Then I really do not know what you mean by
vasanthakokilam wrote:3 b) gathi variations - type 2 - Keep the sub-beat interval the same and vary the number of sub-beats per beat.
3c is a special case of 3b if you are willing to consider the 2 Kalai as consisting of two sub-units, 4 Kalai as consisting of 4 sub-units
What sub-unit, what sub-beat? Are they same? I do not thinks so but then I do not know what you are thinking
The way I interpret the above second statement is a sub-unit for 2kalai would itself consist of ta-ka-dhi-mi (and multiples or halves there of).
But the sub-unit 3b is one that whose duration remains the same across gati switch is the one that is in 4s for 1-kalai i.e.
[ta-ka-dhi-mi] [ta-ka-dhi-mi] [ta-ka-dhi-mi] [ta-ka-dhi-mi] | [ta-ka-dhi-mi] [ta-ka-dhi-mi] | [ta-ka-dhi-mi] [ta-ka-dhi-mi] ||
32 sub-units per Adi. If each sub-unit duration is 1/4th a second, then 8 seconds i.e. 1 second per akshara. Keeping this sub-unit same, if you do tisra the Adi tala duration would change to 6 seconds for 3b. An akshara duration for that tala would be 3/4 seconds.
A "comparative" 2 kalai would be 16 seconds. An akshara becomes 2 seconds (kept as two beats of 1 second), divided into 8 1/4 chunks - the same as 1-kaLai (which is implied by the same gati). A "comparative 3-kalai" would be 24 seconds.
In 3c, what happens is you keep the tala duration and the akshara duration constant and you increase/decrease the sub-unit duration. So for tisra Adi would still be 8 seconds. Each sub-unit increases/stretches to 1/3 seconds. For khaNDa each sub-unit decreases/contracts to 1/5 seconds.
Basically unless I am misunderstanding you, your equivalence of 3b and 3c assumes different kinds of sub-units/sub-beats. I guess I am misunderstanding you
for is that sub-unit which resultts