(Originais Teachy 2024) - Question Hard of Arts

Consider a symphony composed in the classical period, where there is a clear structure of movements and a sophisticated use of sonata form. During the development of this symphony, the composer employs highly complex counterpoint, standing out in the use of canons and fugue. The symphony is performed by a common orchestra of that period, composed of string, woodwind, brass, and percussion instruments. The movement in question begins with an exposition of a main theme, followed by a development section that presents variations and interjections of other melodic and harmonic themes. In an interdisciplinary Mathematics and Physics class, a teacher proposes a study of the vibratory movement of the orchestra instruments' strings and their relationship with music theory, focusing on the phenomenon of resonance and its harmonic frequencies. The teacher asks the students to analyze the vibration pattern of a string fixed at both ends and determine the fundamental frequency (first harmonic) of the sound produced, taking into account the linear density of the string and the tension to which it is subjected. From the understanding of the concept of resonance, the question proposed is: How can the understanding of the resonance phenomenon and the calculation of harmonic frequencies enrich the musical analysis of the development of this symphony, particularly in the identification and understanding of the composer's use of canons and fugue?