Oh my goodness... now I have several pages of posts to catch up, and, what's more, I'm loosing track of some of original definitions of the participants' terms
In what has become my house-completion and moving fortnight, I may never catch up with this thread (but I expect there'll be a next time

)
I really have barely skimmed the last several pages, and was aware of having missed several posts before my last contribution, but I would like still to react to one thing that sticks in my mind, and, probably, to add my repetition to this thread.
Something that stood out to me was the assertion that the nadai change as played by mridangist in a thani is not true nadai, but some sort of effect.
I can only respond with astonishment to that idea! The theory and practice of talam is the same for a mridangist as it is for a vocalist as it is for a veena player. They may have their own repertoire of rhythmic composition, but even much of that may well be shared by the tala-enthusiastic performers among swara and pallavi presenters --- and is certainly shared by dancers.
It may be a common part of the mridangist's performance to change from chatusra nadai to tisra and return to chatusra --- it is hardly unheard of in swara kalpana. Whereas some mridangists may treat us to a stream of different nadais (past my laya-sense ability to count, I'm afraid) and such a progression may be rare in vocal performance, there is no reason that it should not be there if anyone wishes to take it up.
I well remember the days before my first mridangam classes when, in total ignorance of the structure of what I was seeing, I thought that the musician was just speeding up, little by little --- as a western musician, unhampered by such numerical niceties as nadai, is free to do. That
is the effect.
That
is nadai as it is seen during the performance of any one song, or any one thani, and the effect on the ear
will be a speeding or slowing of the rendition.
The fact that a song may be composed in a particular nadai/talam composition from the 35 talas is an entirely different matter altogether. If we discuss nadai change, the talam or its structure is not particularly relevant, as it can be done in any talam (although usually not in the chapu talas????).
The
duration of the akshara or avartanum in any given talam is dependent more on artistic interpretation --- or whether the artist has a train to catch after the concert! Reacting to remembering that train half-way through a song is not permitted
So, I would suggest a re-examination of the topic, removing all mention of individual or different tala structures, or equivalent numbers between them. Nadai change is to do with matra and akshara, pulse and beat. If kryas and angas can be forgotten for a while, and each beat marked by a humble clap, I believe all will be simple and clear.
Oh... and singing 4 syllables in the space of three in a tisra composition would simply be a change to chatusra nadai for the duration.