CV Raman on drums
The Tabla or the Mrudangam, to be more correct. I found this paper by (Sir) CV Raman from Nature,
December 1920 December 1919 – January 1920. It’s brilliant!
The premise is the following. 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 (don’t ask me what I mean by ‘fairly’). What that means is that vibrating membranes cannot be used as musical instruments.
But wait, you say. The Tabla and the Mrudangam 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 Mrudangam, 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.[hr]
Hat Tip: Rama. The woman knows about enough things to throw one out every class. This one came up when she was telling the class about Bessel functions. I, being me, had to do the read-paper-blog-about-it bit.End. Fini. Kaputski. Drums.]
RAMAN, C., & KUMAR, S. (1920). Musical Drums with Harmonic Overtones Nature, 104 (2620), 500-500 DOI: 10.1038/104500a0