Stochastic models for Indian drumming

Abstract

The present article highlights certain bio-stochastic-models (BSM) associated with the musical acoustics through the most popular Indian drums Tablā, Pakhāvaj and Mridangam. A drum happens to be an important source of musical acoustics and communications. In particular, a drumming through Tablā/Pakhāvaj/Mridangam happens to be a sophisticated art based on a random (or stochastic) process. A system of drumming being represented by a particular school (or Gharānā) of Tablā/Pakhāvaj/ Mridangam, happens to be composition of the basic characteristics of that school and it's genealogical features. A sequence of equidurational strokes (∪) and the timing rests (,) forms a jāti. Playing of 'jātis' on a drum is governed by Information theory, and as such the information content (or entropy) for the total number of patterns of a jāti may be determined by musicometric dynamism of jātis. A drumming is governed by psycho-Aesthetic-Control (PAC) due to a drummer, leading further to Audio-Visual-Control (AVC) in the process of drumming. An actual jati played on a drum is influenced by a System-Theoretic-Acoustical-Model (STAM) due to the employment of varieties of strokes at the levels of melody, tone, stress and grace. Consequently, a STAM gives rises to System-Theoretic-Random-Acoustical Function (STRAF), and as such a Stochastic-Model (SM) is built up by the product SM= (JATI) × (STRAF). Hence, AVC is split into Bio-Matrix-Model (BMM) and SM, which happen to combine in the form of a Bio-Stochastic-Model (BSM). A drumming, being characterised by Bio-Muscular-Controls (BMC) of the hands and their associated parts, leads further to BSM. Finally, BSM gives rise to Bio-Control-tensions (BCT) characterised by the Kinetics of the hands and their associated parts leading to drumming. © 2002 Taylor & Francis Ltd.