Tartini Tone: A Geometric Exploration of Music and Mathematics

This GeoGebra example demonstrates the Tartini tone (combination tone) phenomenon by visualizing it through geometric transformations, turning an auditory effect into an observable graphical relationship. The core mathematical concepts involve geometric transformations (rotation), conic sections (ellipse and hyperbola), sequences, and logical reasoning, highlighting the deep connection between musical frequency ratios and geometric structures. Construction details: The Rotate command is applied to the image object imagen4, producing the rotated image imagen4', while the text object texto5 is used for labeling, creating a dynamic visual model. This resource is suitable for upper secondary to university-level interdisciplinary teaching of mathematics and music, enabling exploration of frequency ratios, difference tones, and geometric transformations in artistic contexts, and fostering student interest in the intersection of mathematics and music.