Music is one of the most longstanding and prevalent mediums of self-expression. In society, music carries important civil, cultural, and religious connotations, where the multitude of instruments and vast array of sounds that they can produce are associated with special occasions (Di Giulio et al., 2001). While the acoustics of many instruments belonging to woodwind or string families have been reviewed extensively, percussion instruments have been largely understudied. In particular, studying the manufacturing process and physical properties of cymbals, which are often perceived as untraditional musical instruments, can elucidate how vibrational characteristics affect sound production.
Conventional cymbals are large plates made of bronze or brass, with a bell-like, elevated region at the centre (see Figure 1). Based on the price range and desired sound, the specifications of a cymbal, such as its dimensions or constituent alloys, can be altered. Typical cymbals are made from bell bronze, a mixture of approximately 80% copper and 20% tin, which renders the material hard and resilient, protecting it from oxidation (Di Giulio et al., 2001). In general, when struck with a drumstick or another cymbal, a dissonant and complex sound consisting of many frequencies is produced. These inharmonious frequencies are the direct result of manufacturing techniques, namely hammering and lathing, which change the vibration patterns on the surface of the cymbal (Kuratani et al., 2016).
In essence, hammering refers to the process of changing the tensile and residual stresses within a cymbal by producing many small dents along its surface (Kuratani et al., 2016). Special sound grooves are then lathed into the cymbal in order to amplify vibrations and increase the range of frequencies (Di Giulio et al., 2001). A hammered cymbal is plastically deformed, and is said to be under a thermal load, resulting in different stress distributions. In a study by Kuratani et al. (2016), which used an FE or finite element model to map the stress distributions on the surface of a 16-inch cymbal before and after hammering, it was determined that the number of modes, or the pattern of vibration associated with a specific frequency, increase with an increasing natural frequency (see Figure 2). The study also found that in a hammered cymbal, there was high compressive stress at the location of the thermal loads, and high tensile stress around them (Kuratani et al., 2016).
Another important aspect investigated in the study was the effect of thermal loads on sound frequency. By performing thermal stress and vibrational analysis, the temperature distribution for a thermal load was quantified using a Gaussian distribution function, whose outputs were used to measure the frequency responses and ultimately the stress distribution on the surface of the cymbal (Kuratani et al., 2016). As a whole, the different modal configurations were dependent on frequency, with more complex shapes resulting from the interference of vibration modes at higher frequencies (Rossing, Yoo, and Morrison, 2004; Kuratani et al., 2016). Moreover, it was shown that changes in thermal load distributions generated different modal shapes, and that the presence of a thermal load resulted in a higher sound radiation efficiency, or a louder and more sustained sound (Kuratani et al., 2016).
Overall, recent studies examining the sound produced by cymbals provide insight into the physics behind instruments that are not often considered euphonious. By means of mathematical analysis, the characteristics of manufacturing processes such as hammering, which intensify the frequency of sound emanating from a surface, can be modelled and employed in areas that deal with understanding structure, both within and outside of the scope of music.
References
Anon, 2018. Stagg DH Dual-Hammered Exo Medium Thin Crash Cymbal. [image online] Musician’s Friend. Available at: <http://www.musiciansfriend.com/drums-percussion/stagg-dh-dual-hammered-exo-medium-thin-crash-cymbal> [Accessed 28 Feb. 2018].
Di Giulio, G., Esposito, E., Santolini, C. and Scalise, L., 2001. Experimental vibrational analysis of drum cymbals. 1, pp.724–730.
Kuratani, F., Yoshida, T., Koide, T., Mizuta, T. and Osamura, K., 2016. Understanding the effect of hammering process on the vibration characteristics of cymbals. Journal of Physics: Conference Series, [online] 744, p.012110. Available at: <http://iopscience.iop.org/article/10.1088/1742-6596/744/1/012110/pdf> [Accessed 27 Feb. 2018].
Rossing, T., Yoo, J. and Morrison, A., 2004. Acoustics of percussion instruments: An update. Acoustical Science and Technology, [online] 25(6), pp.406–412. Available at: <https://www.researchgate.net/publication/245525271_Acoustics_of_percussion_instruments_An_update?enrichId=rgreq-eb2f01babeabc4fd2afdcaeac99682e9-XXX&enrichSource=Y292ZXJQYWdlOzI0NTUyNTI3MTtBUzozMDE0OTgxMzIxMjM2NDhAMTQ0ODg5NDE2NDQ2MQ%3D%3D&el=1_x_3&_esc=publicationCoverPdf> [Accessed 28 Feb. 2018].