the opportunities that music and ecology offer for interdisciplinary research to broaden our knowledge of complex systems of people and nature. Full article