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|Indian classical music|
Shruti or śruti (ʃrut̪i) is a Sanskrit term, which in the context of Indian music, is the smallest interval of pitch that the human ear can detect. It has been used in several contexts throughout the history of Indian music. Recent research has provided precise definition of the term Shruti, its difference from Nada and Swara, and pinpointed positions on a string to play 22 shrutis.   
- 1 Contexts
- 2 Resolution of Controversy on Shruti
- 2.1 Definitions of 'Dhwani','Nada', 'Shruti' and 'Swara'
- 2.2 Identification of a 'Shruti', distinct from 'Nada' 
- 2.3 Natural existence of 22 Shrutis on a string
- 2.4 The Evolution of 22 Shrutis from Shadja (Fundamental) and their natural arrangement on a string
- 2.5 Ratios, Frequencies, and % length of string where 22 Shrutis are played
- 2.6 22 Shrutis are a sub-set of Natural 7 Shrutis 
- 2.7 Poorna, Pramana and Nyuna Shrutis
- 2.8 Shrutis in Shadja Grama
- 2.9 Shrutis in Madhyama Grama
- 2.10 A combination of ‘Shrutis’ and ‘Nadas’ is the back-bone of Gamakas, and Alankaras
- 2.11 Why does the Melakarta system (Carnatic) not have prescribed sruthees
- 2.12 Nomenclature of 22 Shrutis/Swaras in Carnatic Music and Hindustani Classical Music
- 2.13 Sanskrit Names of 22 Shrutis
- 2.14 Why an analysis of the performances of Stalwarts will never give true values of 22 Shrutis ?
- 3 Ancient treatises on Indian classical music and performing arts
- 4 References
- 5 External links
To know the real meaning of shruti, it is important to know the various contexts in which the term is used.
Ancient period: Grama system
Bharata Muni uses shruti to mean the interval between two notes such that the difference between them is perceptible. He formulates jatis, which are classes of melodic structures. These can be further grouped into two gramas—shadja-grama and madhyama-grama. The notes (svaras) are separated by intervals, as measured in shrutis.
The shadja-grama is given by the following division: Sa of four shrutis, Ri of three shrutis, Ga of two shrutis, Ma of four shrutis, Pa of four shrutis, Da of three shrutis and Ni of two shrutis. Bharata also describes an experiment to obtain the correct physical configuration of shruti in shadja grama, Sarana Chatushtai.
The madhyama-grama is the same, but the panchama (Pa) has to be diminished by one shruti. That is, the panchama of madhyama-grama is lower than that of shadja-grama by one shruti, according to Bharata. Shruti is only mentioned as a perceptual measure in the music of Bharata's time.
In both the gramas, Ri is three shrutis away from Sa – there are three perceptible intervals between Sa and Ri. The third of these is called trishruti rishabha (Ri). Likewise, the second interval is called dvishruti rishabha, and the first ekashruti rishabha.
Notes 9 and 13 shrutis from each other occur at a ratio of 100:133.33 and 100:150 respectively and are mutually samvādi (consonant). The notes that are at the distance of two and 20 shrutis are mutually vivādi (dissonant). The remaining ones are called anuvādi (assonant).
The shruti table below shows the mathematical ratios considered to correspond to the system described by Bharata and Dattilam, along with the comparable notes in common Western 12-TET tuning. The names of the 22 shrutis were provided by Śārñgadeva.
Medieval period: Mela system
By the time Venkatamakhin formulated the melakarta ("mela") system, the grama system was no longer in use. Unlike the grama system, the mela system uses the same starting swara. It forms the scales by varying the intervals of the subsequent swaras, and does not specify a fixed interval for a swara in terms of shrutis. For example, the intervals of kakali-nishada and shuddha-madhyama vary depending on the dhaivata and the gandhara that precede them, respectively. The interval of kakali-nishada is of three different shruti values depending on whether shuddha, panca-sruti or shat-shruti-dhaivata preceded it. Thus shruti as a measure of interval is not fully employed in the mela system.
Modern period: Controversy
In current practice of Carnatic music, shruti has several meanings. It is used by musicians in several contexts. For instance, the Tamil term "Oru kattai sruti (ஒரு கட்டை ஸ்ருதி)" means that the tonic is set to the pitch C or the first key. The Telugu term "Sruti chesuko (శ్రుతి చేసుకో)" is a way to correspond with the accompanying artists to tune their instruments.
In certain ragas, due to inflexions or gamakas on some of those 12 notes, listeners perceive a sharpened or flattened version of an existing note. Some scholars have attempted to fit such perceived new tones into the non-contextual Bharata's 22 shrutis, which lead to confusion and controversy. It was also wrongly attributed to Bharata, who proposed shruti in a completely different context.
Some scientific evidence shows that these intermediate tones perceived in the contemporary rendition of a raga do not hint at the existence of 22 shrutis. The number 22 is of no practical significance in the current performance of Carnatic and Hindustani music traditions, partly because different musicians use slightly different "shrutis" when performing the same raga. The phenomenon of intermediate tones is pursued as an active area of research in Indian Musicology, which says the number of perceptible intermediate tones may be less or more than 22. N. Ramanathan, a musicologist points this out and says that the idea of 22 shrutis is applicable only to the music system of Bharata's time.
An Indian monograph about shruti claims various opinions about the number (66, 53) of shrutis. In recent times it seems that the number of shrutis is broadly agreed upon to be 22. Recognizing the controversy over the number and the exact ratios of shruti intervals, it also says that not all shruti intervals are equal and known as pramana shruti (22%), nyuna shruti (70% cents) and purana shruti (90%). Еach shruti may be approximated in 53EDO system.
Resolution of Controversy on Shruti
The controversy on Shruti stemmed from the presumed ambiguity of the word 'Shruti'. Although, 'Shruti is intimately linked to the fundamental aspects of Swara' the exact meaning of the term Shruti remained obscure. Expressed as both an 'Interval (Music)' and a 'Audio Frequency', added to the misunderstanding. Also, the performing musicians took the number '22' as arbitrary. Many others misinterpreted Shrutis as 'innumerable' and 'non-measurable'. The role of 'intermediate or fleeting notes' (as in a Meend or glide) muddled the total number 22. However, recent research has shown that the '22-Shruti-Concept' provides both theoretically and practically, a solid foundation for the actual generation of accurate notes in Indian Classical Music (both Hindustani, and Carnatic)
Accomplished over the last 12 years, this research has helped to resolve many of the long standing issues. The work was examined closely by stalwarts and acclaimed in writing as 
Outstanding and deserving due recognition.
Worth a Nobel prize.
Precise and not done by anybody so far.
Undoubtedly useful to both students and practitioners.
Absolute Truth whether people accept or not.
Setting at rest all previous discussions and disputes over the subject of shrutis.
The earlier confusion existed as the musical notes were referred to by 'different' words namely, 'Dhwani', 'Nada', 'Shruti' and 'Swara'. Hence, the meaning and the difference in these words is clarified.
Definitions of 'Dhwani','Nada', 'Shruti' and 'Swara'
Dhwani (Sanskrit) means sound of any kind. Out of all the Dhwanis created in the world, those sounds which are 'musical' and give an experience or perception of a 'musical' sound, are called as 'Nadas'. Simply, the sound of a 'clap' is a Dhwani, but that of a bell is a 'Nada'. The commonest example of 'Nada' is a musical sound made on a stretched string under constant tension, at 'any' point. There are innumerable 'Nadas' in a Saptak (Octave). Chaturdandi Prakashika (Sanskrit) by Pandit Venkatamakhin  in Shloka 3, Chapter 2, stated that,
ShrutirnÂma BhavennÂda Visheshah SwarakÂranam Nanu NÂsti Swarashrutyorbhedo NÂdaikrupayoho
'Shrutis are the 'special' Nadas which 'cause' Swaras. There is 'no' difference between Swaras and Shrutis as both are Nadas'.
Out of the innumerable 'Nadas' on a string, 22 become 'special' and are called as 'Shrutis' because, the perception of the 12 universal pitch classes of Chromatic scale (Swara-prakara) 'changes' with them. Further, Shrutis 'selected' in a Raga 'cause' (or become) the 'Swaras'. Thus, 'Shrutis' are called as 'Swaras' in a Raga and both are primarily 'Nadas'.
In this way, the Sounds (Dhwanis) get progressively classified as,
All sounds in the world are 'Dhwanis',
Selected Dhwanis become 'Nadas', (Innumerable) : Those which give a musical experience or perception,
Selected Nadas become 'Shrutis', (22) : Those where the perception of 12 Swaraprakaras (Universal chromatic pitch classes) changes in a sequence on a string. These are 22 only, as placed by Nature,
Selected Shrutis become 'Swaras', (12 or less) : Those selected in a particular Raga.
Matanga's conclusion is highly significant that 'Swaras' are manifested through the 'Shrutis'. It must be noted that ‘Swara’ in a Raga (1 single frequency), is different from ‘Swaraprakara’ (12 universal pitch classes of Chromatic scale with a range of different frequencies). 'Gamakas' or 'Alankaras' or ‘specific tonal configurations forming the core of a Raga’  are merely a combination of 'Shrutis' and 'Nadas' (See section 2.9).
In a performance, the notes identified as one of the 12 universal pitch classes of Chromatic scale (Swara-prakara) are the 'Shrutis', and the connecting unidentified notes in-between them are 'Nadas'. The time taken by the human ear to 'identify' a note (Time-threshold) is about '20-45 msec' within the range of human voice from 100–1000 Hz. Thus, Shrutis are played/sung for more than this limit and hence get 'identified'; and Nadas are played/sung faster than this limit and hence 'can not be identified but only heard'. Lack of appreciation of this major difference has led to many scientists to opine that because of the meend and the oscillating notes, it is very hard to get the exact numerical frequencies. In a Glide or a Meend e.g., there are 2 'Shrutis' at the 2 ends which are connected by 'Nadas' in-between. This in fact, is the basic structure of any phrase created in Indian Music (Hindustani and Carnatic), as a number of 'Shrutis' (2 or more) connected by 'Nadas'. The Indian Classical Music (both Hindustani and Carnatic) employs a combination of identifiable 'Shrutis' and connecting, fleeting, unidentifiable 'Nadas' in any Alankara or Gamaka (Music).
Natural existence of 22 Shrutis on a string
In ancient times Shruti was described as Shruyate iti Shruti (in Sanskrit) meaning, "what is heard is a shruti". This loose translation created confusion because, Shru (in Sanskrit) does not merely mean "to hear", but to "hear, understand and learn". The "understanding" and "learning" part is the natural fact that on 22 specific points on a string, the perception of notes changes.
Grahanendriya GrĀhyatvĀd Dhwanireva Shrutirbhavet
'Only when the ear understands (the point on the string where the perception of the notes changes), that sound becomes a Shruti'. He further mentions that these points on the string are very precise as in Shloka 28, Chapter 1, in Nadaprakarana (Chapter on Nadas) that,
TĀdĀtmyam Cha Vivartatvam KĀryatvam ParinĀmita AbhivyanjakatĀ Cha api ShrutinĀm Parikathyate 
'Reaching (the point on the string where the perception of the notes changes), and reverting (from there) results in the precision that is called as 'Shruti'.
There are 12 universally identifiable musical notes (pitch classes of Chromatic scale or Swara-prakara) in a Saptak (Octave).They indicate 'a musical note or scale degree, but Shruti is a more subtle division of the octave'. The recent research has shown that 10 out of 12 of these notes (Swaraprakaras) have a 'spread' or a 'region' on a string (Swara-kshetra in Sanskrit) in which, 'any' frequency leads to the perception of the 'same' note by the human ear, and the perception 'changes' at both the ends. The remaining 2 notes, namely the Fundamental frequency (Shadja) and the perfect 5th (Panchama) have a 'single point' on which they are placed on the string by nature. Thus, the 10 notes give 20 Shrutis, and along with the 2 points of Fundamental frequency (Shadja) and the Perfect 5th (Panchama), a natural system of 22 Shrutis can be observed and played on any string.
These 22 Shrutis were not theoretical postulates, but solid musical facts providing the foundation of Indian Music, and have been used for centuries.
Several ancient scholars have cited 22 Shrutis including Dattila (AD 400-100 BC, in Shlokas 12-14), Sarangadeva (AD 1210-1247, after Shloka 11 in Sangeeta Ratnakara), Ramamatya (AD 1550 in Shlokas 24-26 in Swaramelakalanidhi), Somanatha (AD 1609 in Shloka 17, Chapter 1, in Ragavibodha) and Venkatamakhin (AD 1626-1662, in Shloka 5, Chapter 2; Shlokas 2-3, Chapter 3; and Shlokas 94, 105, 106, Chapter 4 in Chaturdandi Prakashika).
The 22 Shrutis can also be called as 'microtones', because they are produced at mathematically defined micro-positions.
The Evolution of 22 Shrutis from Shadja (Fundamental) and their natural arrangement on a string
All the 22 Shrutis evolve from Shadja (Fundamental).
Figure showing the Evolution of 22 Shrutis from Shadja (Fundamental) and their natural arrangement on a string
The sequentially placed 12 universal pitch classes in an Octave on the string, are represented in the above diagram by the Indian synonyms r, R, g, G, M, m, P, d, D, n, N, S'. The Western Music has 12 notes, whereas the Indian Classical Music further divides them into 22 notes. Except for P (Perfect 5th) and S'(Fundamental frequency) which are played at a single point each (13 and 22 respectively), all other 10 notes have a 'spread' or a 'region' on the string (Swara-kshetra). The 'beginning' and 'end' of these regions form a total of 22 points. e.g., For the region of 'r', the perception of r begins at point '1' (called 'Swara-Uday-Bindu' in Sanskrit meaning, the point where the swara emerges or starts) and ends at point '2' (called 'Swara-Asta-Bindu' in Sanskrit meaning, the point where the swara disappears or ends); for the region of 'R', the perception of R begins at point '3' and ends at point '4', and so on.
It is highly significant that Matanga arrives at the conclusion that Swara is manifested through the Shrutis and that Swaras are separated by each other by bands of Shrutis.
Ratios, Frequencies, and % length of string where 22 Shrutis are played
It was shown in this research that 22 Shrutis are essentially related to Shadja (Fundamental frequency), by most natural interval ratios, 100:125 (S:G) or 100:150 (S:P) as shown in the Figure below. This helps us to get their precise positions and frequencies.
Figure showing 22 Shruti-Mandal (Organogram)
1 denotes a 'lower' shruti or the 'beginning' of the region of the note on a string. 2 denotes a 'higher' shruti or the 'end' of the region of the note on a string, Small letters denote 'Komal' or 'flatter' version (except m which is 'Tara'), Capital letters denote 'Tara' or 'sharper' version (except M which is 'Komal'), Vertical arrow indicates an Interval ratio of 100-125. Horizontal arrow indicates an Interval ratio of 100:150.
Fig. showing 22 Shruti-Mandal (Organogram) (Carnatic).
12 Swaras with their 16 names are shown as S, R1, R2/G1, R3, G1, G2/R3, G3, M1, M2, P, D1, D2/N1, D3, N1, N2/D3, N3. Their ‘Lower’ and ‘Higher’ Shruti versions are shown respectively marked as ‘L’ and ‘H’ in Italics. Vertical arrow indicates an Interval ratio of 100-125. Horizontal arrow indicates an Interval ratio of 100:150.
To calculate the frequency of Shrutis, for every horizontal arrow, 50% is added; and for every vertical arrow, 25% is added. e.g., to calculate the 'frequency' of P, consider the frequency of Shadja as 100 hz (for convenience of calculation). Thus, P comes at 100 hz + 50% = 150 hz. The ratio of P thus becomes 150/100. To calculate the 'position' of P on the string, we can use the law of Galileo Galilei, called in India as ‘Dviguna’ relationship, which states that the frequency ratio is 'inversely' proportional to the length of the string. Therefore, when the ratio 150/100 is 'inverted' we get the position of P on the string as 100/150 or 2/3 or 66.66% length of the string. We can calculate the frequencies and the positions of all the 22 shrutis accordingly.
Table showing the Ratios, Frequencies, % length of the string where 22 Shrutis are played (*Frequency of the Fundamental frequency or Shadja taken as 100 hz, as example)
Thus, Shrutis can be expressed as 1) 'Interval ratio', 2) Audio frequency, and 3) The playing position as % length of the string.
Table shows % frequency above Shadja (Fundamental Tone) of the 12-Tone-Equal Temperament Scale and the 22-Shruti-Indian Scale.
New musical instruments have been made to demonstrate the accurate sounds, the position, and the practical use of 22 shrutis in music, including a 22-Shruti-Harmonium (Indian Patent No. 250197), 22-Shruti-Veena, 22-Shruti-Metallophone and 22 Shruti-Tanpura. In both the Hindusthani and Carnatic classical music, the places for playing 22 shrutis (as % length of the string) remain exactly the same  on instruments such as Veena, Sarod, Sitar, Sarangi, Violin as shown in the table and diagram.
An electronic software to play Harmonium is made based on the 22 shrutis. 4 Shrutis each of the notes R, G, M, D and N progress in a symmetrical order  of Poorna, Pramana, Nyuna, Pramana as shown in the diagram.
The Indian Classical Music (both Hindustani and Carnatic) is based on the Tanpura, which produces the 1st 3 natural shrutis, Shadja (1st Harmonic), Gandhar (5th Harmonic), and Pancham (3rd Harmonic), at a ratio of 100:125:150. The basic 7 Shrutis are called ‘Shuddha’ (in Sanskrit meaning pure) in Hindustani Classical Music. They are produced at the same natural ratio as shown in the diagram with a 2-Step process.
Thus, the frequencies of the 1st Natural 7 Shrutis emerge as S=100 (taken for convenience), R=112.5, G=125, M =133.33, P=150, D=166.66, and N=187.5. The 22 Shrutis can be seen as a sub-set of 7 natural Shrutis as shown in the diagram.
Musically, out of the 7 natural Shrutis, (see diagram)
- If R is taken as S, G becomes R1, coming at 111.1111111, a ratio of 10/9.
- If R is taken as S, M becomes g1, coming at 118.518518, a ratio of 32/27.
- If R is taken as S, S’ becomes n1, coming at 177.777777, a ratio of 16/9.
- If G is taken as S, M becomes r2, coming at 106.666666, a ratio of 16/15.
- If G is taken as S, P becomes g2, coming at 120, a ratio of 6/5.
- If G is taken as S, S’ becomes d2, coming at 160, a ratio of 8/5.
- If G is taken as S, R’ becomes n2, coming at 180, a ratio of 9/5.
- If M is taken as S, N becomes m1, coming at 140.625, a ratio of 45/32.
- If M is taken as S, R’ becomes D2, coming at 168.75, a ratio of 27/16.
- If D is taken as S, R’ becomes at M2, coming at 135, a ratio of 27/20.
These 10 Shrutis and the 7 natural Shrutis together make 17 out of 22 Shrutis, directly emerging from 7 natural Shrutis. The remaining 5 Shrutis is just a matter of filling the blanks considering the symmetrical order of R,G,M, D, and N. 
Poorna, Pramana and Nyuna Shrutis
When the frequency and positions of all 22 shrutis are calculated, we get 3 ratios operating between 22 Shrutis as 256/243 (Pythagorean limma or Pythagorean diatonic semitone or Pythagorean minor semitone), 25/24 (a type of Just diatonic semitone) and 81/80 (Syntonic comma). Out of these, 81/80 operates in the 'region' of 10 notes and was called as 'Pramana', in Sanskrit meaning 'Standard' (region of the note). Out of the remaining 2 ratios, the bigger (256/243) was called as Poorna (in Sanskrit meaning 'big'), and the smaller (25/24) was called as 'Nyuna' (in Sanskrit meaning 'small'). Poorna comes between Shrutis 0-1, 4-5, 8-9, 12-13, 13-14, 17-18, and 21-22, Nyuna between Shrutis 2-3, 6-7, 10-11, 15-16, 19-20, and Pramana between Shrutis 1-2, 3-4, 5-6, 7-8, 9-10, 11-12, 14-15, 16-17, 18-19, 20-21. Now, it possible to play a precise note on a string every time without difficulty, because, irrespective of the length of the string or the frequency in which the string is tuned, 7 Poorna, 5 Nyuna, and 10 Pramana Shrutis yield sequentially, perfect playing positions of 22 Shrutis on any string instrument. To eliminate confusion, the words Poorna, Pramana and Nyuna should be called as ‘Shrutyantara’ (in Sanskrit) meaning distance between Shrutis rather than ‘Shruti’, which indicates a musical note. Poorna, Pramana and Nyuna Shrutis correspond respectively to Pythagorean Limma (90 cents), Diatonic Semitone Minor (70 cents), and Comma of Didymus (22 cents).
Shrutis in Shadja Grama
The basic Indian Scale was called as Shadja Grama in Bharata's Natya Shastra. It had 7 notes emanating at Shruti nos. 3, 5, 9, 13, 16, 18, and 22 (See figure below). The precise places to play these 7 notes on a string is already shown in the above table. Bharata divided the scale of 7 notes by 'no.' of shrutis (distance measured by no. of shrutis).
Figure showing Shadja Grama on a stretched string.
The 1st line shows Shruti nos. The 7 notes are in bold. The 2nd line shows the synonyms and the 7 notes as bold and underlined. The 3rd line shows the Shrutis 'in-between the 7 notes' as bold and undelined,
Bharata's Natya Shastra states in Chapter 28, Shloka 24 that S' is situated on the 4th shruti (after n1), M1 is situated on the 4th Shruti (after g1), P is situated on the 4th Shruti (after M1), R1 is situated on the 3rd Shruti (after S', the cycle repeats from the beginning), D1 is situated on the 3rd Shruti (after P), g1 is situated on the 2nd Shruti (after R1), and n1 is situated on the 2nd Shruti (after D1). Chaturdandi Prakashika (Sanskrit) by Pandit Venkatamakhin in Shloka 105 and 106, Chapter 4, narrates the same sequence of Shrutis as,
Chatush Chatush Chatush Cha Eva Shadja Madhyama Panchamou Dve Dve NishĀda GĀndharou Tri Tri Rishabha Dhaivatou 
Shadja, Madhyama and Panchama (situated on) 4, 4, and 4; Nishad and Gandhara (situated on) 2 and 2; Rishabha and Dhaivata (situated on) 3 and 3.
Thus, the 7-Note scale as indicated by this arrangement is R1, g1, M1, P, D1, n1 and S', and is called as 'Shadja Grama' in Natya Shastra. This scale is close to the current version of the Kafi (raga). Thus, the notes of Shadja Grama are situated on Shruti nos. 3, 5, 9, 13, 16, 18, and 22; and these notes are separated by 3, 2, 4, 4, 3, 2, and 4 shrutis respectively.
Shadja Grama (the 7 notes documented by Bharata in Natyashastra) is very much in use today, providing the perfect Swaras for Ragas such as Abhogi, Bageshri, Bhimpalasi, and Gorakh Kalyan in Hindustani Classical Music; and Abheri, Reethigowla, and Suddha Dhanyasi in Carnatic Music. All the other Ragas too are derived from selection of different Shrutis as shown in the diagram.
Shrutis in Madhyama Grama
The ancient Indian musicologists knew that the voice range of females is placed by nature at a 'higher' pitch than males. They, therefore created the scale for females, beginning on the 9th Shruti (M1) with a higher frequency. Hence, this scale was called as Madhyama Grama in Bharata's Natya Shastra. It had 7 notes emanating at the same shruti nos. as in Shadja Grama, i.e., 3, 5, 9, 13, 16, 18, and 22. The precise places to play these 7 notes on a string is already shown in the earlier table. The precise place to play the new shruti, P1 is shown below.
Figure showing Madhyama Grama on a stretched string.
The 1st line shows Shruti nos. The 7 notes are in bold. The 2nd line shows the synonyms and the 7 notes as bold and underlined. The 3rd line shows the Shrutis 'in-between the 7 notes' as bold and undelined
Bharata's Natya Shastra states in Chapter 28, Shloka 27 and 28, the shrutis in Madhyama Grama. As M1 functions as the 'new' Fundamental frequency (Shadja), M2 must become redundant as it is too close to it. Also, in this new scale, P from Shadja Grama operates as P2 or (musically, Ati-Tara Rishabha, see Nomenclature table below), and Tara Rishabha or a shruti at an Interval ratio 10/9 (Just Major Second) is absent. To create this missing Tara Rishabha, P2 must be lowered by Interval ratio of 81/80 (Pramana) creating a new shruti P1. Chaturdandi Prakashika (Sanskrit) by Pandit Venkatamakhin in Shloka 65 and 66, Chapter 3, confirms the positions of Panchama both in Shadja and Madhyama Gramas as,
Shadja GrĀma Panchame Swa Chaturtha Shruti Sansthite Swa-UpĀntya Shruti Sansthe Asmin Madhyama GrĀma Ishyate 
in Shadja Grama, Panchama is positioned on its 4th Shruti, and on its previous Shruti in Madhyama Grama.
This previous Shruti P1 has a frequency of 148.148 (if Shadja is taken as 100 hz), and can be played on 67.56% length on the string. The scale starting from M1 is close to the current version of Khamaj (raga). Now, the notes at 3, 5, 9, 13, 16, 18, and 22 becomes the Madhyama Grama, these notes are separated by 3, 2, 4, 3, 4, 2, and 4 shrutis respectively. Musically, P in Shadja Grama (3/2) operates as the Perfect 5th, and the same shruti (P2 in Madhyama Grama) operates as 9/8 (another ratio for Just Major Second) in Madhyama Grama, because the Fundamental frequency has changed to M1.
A combination of ‘Shrutis’ and ‘Nadas’ is the back-bone of Gamakas, and Alankaras
Both the types of Indian Classical Music namely the Hindustani, and the Carnatic, essentially employ a variety of musical phrases known as Gamaka (Music) (Carnatic) and Alankara (Hindustani). These phrases employ primarily a combination of 'Shrutis' (identified steady notes) and connecting Nadas' (unidentified fleeting notes) only. Chaturdandi Prakashika (Sanskrit) by Pandit Venkatamakhin in Shloka 118, Chapter 3, gives the description of Gamaka as,
Swarasya Kampo Gamakah, Shrotru Chitta SukhĀvah, Sweeya SthĀna Shruti Gatah ChhayĀm anyĀm ĀshrayĀm api 
Swara's movement creates Gamaka, delighting the listeners, going from the position of its own Shruti to reside in the shadow of another. Gamaka or 'Alankara' thus means a Swara goes from its own (identifiable) Shruti to the other, making use of (unidentified connecting) 'Nadas' in-between.
In any Gamaka (Music), Alankara, or 'Inflexion', 'Ornamentation' etc, one can not have a 3rd type of note, other than a 'Shruti' and a 'Nada'. The threshold of identification of a musical note within the range of human voice of 100-1000 Hertz is 20-45 msec. Shrutis can be identified by the human ear because they are played for this time limit or more. As against this, connecting Nadas are played faster than this limit, which disallows the human ear to identify them. The major difference in the 2 systems is the 'way' in which a combination of 'Shrutis' and 'connecting Nadas' is made, resulting in a characteristically different flavour of music in both the styles. Many ancient Sanskrit and Tamil works refer to 22 Shrutis as the foundation of the Indian Music Scale.
The system of 72 basic types of singing or playing scales (Thatas) was evolved with specific mathematical combinations of the universal 12 pitch classes. The selection of the 22 Shrutis (specific frequencies) in each of them depends on the 'Raga' chosen. The Shrutis in a Raga should be ideally related to each other, by natural ratios 100:125, 100:133.33, 100:150, and 100:166.66. 'Raga' can have a 'lesser' no. of notes than those in a 'Thata'. Therefore Shrutis can be selected only 'after' the selection of a Raga. Melakarta 72 Thatas therefore do not have 'prescribed' Shrutis with them. Only 'Raga' can have shrutis, not 'Thata'. Alaku is a name for Shruti in ancient Tamil music and 22 Shrutis are referred to as 22 Alakus. All the 22 Shrutis attain the status of Swaras, in some raga or the other.
Nomenclature of 22 Shrutis/Swaras in Carnatic Music and Hindustani Classical Music
The Nomenclature in Carnatic and Hindustani systems has been imperfect largely due to the ignorance about the scientific facts about 12 Swaraprakaras (Chromatic pitch-classes) and the inter-spaced 22 Shrutis. In Carnatic nomenclature, for example, the 'Eka'-sruthi Rishabham (called as Suddha Rishabham) is followed by 'Chatu'-sruthi Rishabham, omitting the 'Dvi' and 'Tri'-sruthi versions of Rishabham. The same is true of Daivatham too. In reality, the 'Eka'-sruthi Rishabham (as a Swaraprakara) has 'Eka'-sruthi Rishabham and 'Dvi'-sruthi Rishabham (as it's 2 sruthees). Further, the 'Chatu'-sruthi Rishabham (as a Swaraprakara) has 'Tri'-sruthi Rishabham and 'Chatu'-sruthi Rishabham (as it's 2 sruthees). The same is true of Daivatham. Also, there is the creation of an additional name each for Chatu-sruthi Rishabham, Sadharana Gandharam, Chatu-sruthi Daivatham and Kaishiki Nishadam; respectively as Suddha Gandharam, Shat-sruthi Rishabham, Suddha Nishadam and Shat-sruthi Daivatham. These apparent omissions and additions confound the Carnatic Nomenclature. The all-inclusive Nomenclature for 12 Swaraprakaras and 22 Sruthis is shown in the Table.
Table shows Nomenclature for 12 Swara-prakaras and 22 Shrutis in Carnatic Classical Music.
Similarly in Hindustani Music, the names of 'Komal' and 'Shuddha' Swaras have no uniformity. The Rishabha, Gandhar, Dhaivat and Nishad have the 'Komal' version first followed by 'Shuddha'; whereas for Madhyam, there is the 'Shuddha' version first followed by 'Teevra'. These names have also been carried forward due to ignorance about the meanings of these names, and also about 22 Shrutis. 'Komal' is the 'flatter' variety of the note and the correct name for the 'sharper' version is 'Tara', not 'Shuddha'. 'Teevra' (in Sanskrit) means 'of a larger volume', not 'of a higher frequency'! Hence, 'any' note such as Rishabha, Gandhar, Madhyama, Dhaivata and Nishad can be Teevra, or of a larger volume. The correct 12 names of Hindustani 12 notes are 1) Shadja, 2) Komal Rishabha, 3) Tara Rishabha, 4) Komal Gandhara, 5) Tara Gandhara, 6) Komal Madhyama, 7) Tara Madhyama, 8) Panchama, 9) Komal Dhaivata, 10) Tara Dhaivata, 11) Komal Nishada, and 12) Tara Nishad. 'Komal' notes are subdivided into their Shrutis 'Ati-Komal' (Lower frequency version) and 'Komal' (Higher frequency version); and 'Tara' notes into 'Tara' (Lower frequency version) and 'Ati-Tara' (Higher frequency version). Out of the 22 notes thus created, the word 'Shuddha' denotes 'purity' and signifies those notes which come with a natural ratio of 100:125:150. 7 of the 22 notes (see table) are thus adiitionally called as 'Shuddha'. The complete Nomenclature for 12 Swaraprakaras and 22 Shrutis in Hindustani Classical Music is shown in the Table.
Table shows Nomenclature for 12 Swara-prakaras and 22 Shrutis in Hindustani Classical Music.
(* Seven Shuddha Notes in the table are underlined and bold)
The 12 Swaraprakaras and 22 Shrutis in both the Hindustani and Carnatic Tables are exactly the same; in terms of Ratios, Frequencies and % of length of the string where they are played.
Sanskrit Names of 22 Shrutis
Sangita Ratnakara of Sarangadeva states in Chapter 3, shlokas 35 to 38 that Teevra, Kumudvati, Manda and Chandovati are the names of shrutis for Shadja. As Shadja is placed on the 4th shruti in this group, this means that Chandovati is the name for the shruti of Shadja. The reference further mentions in further sequence; Dayavati/ Ranjani/Raktika as shrutis for Rishabha, Roudri/Krodha for Gandhara, Vajrika/ Prasarini/Priti/Marjani for Madhyama, Kshiti/Rakta/Sandipani/Alapini for Panchama, Madanti/Rohini/Ramya for Dhaivata, and Ugra/Kshobhini for Nishada.
Why an analysis of the performances of Stalwarts will never give true values of 22 Shrutis ?
It is suggested time and again that the best way to find the exact positions of Shrutis would be, 'by analyzing the frequencies used by the stalwarts in actual performances'. This sounds simple, but runs the risk of giving multiple inaccurate values. In fact, when different artists performed raga Yaman on flute, sarangi, sitar, and voice; accuracy of pitch was found to be 'relative' and 'subjective', and 'neither rigidly fixed','nor randomly varying'. Further, the 'same Swara was pitched differently at different times by the same artiste in the same raga', and 'different artistes intoned the same swara differently in the same raga'. Such an exercise is akin to finding the centre of a circle by analyzing the positions of arrows shot by the archers on the board. This can give multiple answers without any indication of which one is accurate. It would be more scientific to find the centre of a circle by 'Mathematical' means. Similarly, the values of 22 shrutis can be precisely found out by 'Mathematics' based on their natural relationships from the 22 Shruti-Mandal (Organogram) rather than an analysis of performances by stalwarts.
Ancient treatises on Indian classical music and performing arts
- Natya Shastra by Bharata
- Dattilam by Dattila
- Brihaddeshi by Matanga Muni
- Abhinavabharati - Abhinava Gupta's commentary on Natya Shastra
- Sangita Ratnakara by Sarangadeva
- Svaramelakalanidhi by Ramamatya
- Charurdandi Prakashika by Venkatamakhin
- Ragavibodha by Somanatha
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- Ibidem. p. 28.
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