Acoustical properties
and construction of the tabla

 

Basic physics of the ideal circular membrane

We begin by analyzing the resonant properties of an ideal circular mem-brane. although not restricted to a circular shape, many drums feature this property, providing a convenient starting point for discussion.

We solve for the harmonic frequencies of an ideal, thin, homogeneous, stretched, circular membrane using Bessel's functions. we assume the outer circular edge of the membrane constitutes a fixed boundary condi-tion, as with any standard drum. for such a membrane we find the funda-mental frequency inversely proportional to the radius, directly proportional to the square root of the tension, and inversely proportional to the square root of the mass per unit area.

Because of the nature of the material and its boundary conditions, the vi-brational energy exhibits different observable "modes". each of these mo-des represents a manner in which the material moves in response to the vibrational energy. we distinguish these modes by noting which areas of the membrane moves, and which areas do not. we find it convenient to de-signate the stationary points on the surface of the membrane where the material remains in a fixed position, as "nodes". the nodes, in effect, draw boundaries around the material which vibrates. these boundaries, or no-des, consist of three basic types: nodal points, nodal diameters and nodal circles.

For circular membranes, we designate the normal modes of vibration by the notation "(x,y)", where x indicates the number of nodal diameters, and y indicates the number of nodal circles. we leave nodal points out of this discussion for simplicity, due to the rarity of the phenomenon. to see the first 14 modes of an ideal circular membrane, their mode designations, and their relative modal frequency, click here. note that, none of the modal frequencies consist of multiples of the fundamental, and thus do not consti-tute a harmonic series. note here that two headed drums complicate ana-lysis by introducing coupling between the to resonating membranes. (click here to see some details on that subject). also note the addition of each diametric division of the membrane results in the next harmonic mode (e.g. 3 diametric divisions, third harmonic). whereas the addition of each circular node results in the next odd harmonic (e.g. three circular nodes, fifth harmonic). when considering the circular nodes, always consider the fixed boundary of the membrane itself.

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Acoustic properties of the timpani

By modifying or introducing certain design features, we may emphasize particular overtones, and even alter them completely. a carefully tuned classical western timpani is known to have a strong principle note, as well as two or more harmonic overtones, including a prefect fifth, major se-venth, and an octave. these overtones come from the (2,1),(3,1), and (1,2) modes respectively. furthermore, recent measurements indicate the mo-des (1,1), (4,1) and (5,1) have ratios 1, 2.44, and 2.9 respectively. both of these represent frequencies within a semitones, from the ratios 2.5 and 3, respectively. thus the first five nodal diameters (0,1),(1,1),(2,1),(3,1), and (4,1) give the timpani the frequency profile of 1:2:3:4:5:6 -- yielding a strong sense of pitch. the timpani employs several features to alter the overtones of an ideal circ
The largest factor for the "correction" of the overtones, into a close appro-ximation of a harmonic series, stems from the mass of the air which the membrane vibrates against. the timpani features a large surface area and thus interacts with a large volume of air. this air mass serves to lower the frequencies of the principle modes of vibration. the shape of the timpani's large conical shell exhibits resonance properties of its own. modes with similar shapes interact and reinforce each other, though the medium of the air trapped inside it the timpani. the stiffness of the preferred timpani membrane, raises the frequencies of higher overtones. all of these proper-ties shift the harmonic overtones and result in a close approxima-tion of a harmonic series (from which to designate pitch). ular membrane.

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Acoustical properties of the bass drum

With similar design features as the timpani, the bass drum also exhibits these features. a large symphonic bass drum exhibits a near harmonic series in the low frequency range from 32hz to 200hz. however, the ear hears frequencies above 200hz much better than between 32hz - 200hz. inharmonic frequencies above 200hz saturate the bass drum's frequency spectrum, and thus gives the drum an undecernable relative pitch.

The tabla employs many interesting features to "re-normalize" its overto-nes into a true harmonic series. having a perfect harmonic series, the tab-la exhibits a perfect tunable pitch. the main feature, which "corrects" the overtones, results from loading the membrane with a graduated weight (heaviest at the center of the membrane, decreasing towards the outer edge, and stops abruptly approximately half-way towards the outer edge). this modification results from applying concentric layers of wet flour (or rice) paste, mixed with iron powder. a skilled tabla maker uses a small soft stone to dry the paste, pack the material, and create a smooth sur-face. once hard, the tabla maker applies the next layer (ontop), with slightly smaller radius (from the center). the tabla maker assures the harmonics become properly adjusted during this process by monitoring the tone of the drum at each stage, and adjusting the weight of each layer according-ly. research demonstrates with the application of each new layer, certain overtone frequencies which ordinarily result from different modes, shift closer and closer towards each other (towards an appropriate harmonic overtone). upon completion, several ordinarily distinct overtones have the same frequency. for example, with each application of the another layer to the shiyahi, the (0,2) and (2,1) modes gradually approach the third harmo-nic. to see nodal pattern of nine normal and seven combination modes of the tabla, their mode designations, and their relative modal frequency, click here.

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The tabla's acoustical properties, its harmonic series, application of the shiyahi.

When complete, this black patch (called the shiyahi, or gob), not only re-sults in the drum's harmonic series (thus tunable pitch), but also gives the drum a unique surface on which to create sounds, unavailable to drums with an unmodified membrane.

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The bayan's aco

With the bayan, the shiyahi is placed off-center. the performer rests their hand on membrane, generally on the side furthest from the shiyahi. this results completely dampens a portion of the membrane, and effectively re-centers the shiyahi. with less research on this drum, we can not thoroughly discuss the harmonics of this drum. we note, that due to the asymmetrical nature of the bayan (without a hand resting on the drum) the overtones will not constitute of a harmonic series and will not result a discernible pitch, as with the dayan. this is well known empirically. as a unique feature of the bayan, performers change the its pitch both by siding their hand across the drum, and sometimes by applying pressure on the membrane. siding of the hand across the bayan decreases the radius of area of the resonant area of the drum (which is inversely proportional to pitch). this renders a strong sense of pitch over a wide range of frequencies. an advanced performer uses the lyrical qualities of this drum to embellish the rhythm.

ustical properties, and modulation of pitch.

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The multi-layered composite membrane design and construction.

Both the tabla and the bayan have a multi-layered membrane. The main layer, complete covers the "mouth" of the drum. Two layers, one above this main layer and one below, cover only a small outer portion of this area. An annular strip covers approximately two centimeters of the drum. These an-nular strips serve to dampen higher harmonics, which rely more on the ou-ter portions of the membrane than the lower harmonics. Performers may also place a string between the top annular strip (accessible from the top of the drum) and the main layer, to adjust this effect by controlling the amount of contact between these layers.

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Fastening the membrane to the tabla, and its tuning.

This membrane is assembled together with a interwoven leather thread, and given 16 holes around the edge. another leather thread weaves these 16 points on the membrane to a leather hoop located at the bottom of the drum. thus fastening the membrane to the drum itself. by decreasing the length of this weave, one may increase the tension on the membrane, and thus increase the pitch. In addition, wooden pegs placed between the drum and these straps increase the tension on the membrane by pulling on the straps. this is essential for the tabla, which uses eight pegs equally placed around the drum. a tablist tunes the tabla by adjusting the peg's position. due to the geometry of the tabla, lowering the pegs position in-creases the tension on the membrane by pulling on the straps. a tablist fine tunes the drum by tapping on the edge of the membrane, adjusting the position of the membrane, which increases/decreases the membrane's tension, and thus increases/decreases the pitch. equal tension around the drum is critical to proper tuning of the dayan.

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Properties and materials of the shell.

The tabla's shell consist of a very hard wood. The tabla's shell is much thicker than most other drums, of any size. furthermore its inner cavity is rather shallow. these features yields a much smaller volume (of trapped air) inside than its outer shape or appearance implies (when compared with most other drums). the thick shell increases sustained resonance of the membrane by minimizing energy dissipation through the shell. recent research of making a dayan with an aluminum shell resulted in a extremely heavy dayan with remarkable tonal quality.

The bayan's shell on the other hand, consists of a "thin" polished bronze layer, which accurately portrays the volume of air trapped inside the drum. the bayan's shell seldomly consist of clay, or even less frequently (and ge-nerally much smaller in size) with wood -- usually found in rural areas.

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