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UPCOMING SEMINAR :30th FRSM-2026- August 21-22, 2026 .Venue: Birla Institute of Technology (BIT) Mesra, Ranchi.
Vibrating membranes don’t produce harmonic overtones; i.e, they don’t produce integer multiples of the fundamental frequency. They, in fact, produce fairly broadband noise. What that means is that vibrating membranes cannot be used as musical instruments.
But the Tabla and the Mridangam are musical instruments and they do fine. Yes! The paper explains why it is that this class of Indian musical instrument can produce pure harmonics even though the basic element is a vibrating membrane. The reason, it turns out, is that black patch you see in the middle of the Tabla’s operational surface.
It will be noticed (1) that the drumhead carries a symmetrical distributed load, decreasing in superficial density from the centre outwards (this appears as a dark circle in the middle of the membrane, the load consisting of a firmly adherent but flexible composition, in which the principal constituent is finely divided metallic iron); and (2) that a second membrane in the form of a ring is superimposed on the circular membrane round its margin.
The paper goes on to note that of the five harmonics that can be obtained from a Tabla or a Mridangam, the first three are especially well-sustained and ‘purer’ harmonics. Expectedly, the first harmonic – the fundamental frequency – is produced by a mode of vibration that has no nodes at all. The second mode is produced by a mode that has one nodal diameter (picture a string tied at both ends with a node in the middle; now span that setup keeping the node on one diameter of a circle and that’s a nodal diameter.)
They report that the third harmonic is a combination of two different modes of vibration: one with two nodal diameters and one with a nodal circle. Both of these modes have the same frequency. They surmise that the fourth and fifth harmonics that are seen are also some combinations of more complex modes of vibration.
They also note that because the black patch is denser than the surrounding membrane, it carries more energy. This means that the vibrations can be sustained for longer.
RAMAN, C. V. & KUMAR, S. (1920). Musical Drums with Harmonic Overtones Nature, 104 (2620), 500
Chandrasekhara Venkata Raman (7 November 1888 – 21 November 1970) was an Indian physicist known for his work in the field of light scattering. Sir C.V. Raman was a pioneer in the physics of acoustics. Long before his Nobel Prize-winning work on light scattering, he conducted exhaustive research into the mechanics of musical instruments(1909 to 1935). He investigated the complex vibrations of both Indian and Western instruments, establishing the mathematical foundations of their unique tonal qualities. Raman’s fascination with sound stemmed from his deep love for music and his trained ear as a violinist.
In India, Sir C V Raman, working at Kolkata did some pioneer research on Indian musical instruments. Raman worked on the acoustics of musical instruments from 1909 to 1935 and regularly published his research work on musical instruments in reputed journal like Nature (London), journal Dept. of science, University of Calcutta, Philosophical magazine, Indian association for cultivation of science etc. and also in various proceedings of national and international repute. He worked out the theory of transverse vibration of bowed strings, on the basis of superposition velocities. He was also the first to investigate the harmonic nature of the sound of the Indian drums such as the tabla and the mridangam. He had some pioneer work on violin family and ektara. “On the wolf note of the violin and cello”, “The kinematics of bowed string”, “The musical instruments and their tones”, “Musical drums with harmonic overtones” etc are some examples of his published work. Raman was fascinated by waves and sounds and is always carried in his mind the memory of reading Helmholtz’s book on ‘The Sensations of Tone’ in his school days. His work on musical instruments is the biggest motivation of research in the area. After Sir C V Raman, research work on musical instruments was carried forward by S Kumar, K C Kar, B S Ramakrishnan and B M Banerji during mid of nineteenth century. After that there was a big void in the research of Indian musical instrument sound.
Other publications of C.V. Raman are given as link below
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