7. Modeling Musical Performance Data with Statistics

Today, the relationship between music and mathematics is a common factor. In the last two or three decades, the advances in mathematics, computer science, psychology, semiotics, and related fields, together with technological progress (in particular computer technology), lead to a revival of quantitative thinking in music [see, e.g., Archibald (1972), Babbitt (1961), Balzano (1980), Lewin (1987), Lendvai (1993), Forte (1964, 1973), Morris (1987, 1995), Johnson and Wichern (2002), Leyton (2001), Andreatta (1997), Solomon (1973), Beran and Mazzola (1999), Meyer (1989)]. Musical events can be expressed as a specific ordered temporal sequence, and time series analysis is the observations indexed by an ordered variable (usually time). It is therefore not surprising that time series analysis is important for analyzing musical data as it is always be the function of time. Music is an organized sound. But the equation of these sounds does not produce the formula of how and why sounds are connected. Statistics is a subject which can connect theoretical concept with observable phenomenon and statistical tools that can used to find and analyzing the structure to build a model. But applications of statistical methods in Indian musicology and performance research are very rare. There were some researches that had been done on Western musicology and mostly consist of simple applications of standard statistical tools. Due to the complex nature of music, statistics is likely to play an important role where the random variables are the musical notes which are function of time.