Shri Chitravina Narasimhan gives an introduction to the origin of laya patterns in Carnatic Music.
Here is a summary:
Laya patterns in music can be traced to ancient literature. The short syllable ‘A’ denotes laghu, the longer syllable ‘Aa’, guru and the combination of laghu and guru denotes plutam. Laghu represents a unit of 1, guru represents 2 and plutam results in the combination thereby representing 3. Shri Narasimhan explains that various combinations of these fundamental units of laghu, guru and plutam resulted in akshara ganams and matra ganams. Examples are given in the video. It is clear from the explanation that matra ganam comprises only the short duration syllable laghu. Various examples of akshara and matra ganams have been illustrated in this video to draw a parallel to the laya patterns that exist in common usage today. It is indeed fascinating to learn that the laya patterns in music originated from literature.