Melakarta Ragams

(i) All Melakarta Ragams from 1 to 36 use Ma 1. Those from 37 to 72 use Ma 2.
(ii) The ri ga assignment is as follows:
Ri 1 - Ga 1 Melakartas 1 through 6, 37 through 42
Ri 1 - Ga 2 Melakartas 7 through 12, 43 through 48
Ri 1 - Ga 3 Melakartas 13 through 18, 49 through 54
Ri 2 - Ga 2 Melakartas 19 through 24, 55 through 60
Ri 2 - Ga 3 Melakartas 25 through 30, 61 through 66
Ri 3 - Ga 3 Melakartas 31 through 36, 67 through 72
(iii) The dha ni assignment is as follows:
Take the Melakarta number and divide it by six and look at the remainder.
Dha 1 - Ni 1 if the remainder is 1
Dha 1 - Ni 2 if the remainder is 2
Dha 1 - Ni 3 if the remainder is 3
Dha 2 - Ni 2 if the remainder is 4
Dha 2 - Ni 3 if the remainder is 5
Dha 3 - Ni 3 if the remainder is zero
So all you have to do is take a melakarta ragam. From its name determine its number in the scheme. From the number, figure out the Arohanam and Avarohanam. Simple enough !
Again, among the 72 such major ragams, not all of them are equally popular. Some of them are quite obscure, especially the ones whose keys are not spread apart well throughout the octave. However, many musicians have composed in all 72 melakartas - Koteeswara Iyer for one. Musicians like M. S. Subbulakshmi and S. Balachandar have recorded all 72 melakartas. The Suddha Madhyamam (Suddha Madhyamam is just the official name for Ma 1) group of 36 ragams are by and large more popular than the Prati Madhyamam (Prati Madhyamam is the same as Ma 2) group. The Ma2 is supposed to be more 'negative' and 'sad' !! The more unpopular ragams are the ones like Kanakangi, which use closely spaced keys. The ragam Mayamalavagaulai on the other hand has a well spread out keys - Sa-ri1-space-ga2-ma1-space-pa-dha1-space-ni2-sa. This is the ragam all beginners are taught, essentially because such a dispersed set of notes is more easy for a beginner to learn.
>From these complete ragams, you can derive 'child ragams' omitting a key here and a key there in the arohanam or avarohanam. Some melakartas are parents of a large number of popular 'child' or 'Janya' or 'derived' ragams - melakartas like Natabhairavi, Kharaharapriya, Harikambhoji for example. We will see this in the next section.
You may wonder how just one key makes a difference. I just told you that the ragams Kalyani and Shankarabharanam have identical arohanam and avarohanam, except for the key used to produce the 'ma' syllable. You have to listen to your keyboard. Play Kalyani and Shankarabharanam on the keyboard (and even though you don't produce the 'microtones' and even though you are playing an 'eqully tempered instrument') you can tell the two apart. The ma key makes a big difference and one has to simply listen to music a lot to train one's ears.
Since melakartas have the maximum allowed seven notes in a ragam, they have an enormous scope for melody making, compared to a derived ragam which may have less than seven notes. Thus melakarta ragams are very popular in concerts. Musicians choose them for the 'heavy' part of the concert and try to exhibit their mastery.