I think this was discussed somewhere ( probably kORvai thread - by @mridhangam - not able to locate it.

If you observe here for miSRa capu - https://youtu.be/uU9YAALt828?t=6540 ( Video Rec. of Sri Arun Prakash playing the Mohra - we discussed the kOrvai that follows in the Structure of Korvai thread ), Instead of 4 16(s), he does a 12, 16, 12, 16 to occupy 2 Avartas.

In the higher kALam reckoning ( 8 mAtras per beat), all tAlAs come to even number of mAtRas per Avarta and that is handy.

Here is one scheme that retains some EVEN symmetry - I am not saying mOHras cannot go beyond this. Leaving it to higher experts.

We start with a scheme (A, B, C are integers):

2*A + B + 4*C = N * (mAtra count per Avarta of the given tALam) - Where N can be as low as (1/4) , (1/2) , 1, 2 , 4 - depending on the speed of execution.

For sUlAdi tALAS we can use N = 1 and then scale it to lower or higher speeds. 1 - kALAI here and caturaSRA naDAI. For cApu tALAS - choose an appropriate N - most likely 2 or 4 for shorter tAlAMS.

where 2*A + B + 4*C is executed in the order

**A, B , A, 4*C**. The reason for saying 4C will become clear soon.

A, B , A, 4*C - this pattern is executed 2 times.

For the third time it goes like:

A , B , A + 2*C, A + 2*C, A + 3*C , 3*C , [2*C]

The first two rounds and the third together make for a total of 4 rounds - i.e. 4 times the starting structure : 4 *(2*A + B + 4*C )

In other words - the third round pattern's time duration = twice the time period of starting structure pattern.

Now lets analyze the structure of 4*C for the case where 4*C is 16. It is usually (popularly) a dramatic - cApu expressing one like talAngu-dhin-ta-talAngu-thom(16). 2*C in the last part is done (popularly) as talAngu-thom(8). 3*C is done as talAngu-dhin-ta-thom (12). The last [2*c] in square brackets is actually a part of 3*C - with thom cut off because thom goes away with reaching a samam or an eDuppu - and that is : talAngu-dhin-ta - after which any following kORvai is started.

Now we said A , B , A 2*C, A + 2*C, A + 3*C , 3*C , [2*C] goes for two rounds of the basic starting pattern.

So 4*A + B + 12*C = 2 *(2*A + B + 4*C) --> B + 12*C = 2B + 8*C --> B = 4*C

So listing the constraints: With A, B, C as integers. In the 8 mAtras per beat setting - where tagutarikiTataka - goes for 1 beat.

1) 2*A + B + 4*C should equal N( mAtra count per Avarta of the given tALam). N is 1, 2, 4 etc - enough to fit one round of the pattern.

2) B should be divisible by 4 - since it has to equal 4*C.

3) The pattern chosen for 4*C ( which is equal to B in duration) , should be modifiable to similar sounding patterns in durations 2C and 3C. As explained above.

4) (3) above puts a minimum value on C - which should be 4 mAtRas - in the 8 mAtRas per beat setting. Less than that, patterns for 2C and 3C cannot be set appropriately.

5) (3) above Also restricts C to even integers - as executing to odd mAtra positions with 3C is impossible.

Based on this we can work out for rUpakam ( the ordinary usage) and khanDa cApu easily - next post!.