Shri Chitravina Narasimhan talks about Jati and Graham,related to the Tala Dasha Pranas.

Here is a summary:

 

Jatis

There are five Jathis, ordered as Chaturashra(4), Tishra(3), Mishra (7) , Khanda(5) and Sankeernam. (9). The Jatis indicate the number of counts in the Laghu of a tala and does not apply to any other angas. A very simple example is given in the video to help one remember the sequence of the Jatis and how they were derived .

  1. Chaturashra is the original universal beat similar to a heartbeat.
  2.  If one is removed from that , it gives rise to Tishram (3).
  3. Tishram(3) and Chaturashram(4) combine to give rise to Mishram (Mishram means mix)  or 7.
  4. Mishram and Tishram  combine to form 10 which when split in half results in Khandam or 5.  (Khandam means split)
  5. Chaturashram and Khandam combine to give Sankeernam or 9. Sankeernam means combination and rightly so as all the Jatis are embedded in it.

Graham

Graham or Eduppu refers to the starting point of the song or composition with respect to the Tala. Samam refers to the start of the composition on the beat itself. Vishamam refers to the start of the song either before or after the beat and therefore are of two varieties, Anagatam and Ateetham. Anagatam refers to the start of the composition after the beat and Ateetham refers to the start of the composition before the beat.