Scale, Pitch and Tonality: Mathematical Structures in Music

① This GeoGebra example dynamically illustrates the concepts of musical scale, pitch, and tonality, transforming auditory interval relationships into visual geometric and algebraic structures. ② Core mathematical concepts include ratios, fractions, sequences, and geometric construction, such as using orthogonal lines and midpoints to represent intervals, linking frequency ratios to mathematical proportions. ③ Construction highlights: from the summary, commands like OrthogonalLine, Point, Midpoint, and Intersect are used, along with multiple objects (A, B, C, D, etc.) and circles c1-c4, likely modeling interval geometry or tonal cycles. ④ Suitable for secondary school and above, this resource supports interdisciplinary teaching of music and mathematics, helping students grasp the mathematical foundations of scales, geometric representations of tonality, and the role of fractional ratios in music theory.