Svara
The Sanskrit term that corresponds to that of "musical note" is svara. According to Śāraṅgadeva, svara is composed of the term rañja, to which is added the neutral prefix sva (self): "Immediately consequent upon śruti, creamy and resonating, the sound that delights the listeners’ minds by itself is called svara". (SR, vols I, 3, 24c-25b, as translated by Shringy, R.K. & Sharma, P. L., 1999: 130)
Since the Nāṭyaśāstra, Indian musicologists have recognized seven svara: ṣaḍja, ṛṣabha, gāndhāra, madhyama, paṅcama, dhaivata and niṣāda. They are usually called by their diminutive form: Sa, Re, Ga, ma, Pa, Dha, Ni. With the exception of Sa and Pa, all the svara have two forms: pure (śuddha) or altered (vikṛita). The svara Re, Ga, Dha and Ni can be diminished by a semitone, they are then called komala re, komala ga, komala dha and komala ni; ma can be increased by a semitone to become tivra Ma.
This gives an octave that can be divided into 12 degrees; seven pure and five altered. So, contrary to popular belief, there are no quarter tones in hindustani music, but twelve degrees separated by semitones as in the chromatic scale of Western music. We must note, however, that Indian musicologists have demonstrated that the octave can be divided into 22 micro-intervals called śruti*. Suffice it to mention here that svara in Indian music are not based on a tempered scale and that they thus have a great variation of frequencies. All svara are established in relation to the tonic, Sa, matrix of all the svara. Sa has no fixed frequency, but is set according to each voice or instrument: a singer may sing his Sa on a C#, while another will sing his Sa on a note somewhere between D# and E. It is from this tonic that the scale of a raga is constructed, each svara of raga having its own range of frequencies: a single svara can be sung or played a little higher or a little lower depending on the raga. For example, the komala re of raga Todī is traditionally sung / played slightly lower than that of Māravā. The specific pitch of each svara is not the result of a mathematical operation, it is adjusted "to the ear" and is conditioned by the type of ornamentation used in performance.
Reference:
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Śāraṅgadeva. (2013). Sangitaratnakara of Sarngadeva (R. K. Shringy et P. L. Sharma, Trad.) (Vol. 1). New Delhi : Munshiram Manoharlal.
*The reader who finds interest in the question of śruti will certainly enjoy reading Clements, E. (1913). Introduction to the Study of Indian Music (1966 ed.). Allahabad: Kitab Mahal (Wholesale Division) Private Limited; Daniélou, A. (1980). The Raga-s of Northern Indian Music. New-Delhi: Munshiram Manoharlal; and Rao, S. (2000). Acoustical perspective on raga-rasa theory. Munshiram Manoharlal Publishers. I would also suggest the same reader to read this excellent critical analysis of this type of approach to Indian music: Jairazbhoy, N. A. (2008). What Happened to Indian Music Theory? Indo-Occidentalism? Ethnomusicology, 52(3), 349-377.