The Seven of Music

I have always loved listening to music but never had the ear to appreciate the nuances. Ever since I took up listening to Carnatic Music I have longed to join that throng of people who listen to the first three notes of the rendition and exclaim knowledgeably, "Ah! Abheri" or some such name of a raga. Sadly for me, all I can manage is "I liked it" thereby labeling myself that most crass of people - the "I know what I like" brigade.
Well - if I could not recognize ragas I could at least get into the math of it. Idle curiosity had always existed about how the seven swaras - Sa, Ri, Ga, Ma, Pa, Dha, Ni - could give rise to multiple sampoorna ragas (meaning ragas containing all the seven notes) particularly when the swaras had also to be sung in the same order. I mean if I had seven things and I also had to arrange all of them in only one order, I could only have one arrangement, right?
It is later I learnt that these seven swaras are actually to be used on a scale of 12 notes. Once you thought of it as arranging seven items in twelve slots according to preset rules, the possibility of multiple arrangements seemed credible.
The first of the twelve had to be Sa and the and the eighth had to be Pa. Either the sixth or the seventh could be used for  Ma. So, between these three swaras you had only two possible arrangements.
The game gets interesting - or boring, depending on where you stand on permutations and combinations - when it comes to Ri and Ga. The four notes after Sa (second to fifth on your scale of 12) can be used for these two swaras and, of course, Ga can only be played on a note subsequent to Ri. Thus, if the second note is used for Ri, you have three options (3rd to 5th) for Ga; if the third note is used for Ri, you have two options (4th and 5th) for Ga and if the fourth note is used for Ri you have only the option of the fifth for Ga. Thus, between Ri and Ga, you have six alternative arrangements.
The same thing applies Dha and Ni with respect to the 9th to 12th notes on your scale. So, you have another six arrangements for these two swaras. Thus, the total possible sampoorna ragas is 2 x 6 x 6 = 72, which is the basis of the Melakarta system of classifying Carnatic Music ragas.
Of course, you do have ragas with six swaras, five swaras etc. (4 and below tend to be rare to non-existent since the output tends more to cacophony than symphony) leading to an infinity of ragas. These ragas are called 'janya ragas' since they are considered to be born of a Melakarta raga (Sampoorna raga as above) from which one or more of the swaras are shorn. In this context, the concerned Melakarta raga is called a 'Janana raga' - the parent raga.
Having dazzled you all with my 'command' over the lexicon of music let me go back to wondering about how one identifies ragas from the singing.
I am taking part in The Write Tribe Festival of Words 1st - 7th September 2013