First key - Choose any...

Second key - Skip the adjacent key to the right, choose the one after that. In effect, you have moved a 'whole tone' from the first key. Remember the concept of 'whole tones' and 'semitones' from the previous chapter. And that the whole tone equals shifting two semitones.
Third key - Again, skip the adjacent key to the right, choose the second one (again, you have moved a 'whole tone')
Fourth key - select the adjacent key. (you have moved a 'half tone' or a semitone)
Fifth key - Skip the next key, but select the one after that. Onceagain, you have have moved a full tone.
Sixth key - Skip the next key and select the one after that.
Seventh key - Select the adjacent key.
In short, your frequency selection is:
Select a key and then move,
Whole tone - whole tone - half tone - whole tone - whole tone - whole tone - half tone
If you started with the usual C key, the first white key, you will see that the 'C Major scale' is simply all white keys. This is a very 'major' scale, really, with a lot of popular compositions. And in the process of introducing this algorithm, we have also defined the term 'scale', which is simply a sequence of keys. Also, the algorithm 'wraps around itself'. That is, if you started out with the F key for example, and created the F Major Scale, you will spill over to the next octave. But that is okay, because you can fill up the rest of your scale by starting out with the F key of the PREVIOUS octave. That is, with this algorithm, you will always select seven keys in an octave. A question to ask is - will we get unique sequences using this algorithm every time we start off with a new key ? Or is there a possibility of our sequence repeating itself for two different starting keys, i.e, is the C Major scale different from D Major and are there twelve unique Major scales ? (I will leave this as an exercise for the very enthusiastic reader !)
Similarly, other algorithms can also be defined. One other choice is called the Minor scale - which is in reality a generic name for three different algorithms. One of them goes as
Whole - half - whole - whole - half - whole - whole (with the freedom to choose the first key)
I am not giving the selection rules for the other two 'Minor' algorithms. Again there are twelve keys we can select as our first key and therefore we can generate twelve sequences per Minor algorithm and there are three such 'Minor' algorithms, bringing a grand total of twelve times three, thirty six possible Minor scales. But we discover that many of the scales repeat themselves and in reality the number of unique 'scales' are fewer than thirty six Minor plus twelve Major scales.
Coming back to Indian system, even the ancient Tamil literary work, Silappadhikaram talks of an algorithm called 'Ilikramam', fascinating as it sounds. The rules of Ilikramam are quite similar to the selection of Major and Minor scales. It is really fun to work out this algorithm and derive a bunch of scales. (If you are more interested in this, refer to Prof. Ramanathan's book in the Reference section) In fact, nothing stops you at this point to go ahead and create your own selection rules to choose seven keys out of the twelve in the octave.
But let us turn our attention to Karnatic music. (Also, at this point, I will depart from talking about Indian classical music in general and stick only to South Indian music. Wherever relevant, references will be made to Hindustani music)
In Karnatic music, a very famous algorithm exists to select the keys in an octave, which forms the basis of important scales, which are called the 'Melakarta Scheme'. The Melakarta scheme selection algorithm is as follows: Please refer to Fig. 3 or Table II)