According to the Merriam Webster dictionary, any model refers to a system of postulates, data, and/or inferences that mathematically describes an entity or state of affairs. A statistical model differs from models of any other scientific discipline in its exactness. While other disciplines try to mimic the exact reality, statistical models offer an estimate of the reality that not only recognises that error can creep in but also suggests ways of managing the error. But the forefathers of this subject may not have anticipated that this would be used to model melodies.
In 1998, David M. Franz modelled John Coltrane’s “Giant Steps” and analysed it against its improvisations. In 2002, Yi-Wen Liu and Eleanor Selfridge-Field too thought that music can be treated as a random process. Any musical composition consists of a random sequence of notes, chords, dynamics, and tempo that change over time. For example, Hindustani music is based on seven notes (sa, re, ga, ma, pa, dha, ni). Any musical episode is a time-sequence of such notes where each note corresponds to any one of the three octaves (lower, middle and higher) as permitted by the raga. If one can postulate that during each transition (sa to ni), the resultant note depends on the previous note or notes, one can use the Markov Chain to model a song. Liu and Field suggested four steps to deduce the underlying transition probability matrix to define the Markov Chain of a particular style of music: i) build the repertoire of any particular style with as many compositions as possible ii) encode all the works in that repertoire using musical notations iii) note down all possible states the compositions pass through iv) derive the MC defining TPM basedon the actual number of transitions noted for all the compositions within the repertoire.
Nandini Sarma and Pranita Sarmah have published their research that deals with the identification of an allied raga from a piece of music. They took up the song, “Dil Hoom Hoom Kare”, picked up the sargam notation of the song from the website, www.notesandsargam.com, and the notation for Indian classical raga from six volumes of Vishnu Narayan Bhatkhande’s book, Kramik Pustak Malika: Hindustani Sangeet Paddhati. Corresponding to the occurrence of notes and octaves, it was observed that the song was similar to both Raga Bhupali and Raga Deshkar. However, these two ragas differ in their prominence to the Vadi note. In order to find out the raga the song is closer to, the researchers used the Kullback-Leibler divergence, a useful statistical tool, as a measure of their ‘distance’. They finally concluded that the song is more aligned to Raga Deshkar with regard to notes and octaves.
In 2005, the French scholars, Pierre Roy, Jean-Julien Aucouturier, Francois Pachet and Anthony Beurive, first introduced KLD, a tool so far used in pattern recognition problems, in the realm of music. In 2002, Liu and Field experimented with string quartets of 100 movements by Mozart and 212 movements by Haydn. After ‘learning’ their patterns, they ran a composer identification problem between the computer and human beings and found that the computer’s performance is significant. In 2010, C. Charbuillet and three others proposed and successfully tested a fast algorithm for searching music by similarity in large databases using the Symmetrized KLD measure. In 2012, D. Schnitzer, A. Flexer and G. Widmer used a filter-and-refine method and built a prototype music recommendation web service, which worked on a collection of 2.5 million tracks. They, too, used the KLD measure for deriving acoustic similarity and genre classification. The list continues.
Over the years, we see that statistical modelling in musicology had been used for music similarity search in large collections, music recommendation, composer identification and genre classification. In the era of Artificial Intelligence and Machine Learning, the day is probably not very far when the new-age ChatGPTs will start creating new ragas, tunes, or pieces of music.
Subhasis Ray is the author of Management of the Cricketing Ecosystem: An Analytic Approach
