Matrameru

“Prosody is a generating function of rhythmic complexity. It is a study which provides us with valuable insights into some of the methods used by poets who excelled in composing rhythmic verse, and the connection between these methods and the grammar of rhythm”.

 

There is a fundamental connection between rhythmic verse and the grammar of rhythm in Indian Classical Music. The earliest reference to a comparable scheme of expansion for rhythmic cycles (tala) – called Tālaprastāra - can be found in the texts of Parsvadeva (c.13th Century CE). Similar to the structures of Sanskrit verse, mātrās (syllabic instants) characterise the duration of the tala cycle, and they are formed by partitioning units of durations (laghu, guru, pluta). These are then organised in different arrangements which are distinct from the previous ones. Ancient Vedic grammarian and mathematician Pingala enumerates over 600 poetic forms in his renowned text the Chandrashastra, detailing the highly mathematical structures of their composition. Within this text, as it was later summarised by classical Sanskrit prosody scholars Virahanka (700 CE) and Hemachandra (1150), Pingala discusses the concept of mātrāmeru (“the two are mixed”). This is the art of counting sequences such as 0, 1, 1, 2, 3, 5, 8..., and incorporating properties of these numbers within the poetic form. For the purposes of this project, I was interested in researching how this mathematical sequence was being employed in India, some 2500 years before their discovery by Fibonacci in 1170.

I have experimented with these ideas through two contrasting studies for piano. The first utilises fundamental components of raga scales in a canon between the left and right hand. The phrase structure is generated from the permutations of a mattra-vrtta line with 7 syllabic instants, resulting in an exciting polyrhythmic pattern within the canon. The second exhibits a harmonic rhythm based on the basic verse structure of mattra-vrttas line with 6 syllables. These are then stretched through “Fibonacci-like” transformations. In order to approach this from the most impartial perspective and to detach from culture specific cues, I have referred to Vishnu Narayan Bhatkhande's thaat structure.