Arun, I have been re-reading the last few posts multiple times but still I am not sure if we are indeed saying the same thing or not. At one level, we seem to be saying the same thing and then we are adding possibly different interpretations to what Sri. Rangarajan does. Without worrying about it too much, let me re-present it in a simpler way. You can then add your commentary/addition. Model 1:
There are three things: 1. kaLai 2. Beats 3. Sub-beats
1) 1 KaLai consists of 1 beat
2) 2 Kalai consists of 2 beats
3) 3 Kalai consists of 3 beats ( let us call it Tisra kaLai )
4) 4 Kalai consists of 4 beats
5) 5 Kalai consists of 5 beats ( let us call it khanda kaLai )
B) Each beat consists of the following sub-beats. The beat interval does not change.
1) 1 sub-beat ( 1st speed chathusra nadai)
2) 2 sub-beats ( 2nd speed chathusra nadai)
3) 3 sub-beats ( Thisra nadai )
4) 4 sub-beats ( 3rd speed chathusra nadai )
5) 5 sub-beats ( khanda nadai )
6) 6 sub-beats ( thisra nadai mel kalam )
7) 7 sub-beats ( misra nadai )
Using this scheme, we can describe Sri. Rangarajan RTP as A5
with B1, B2, B3, B4, B5,B6 and B7 variations
There is another way of looking at things. There are only beats and sub-beats.
A) Constat sub - beat interval ( let us call this Gathi variation ). Here the beat duration is not the same. Higher the sub-units, higher the beat interval
1) 1 sub-unit per beat
2) 2 sub-units per beat
3) 3 sub-units per beat <- Thisram
4) 4 sub-units per beat <---This will be 1 kaLai
5) 5 sub-units per beat<--Khanam
6) 6 sub-units per beat<-thisram (2 kaLai?)
7) 7 sub-units per beat<-- Misram
8 sub-units per beat <---This will be 2 kaLai Here the gathi variations are in a continuum that includes the kaLai.
B) Non-constant sub - beat interval ( let us call this Nadai Variation ). Here the beat duration is the same. Higher the sub-beats, smaller the sub-beat interval.
1) 1 sub beat per beat ( chatusram 1st speed )
2) 2 sub beats per beat ( chathusram 2nd speed )
3) 3 sub beats per beat ( thisram 1st speed )
4) 4 sub beats per beat ( chathusram 3rd speed )
5) 5 sub beats per beat ( khandam )
6) 6 sub beats per beat ( thisram 2nd speed )
7) 7 sub beats per beat ( misram )
etc.Here Nadai variations are in a continuum that includes the kAlam.
Normally people do not adopt both variations within the same piece, it is one type of variation or the other. The Model 2 Variation B is the more common one.
Model 2 A8 to A4 variation is sometimes done ( changing from 2 kaLai to 1 kaLai ).
Question: Can these two models of looking at things be integrated into one consistent model.