Sri Ramakrishna Arti

This is a song I had heard for the first time in 2013. It is called Ramakrishna Arti and was composed by Swami Vivekananda for his guru, Ramakrishna Paramahamsa.
It is a hauntingly beautiful song and at least for me, it stays in my head because I find the tune completely unpredictable.
The type of classical music from I am familiar with is called Carnatic. This is the system I learned when young and have listened to nearly all my life. I don't know the theory or much of the history to this system, but to my mind, Carnatic music follows a fairly rigid structure. There are raagams, or "patterns" of escalating and decreasing notes and when you sing a song, the tune has to follow a particular pattern. I guess all music is like that, but in both Carnatic and its north Indian counterpart, Hindustani, the patterns are given names, such as Hamsadhvani raagam (song of the swan "pattern") or Mohini raagam (that which dazzles the mind) or whatever. So if I were to tell you that the raagam for my song is Mohini, no matter the lyrics, you would be able to figure out the general tune of the song.
I am also a bit familiar with Western classical music, having hung around people in my old lab who listened to it often.
This song, however, falls completely outside my area of familiarity. When it began, I started reciting the words aloud expecting that the tune would ultimately fall into some familiar pattern, but it didn't. The tune rises and falls dramatically and completely unexpectedly. If I were to draw it out, it would look like hills and valleys, punctuated by hillocks. Then there are the long drawn out last syllables, always going on either a bit longer or shorter than expected.

I think one of the reasons why it doesn't fall into an expected pattern is because of the number of beats: each line to this song has 12 beats, whereas most Carnatic music pieces have 8 or multiples of 8. So do most Western classical pieces. The 12-beat system really threw me off. I think that's why I find the timing of it so confusing and always end up feeling like Mr.Bean.