Tonal system

Svar
A svar is a scale degree in a context, and is the basic unit of melodic structure in Indian music. There are seven svar-s, which are known as Sa, Re, Ga, Ma, Pa, Dha and Ni. Together they are referred to as SARGAM. Each symbol used to represent these notes is an abbreviated form of the real note names in Sanskrit, which are Shadj, Rishabh, Gandhar, Madhyam, Pancham, Dhaivat and Nishad. In notation, the names could be further abbreviated to S R G m P D N.

Hindustani Music is invariably performed with a drone instrument, usually the tanpura. The two middle strings are tuned to the tonic Sa, the outer strings to the perfect fourth below and the octave below Sa. Vocalists have the freedom to choose a pitch of Sa that allows them to reach at least the fifth below and an octave and a half above the tonic. For male vocalist this is usually C or D, for female vocalists G or A. In instrumental music the pitch of Sa varies according to the size of the instrument, for instance C or C # for sitar. In Hindustani system the natural notes corresponding to the western major scale are called shuddh (lit. pure). Re, Ga, Dha and Ni can be flattened by a semitone and are then known as komal (lit. soft). Ma can be sharpened by a semitone and is then referred to as tivr (lit. sharp). Sa and Pa are immovable (achal) and hence their position can not be altered. Thus an octave consists of 12 tones (seven natural and 5 chromatic).
Mainly three octaves are used: low (mandr), middle (madhy) and high (tar).

Shruti
Although a svar in any specific rag is located at one of the twelve abstract theoretical pitch positions, the exact pitch of the notes has never been standardised in frequencies or ratios. It is  accepted that the actual position of the semitones excluding Sa and Pa can vary  slightly. The flat notes can be lowered by approximately 20 cents, and are then called ati komal (extra low). Similarly, tivr Ma can become tivrtar (sharper). These microtonal variations are often referred to as shruti (lit.that which is audible) in the sense of the smallest perceptible increment in pitch. Since the ancient time, an octave (or heptad-saptak) was assigned 22 shruti-s spread over 12 tones.
In the context of contemporary performance practice, as far as steady pitches (khada sur lit. standing note) are concerned, empirical research indicates that intonation is fairly standardised and that no significant deviations can be correlated to specific rag-s, as has often been maintained by protagonists of the shruti theory (Levy : 1982, corroborated by research Bel, Meer, Rao). The actual frequency ratios of the notes in comparison to Sa are consistent for a particular tuning of the tanpura and follow a system that could best be described as a just harmonic system.
This means that the simplest frequency ratios are used, except when two such tunings compete with each other, in which case some form of interpolation (or temperament) is used. Thus the Pa (702 cents) is a perfect fifth above the tonic, and Re (204 cents) a perfect fourth below the Pa. The Ga is a harmonic major third above the tonic (386 cents).  The Dha then, could either be tuned as a fifth above Re (making it 906 cents) or as a fourth above Ga (884 cents). Measurements show it to be in between both theoretical tunings at 895 cents.
The expected differentiation of intonation in different rag-s is not corroborated by empirical research. However, two salient factors which are responsible for consistent differentiation of intonation have come to light during the empirical studies on context-related intonation. The first, which was already indicated by Ratanjankar (1940) and corroborated by Levy, is that in ascending passages notes are intoned higher, while in descending passages they become lower. The second is the tuning of the fourth string of tanpura which can be either in Ma, Pa, or Ni of the lower octave. In the so called Ma-tuning (m S S S-lower), the Ga is higher, at almost 400 cents, while the Dha is lower, a harmonic major third above the Ma (884 cents). In the Ni tuning (N S S S-lower),with Ni at about 1105 cents) all notes tend to be higher.
As summarised by Powers, it is true that the numerous inflections of svar in musical contexts cannot be described fully in terms of a system of 12 fixed positions. But to say that particular shadings of pitch are essential in a particular kind of musical context is not to say that those shadings are best described in terms of some sort of microtonal scale (Powers [Grove’s Dictionary] 1980: 98). For a historical review of shruti from ancient period till to-date, refer to Rao & Meer 2010.

That-s or Scales
In the medieval period, the term that was exclusively associated with the fretted string instruments in which a particular fret-arrangement had to be made by moving some of them to obtain the desired scales. The instruments were accordingly known as chal-that (requiring shifting of frets) and achal-that (requiring no such change).
The concept of that is essentially synonymous with the concept of mel prevalent in the South Indian tradition. That (lit. type or group)  can be defined as an arrangement of notes having a potential to generate rag-s. That is a genus whereas a rag is a species arising out of it. Thus a that is a heptatonic scale using each of the seven svar-s. Venkatmakhi (1660 A.D.) showed how the semitonal scale of pitches produced by the vina with fixed frets could be permuted to produce 72 seven-degree scale types with fixed tonic and fifth, and five variable degrees (ibid: 82).
It is generally assumed that the original Indian scale had a lowered third and seventh: S R g m P D n. From this parent scale six other scales were derived by shifting the tonic to each of the seven notes. These are :

S R g m P D n  Kafi that
n S r g m P d  Bhairavi that
D N S R G M P  Kalyan that
P D n S R G m  Khamaj that
m P d n S R g m  Asavari that
R G m P D N S  Bilaval that
In addition to the above scales, the following chromatic scales were derived.
D N S r G M P  Marva that
N S r G M P d  Purvi that
d N S r g M P  Todi that
S r G m P d N  Bhairav that

The above mentioned ten scales form the that system of V. N. Bhatkhande (1860-1936), which he used as a pragmatic model for classifying his collection of thousands of compositions in over two hundred Hindustani rag-s. Incidentally, Bhatkhande was inspired by the southern system of 72 mel, propounded by Venkatmakhi (ibid: 84). As pointed by his adversaries like Omkarnath Thakur, this system is not without limitations, e.g. this classification does not satisfactorily cover some of the scale-types like Lalit, Patdip, Ahir bhairav and pentatonic rag-s like Malkauns, Bhupali etc. Further, the classification becomes ambiguous as it relies totally on the scale-type as a supreme classificatory tool (Thakur [Sangitajnali] 1938-1962). These short comings aside, Bhatkhande’s ten that system provided a sufficient framework for defining and classifying the most common tone material used in rag-s practiced in Hindustani tradition, and has since become standard.