There are three ways to express a scale:
METHOD ONE: SOLFEGE
That is to say: use Sa, Re, Ga, Ma, Pa, Dha, and Ni along w/ forms.
In Western: they use Do, Re, Mi, Fa, So, La, and Ti.
*** This is important that C, D, E, F#, etc. etc. notation is NOT comparable with Sa Re Ga Ma Pa..." ***
METHOD TWO: FREQUENCY
In Western: we say C, D, E, F, G, A, B, C, along with sharpened versions (#) or flattened versions (b).
In Indian music: after the British introduced Western music, the notes are Safed Ek, Kali Ek, Safed Do, Kali Do, Safed Tin, Safed Char, Kali Tin, Safed Panch, Kali Char, Safed Cheh, Kali Panch, Safed Saat.
These notes are nothing more than frequency. They do NOT imply origin or position of notes in a scale. They imply the frequency in Hertz. (Letters meant to represent pitch or sound wave frequency).
METHOD THREE: STEPS
The steps method is based on see how far two consecutives notes are apart.
In Western music, we express these as steps. One half-step is one semi-tone apart, while a whole-step is two semi-tones apart. In Indian music, Sa and komal re are HALF STEP, while Sa and shuddha Re are WHOLE-STEP. Be careful, because Ga and Tivra Ma are WHOLE STEPS, and komal ga and shudhda ma are WHOLE STEPS.
Looking at Bilawal; let's see the ways we can represent it:
Step 1: S R G m P D N S'
Step 2: in the key of C: C D E F G A B C'
Step 3: (Sa)Whole-(Re)Whole-(Ga)Whole-(Ma)Half-(Pa)Whole-(Dha)Whole- (Ni)Whole- (Sa)Half
Using the Bilawal scale, it is believed that by moving the Sa around in the other six notes, seven shuddha ragas formed.
THe first shuddha raga is Bilawal, as it is.
The second shuddha raga is by placing the S on the place of R.
S R G m P D N S'
X S R g m P D n S'
Based on the steps method, we see that the FIRST instance of komal ga and komal ni are found. This shuddha raga is Kafi.
THe third shuddha raga is by placing S on the place of G.
S R G m P D N S'
X X S r g m P d n S'
This is Bhairavi. FIRST instance of komal re and komal dha.
Fourth is by placing Sa on Ma.
S R G m P D N S'
X X X S R G M P D N S'
This is Kalyana That (Raga Yaman). First instace of tivra Ma.
Fifth is by placing Sa on Pa
S R G m P D N S'
X X X X S R G m P D n S'
This is Raga Jhinjhoti of the Khamaja That
Sixth is by placing Sa on Dha
S R G m P D N S'
X X X X X S R g m P d n S'
Asavari That!
Last is seventh: Placing Sa on Ni.
S R G m P D N S'
X X X X X X S r g m M d n S'
This raga is nonexistant in North Indian music, but it is known as Ragam Rohinipriya in Carnatic music.
Since these seven ragas were derived by the shuddha swars, they are called shuddha ragas. These ragas were believed to be the source of "vikrta swars" (i.e. komal re, komal ga, tivra ma, komal dha, and komal ni.)