Mathematics of Music: Sound, Rhythm and Harmony

The Department of Statistics and Data Science, CHRIST (Deemed to be University), Pune Lavasa Campus, organised an online lecture titled “Mathematics of Music: Sound, Rhythm and Harmony” on 24 September 2026 as part of the Mathematics for Planet Earth Online Lecture Series. The session was delivered by Prof. Preeti Rao, Professor, Department of Electrical Engineering, Indian Institute of Technology Bombay (IIT Bombay). The event brought together a diverse audience comprising school and college students, research scholars, faculty members, and mathematics enthusiasts, reflecting the interdisciplinary spirit of the lecture series.

Prof. Rao began the session by exploring the fundamental nature of sound and how it can be understood mathematically. Using the example of a tuning fork, she explained how a pure tone produces a sinusoidal waveform and how frequency determines the pitch that we perceive. This provided an intuitive introduction to Fourier analysis, which allows complex periodic waveforms to be decomposed into simpler sinusoidal components. The discussion demonstrated how mathematical representations can reveal the underlying structure of sounds that appear complex to the human ear.

The lecture then examined harmonics, vibrating strings, pitch, and timbre. Prof. Rao explained that harmonics occur at integer multiples of a fundamental frequency and showed how the length, thickness, and tension of a vibrating string influence the frequencies produced. She further illustrated how different combinations and strengths of harmonics create different timbres, allowing listeners to distinguish between musical instruments even when they are playing the same pitch.

The session subsequently moved from individual sounds to the broader structure of music. Prof. Rao discussed melody, harmony, rhythm, and timbre as important dimensions of music. Rhythm was explained as the organisation of time through an underlying pulse or beat, with note durations forming structured relationships. The discussion also introduced musical intervals, consonance, and dissonance, showing how simple frequency ratios such as 2:1 and 3:2 are associated with consonant intervals. Connections between Indian swaras and Western musical notes further illustrated the mathematical relationships present across musical traditions.

Another significant part of the lecture focused on how computers analyse and interpret music. Prof. Rao introduced spectrograms as visual representations of how frequency components change over time and explained their role in machine-based audio analysis. Participants were introduced to applications such as music identification, genre and instrument recognition, recommendation systems, audio fingerprinting, teaching feedback, cultural comparison, and copyright protection. The discussion also touched upon artificial intelligence and deep learning approaches used for music enhancement and separation.

The lecture was particularly valuable because it connected familiar experiences of listening to music with concepts from mathematics, physics, signal processing, and computation. Rather than presenting mathematics as an isolated collection of formulas, the session demonstrated how mathematical thinking can help explain why musical sounds behave as they do and how technology can analyse them.

Overall, “Mathematics of Music: Sound, Rhythm and Harmony” was an engaging and enriching session that successfully showcased the interdisciplinary character of mathematics. It encouraged participants to look beyond conventional classroom applications and recognise mathematics in everyday experiences. The lecture strongly reflected the purpose of the Mathematics for Planet Earth series: to spark curiosity and help learners appreciate mathematics as a powerful way of understanding patterns, structures, and phenomena in the world around us.