A matemática das figuras musicais: os conceitos de razão e proporção na compreensão da leitura das figuras musicais por licenciandos em música - Wurmli, Ana Cristina Maia (Universidade Estadual de Ponta Grossa (UEPG), 2026)
Musical figures are fundamental to musical notation, as they ensure the correct reading of scores and precise rhythmic execution. This research starts from the following problem: how can understanding these figures compromise both the reading of scores and rhythmic precision in musical performance, and to what extent can mathematical concepts contribute to this understanding? Thus, the overall objective was to analyze the contributions of the mathematical concepts of Ratio and Proportion to the understanding of the subdivisions and proportions of musical figures applied to the score in a group of first-year students in the Music degree program at the State University of Ponta Grossa/Pr. .As a theoretical reference, Piaget's Theory of Equilibration (1976) guided our study on how the subjects of this research construct and reconstruct the knowledge they have acquired. This research is qualitative in nature, descriptive and interpretive, adopting the design of two experiments by Stanley and Campbell (1979), which use pre-tests and post-tests as tools to identify variables in group studies. Data collection was carried out using a semi-structured questionnaire for the pre-test. The group then participated in a workshop that addressed mathematical and musical concepts, after which they took the post-test, which consisted of a questionnaire similar to the pre-test. The analysis of the research data followed three main stages: first, for the pre-test, MAXQDA software was used to profile the participants. The same tool was used in the second stage of analysis to compare the responses on music theory in the pre- and post-tests, which helped us to assess the individual performance of each participant. Next, Grounded Theory (GT) was applied in the third stage to analyze the post-test essay responses, allowing for a deeper understanding of the participants' perceptions of the workshop content and activities. Based on Piaget's concept of awareness, an analysis was conducted to verify whether there were any changes capable of altering the musicians' understanding of musical figures. The relevance of this research lies in its ability to use the mathematical concepts of ratio and proportion to aid in the understanding of musical subdivisions and proportions. By adopting an interdisciplinary perspective, the study not only offers new possibilities for music teaching, but also proves that a practical and well-structured approach is capable of overcoming theoretical difficulties, promoting students' musical development and appreciation.
Keywords: música e matemática; educação musical; figuras musicais; razão e proporção