72 parents, thousands of children: How India classified ragas using mathematics

In a groundbreaking effort to quantify the intricate world of Indian classical music, two mathematicians from different eras and regions of India independently devised systems to classify the vast array of ragas, melodic frameworks central to Indian music. Their work, rooted in mathematical precision, sought to organize the seemingly infinite variations of these musical forms into a structured framework. One scholar identified 72 distinct ragas, while another settled on 32, keeping only 10 of them. This classification system, born from centuries of musical tradition and scholarly inquiry, represents a unique intersection of art and science. The origins of this mathematical approach trace back to the late 18th century, when a musician-scholar from the northern state of Uttar Pradesh undertook a meticulous study of the melodic structures known as ragas. His work laid the foundation for a systematic method of categorizing these melodies based on specific intervals and tonal patterns. Centuries later, in the southern state of Tamil Nadu, another scholar developed a similar yet distinct methodology, arriving at a slightly different number of classifications. These two independent efforts reflect the deep-rooted tradition of analytical thinking within Indian musicology. At the heart of this classification lies the concept of the octave, a fundamental unit of musical organization. Within a single octave, there are 12 distinct pitches, often referred to as the 12 notes of the scale. These notes serve as the building blocks for all ragas, much like letters form the basis of written language. Musicians navigate these pitches with great care, adhering to strict rules regarding which notes can appear in sequence and how they can be modified. One key element of this system involves the concept of "shuddha," "komal," and "teevra", terms that describe the purity, softness, and sharpness of individual notes. For instance, the note "Re" can appear in two forms: a natural (shuddha) version and a flattened (komal) version. Similarly, the note "Ma" has a unique variation known as "teevra," which is raised in pitch. These modifications allow for subtle tonal shifts that define the character of each raga. The process of classifying ragas involves placing these notes within the 12-pitch framework, ensuring that they maintain their traditional order. This ordering is crucial, as it dictates the emotional and atmospheric qualities associated with each raga. For example, the raga "Bhairav" is traditionally performed during the early hours of the day, evoking feelings of introspection and melancholy. Such associations are not arbitrary but stem from centuries of cultural and musical practice. Padma Shri Malini Awasthi, a renowned folk singer and exponent of Indian music, offers insight into the significance of this structured approach. She emphasizes that the classification of ragas is not a modern invention but rather a culmination of generations of musical knowledge. According to her, the placement of each raga within a specific time of day or mood is the result of careful observation and experience, not mere speculation. This mathematical classification serves as a bridge between the intuitive aspects of music and the scientific principles underlying its structure. By quantifying the elements of ragas, scholars and musicians alike gain a deeper understanding of the complexities inherent in Indian classical music. As such, this endeavor continues to inspire new generations of artists and researchers, ensuring that the rich heritage of Indian music remains both preserved and evolving.