The vibration of a homogeneous circular membrane backed by two taut strings is shown to yield several harmonic overtones for a wide range of physical and geometric parameters. Such a membrane is present at each end of the barrel of an idakkā, an Indian snare drum well known for its rich musicality. The audio recordings of the musical drum are analyzed and a case is made for the strong sense of pitch associated with the drum. A computationally inexpensive model of the string-membrane interaction is proposed assuming the strings to be without inertia. The interaction essentially entails wrapping/unwrapping of the string around a curve on the deforming membrane unlike the colliding strings in Western snare drums. The range of parameters for which harmonicity is achieved is examined and is found to be conforming with what is used in actual drum playing and construction.