syllables of the Melakarta ragam

The above scheme works as follows:
(1) Assign numbers to the first two syllables of the Melakarta ragam. Example, Harikambhoji, the syllable 'Ha' is 8 and 'ra' is 2 and thus Hari is 82. The melakarta number of this ragam is obtained by simply interchanging the digits, i. e 82 becomes 28 and in fact, Harikambhoji is the 28 th melakarta ragam.
(2) A few more example, Kanakangi. Ka is 1 and Na is 0 and thus Kana is 10. Interchanging the digits we get 10 -- 01 and thus this is the first melakarta ragam.
DhheeraShankarabharanam, here Dhha is 9 and ra is 2 and thus Dhheera is 92, transposing which we get 29 which is the position of the ragam. You can see that Shankarabharanam probably existed before the scheme was invented and thus the author had to alias it to conform to his look-up table scheme. There are other such aliased ragams. The popular ragam Todi is aliased to become Hanumatodi and Kalyani is officially Mechakalyani, just so that they follow the Katayapadi naming scheme. Another example, Mayamalavagaulai, (used to be called just Malavagaulai) has Ma which is 5 and Ya which is 1 and thus yielding 51, which when inverted gives 15, which is the place in the order.
Take SimhendraMadhyamam. Sa is 7 and Ma is 5 and thus Simha is 75 and the melakarta number is 57. However you must notice that the second syllable, Mha is a compound syllable combining ma and ha. In these cases, we usually take the first of the two sounds. There are some exceptions too. In Ratnangi, Ra is 2 and we take the 'Na' part of 'Thna' and arrive at the destination 02. If you used 'Th' instead of 'Na', you will get the number 62 for this melakarta, which is firmly occupied by ragam Rishabhapriya.
What are the advantages of such mathematical and almost 'hackers' kind of scheme ?
(1) The melakarta scheme does not tell you if a given ragam is a melakarta or not. If you know it is a melakarta ragam, you can find out what number it has in the sequence. For example, you can try to see what number is ragam Poorvikalyani, which is not a melakarta. This would be 21 if you consider Pa ra. (or if you considered Pa and Va it is 41) However, it is not even a melakarta ragam and you cannot use the above look-up table.
(2) Incidentally, if you look up Table IV which lists all the melakarta ragam, you will see that the two very famous ragams Shankarabharanam (called DhheeraShankarabharanam) and Kalyani (called Mechakalyani) have almost identical notes except for the Ma. Shankarabharanam uses Ma1, which is called Shuddha Madhyamam, whereas Kalyani uses Ma2 which is called Prati Madhyamam. Thus the table is divided into two groups of 36 ragams each and the only difference between the ragam on the left and the one on the right is the Ma key used. The first 36 from Kanakangi to Chalanattai are called Suddha Madhyamam ragams and the other 36 are called Prati Madhyamam ragams. Melakartas which differ from each other by 36 (Such as Harikambhoji and Vachaspati, Keeravani and Simhendramadhyamam) have the same Arohanam and Avarohanam except for the Ma.
(3) How do we figure out the Arohanam and Avarohanam or which keys to use from the name of the melakarta ragam ? If somebody tells you Keeravani, can you quickly locate the keys on a keyboard corresponding to the ragam ? You just have to look at the Table IV to see how cyclical the whole thing is. All melakarta ragams in the same group of six (i. e, 1 to 6, 7 to 12, 25 to 30 etc) have the same Sa ri ga ma. All ragams which differ from each other by six have the same Pa dha ni sa. (Karaharapriya(22), Harikambhoji(28), Hemavati(58), Nasikabhoosani(70) all have the same Pa dha ni sa, because they all leave a remainder of 4 when divided by 6)