Shruti Veena: Manifestation of Bharat’s Gram and ChatuhSarana

By Dr. Lalmani Misra



The subject fundamentally expounded by Bharat is Natya (theatre). There is no knowledge, skill or art that is not employed by it.

Na tachchutam na sa vidya na sa nyaso na sa kala

Na Sa yogo na tatkarm yannatyeδsminna drishyate

Hence music too has been discussed as a part of this natya. Maharishi Bharat has categorised music into ten elements: Shruti, Swar, Gram, Murchhana, Vritti, Sthan, Varna, Alankar, Dhatu and Jati. Here we shall discuss Shruti, Swar, Gram and see how they can be determined.

The seven swar-s mentioned by Bharat are Shadja, Rishabh, Gandhar, Madhyam, Panchan, Dhaivat, and Nishad.

Shadjascha rishabhashchaiva gandharo madhyamstatha

Panchamodhaiwatashchaiv saptamashcha nishadavan

In the nomenclature thus obtained, he has indicated by calling Nishad the seventh that the notes follow the order from Shadja. From Shadja to Tar Shadja there are twenty two Shruti-s in the order, three, two, four, three, two, four.

Tisro dwei cha chatasrascha chatasrastisra eva cha

Dwei chatasrashcha shadjakhye grame shrutinidarshanam

These Shruti-s are smaller fragments of sound which can be called micro-tones. The collection of these sounds is called Gram. The Shruti-s in gram move down the scale, i.e., four Shruti-s of Shadja lie between Shadja and Nishad, the two of Nishad between Nishad and Dhaivat. This is in contrast to order of the swara-s moving from Shadja to Nishad; in other words gram is awarohi (descending).























































On the number of Shruti-s, Bharat has determined the inter-relationship between notes. He ordains that on considering any note in the gram as sonant the note nine or thirteen Shruti-s away would act as consonant and the one distanced two or twenty Shruti-s away would act as dissonant to it; the rest would be assonant to it.

Yayoshcha nava trayodashakam parasparatah shrutyantare tavanyonyasamvadinou

Yatha shdja-panchamou, rishabh-dhaivatou, gandhar-nishadou, shadja-madhyamviti shadjagrame

Hence notes situated nine or thirteen Shruti-s away are mutually consonant, e.g. in Shadja-gram, notes Shadja-Pancham, Rishabh-Dhaivat and Gandhar-Nishad are consonant to each other. The institution of consonant and dissonant is very important. The two notes that on simultaneous production give forth pleasant or desirable sound are consonant; the two which create harsh or unpleasant sound are dissonant to each other.

The Swara-s of Bharat

In the modern times, scholars have endeavoured to uncover the notes used in Bharat Gram. Influenced by Sharangdev, some have assumed the 22 Shruti-s to be equidistant. If we start with this premise, the value of a Shruti can calculated to be 22√2 or twenty times the root of 2. In the decimal calculation it comes to 1.032. The value thus of bi-microtone would be (1.032)2 of the tri-microtone (1.032)3 and the tetra-microtone, (1.032)4. If with the above calculation we prepare a scale, the notes obtained create discord1. So much so, that the melodic affinity or consonance of Shadja-Madhyam, Shadja-Pancham too get destroyed. The law of consonance is so universal that it is found in the music of aborigines and even in animal-music.2 Hence hypothesis of equi-distant Shruti-s is not valid.

The western scholars of music have tried to interpret Indian scale by approximating tetra-microtone to major tone (9/8) guruswar, tri-microtone to minor tone (10/9) laghuswar and di-microtone to semitone (15/16) ardhaswar

It can be assumed that with advent of civilization, the music-scholars of those times might have realised the Shadja-Madhyam and Shadja-Pancham consonance. In keeping with the universal law of consonance the places of Madhyam and Pancham in Bharat gram get fixed. The Gandhar-Madhyam and Nishad-Shadja interval too is tetra-microtonic. Thus their value is 9/8. On reducing 9/8 from Madhyam (fixed at 4/3) we obtain the interval of Gandhar from Shadja to be 4/3 x 8/9 = 32/27. Similarly on reducing Shadja by 9/8 we get interval of Nishad from Shadja to be 2 x 8/9 = 16/9.

On the principle of consonance we can obtain value of Gandhar, Madhyam, Pancham and Nishad in Bharat gram on basis of present practice. Two notes of the gram can be fixed through principle of dissonance. Bharat points that notes with interval of two or twenty are dissonant as are Rishabh-Gandhar and Dhaivat-Nishad. Like consonance this too is backed by universal experience. That Bharat pointed out dissonance not only proximate notes but in notes situated twenty Shruti-s apart in Madhya-Tar and Madhya-Mandra. Helmholtz has established scientifically that the maximum dissonance occurs when the interval between them is 16/15. It can thus be assumed that the value of Bharat’s di-microtonic dissonant interval is 16/15. Reducing 16/15 from Gandhar 32/27, we get 10/9 as value of Rishabh and the same from Nishad 16/9, 3/5 is obtained as value of Dhaivat.

So, on the basis of consonance and dissonance we obtain the notes in Bharat’s gram.



































Indian Musical Scale?

Bharat did not start with Shruti as the unit of musical scale. (It was to recreate the lost Bharat gram that we used reverse logic here). With notes as fundamental, he determines Shruti-s from them. He dictates that taking two similar Veena-s they should be tuned together in Shadja. He says,

Dwe Veene tulyapramantantryupavadanadand murchhane Shadja gramashritekaryaye

He clearly ordains that for Sarana two absolutely similar Veena should be taken that have same kind of strings, the Shadja gramic saptak is tuned in unison, the plectrums for strumming them should be similar and murchhana for both should be same.

Bharat prefers a single hand for this process. He says,

Etesham cha swaranam nyunadhikatwam tantrivadanadandendriyaveyigunyadupajayate

Let a single person do the Sarana, for a slight difference in string, plectrum or sense gives rise to unwanted increase or decrease in notes. Of the two Veena-s used the standard or reference one is called Achal or fixed Veena. The other is known as Chal or changeable Veena.

Tayorekatarasyam madhyamgramikim kritwa panchamasyapkarshe shrutim

First Descension

Lower the Pancham of ChalVeena so that it is in consonance with Rishabh of AchalVeena. The difference between the original and changed Pancham of ChalVeena is the first or PramanaShruti. In the next step, the remaining strings of ChalVeena are lowered as much as Pancham was lowered.

Tameva pancham vashat Shadja gramashritekuryat

Now all notes of ChalVeena are one Shruti lower than AchalVeena.

Second Descension

Once again, lower Gandhar and Nishad of ChalVeena to match Rishabh and Dhaivat of AchalVeena.

Punarapi tadvadevapkarshad gandharnishadavantavitarasyam

Dhaivatarshabhou pravishatah (dwi) shrutyadhikatvat

Next the remaining notes are to be lowered in proportion to Shadja gramik scale. After the second Sarana, all notes of ChalVeena are two Shruti-s lower than the reference AchalVeena. It would be meet to point out that some scholars get disoriented by the phrase tadvat It has been used as an adverb in keeping with spirit of Maharishi Panini’s sutra, “ten tulyam kriya chedvatih". Bharat does not mean that each time the lowering begins with Pancham when he uses “tadvat”.

Third Descension

Lower the Rishabh and Dhaivat enough to tune absolutely with Shadja and Pancham of AchalVeena.

Punastadvadevapkarshad dhaivatarshabhavitarasyam

pancham shadjou pravishatah (tri) shrutyadhikatvat

Lower the other notes to tune in Shadja gramik scale. Now every note in the ChalVeena is lower than corresponding ones in AchalVeena by three Shruti-s.

Fourth Descension

The MadhyamPancham and Shadja of ChalVeena should be lowered now to tune with Gandhar, Madhyam and Nishad of of AchalVeena respectively.

Tadvutpunarapakrishtayam cha tasyam panchamamadhyashadja itarayam

Madhyamagandhar nishadavantah pravekshyantih chatuh shrutyadhikatvat

On tuning the remaining notes proportionate to Shadja gramik scale, we shall obtain a scale four Shruti-s lower than the standard one on AchalVeena.

Value of the Shruti-s

By Sarana or lowering of the notes in manner described above, the value of Shruti-s can be mathematically expressed as:

Shruti -s of the first Sarana or descension: 81/80 ≈ 5 Savart

Shruti -s of the second Sarana or descension: 256/243 ≈ 23Savart

Shruti -s of the third Sarana or descension: 25/24 ≈ 18 Savart

Shruti -s of the fourth Sarana or descension: 81/80 ≈ 5 Savart

The value 81/80 is called coma, 256/243 limma and 25/24 is called semitone. According to this analysis the following may be derived:

1. Chtauh Shrutik swar = comma+ limma+ semitone+ comma

≈ 81/80x 256/243x25/24x81/80

≈ 5 + 23+ 18 + 5 = 51 Savart

2. Tri Shrutik swar = comma+ limma+ semitone

≈ 81/80x 256/243x25/24

≈ 5 + 23+ 18 = 46 Savart

3. Dwi Shrutik swar = comma+ limma

≈ 81/80x 256/243

≈ 5 + 23 = 28 Savart

In this manner through process of Sarana on two similar Veena-s, we are able to determine the twenty two Shruti-s, but the earlier notes on ChalVeena vanish after each descension. Hence it is not possible to know all the twenty two Shruti-s at the same time. This drawback of the process kept irking me and inspired me to create an instrument on which we would we able to produce all the Shruti-s together and understand their interrelationship by listening to them simultaneously. Thus, experimenting in various ways I could finally find an instrument on which this would be possible. I modified the north Indian RudraVeena so that it could produce all twenty two Shruti-s simultaneously. I wish to describe it so that all desirous of listening to them may create an instrument and hear Bharat’s Shruti-s.

I first describe how I determined the Shadja gram of Bharat and carrying out the four descensions of Sarana heard the twenty two Shruti-s.

Before venturing forth for Sarana as described by Bharat, it is essential to obtain his Shadja gram. It has been stated earlier that this is founded upon the Shadja-Pancham union; hence, I started with this premise.

I selected two Sitar-s of equal build with open Jawari. As all practising artistes know that unless the jawari is well done it is difficult, if not impossible, to tune any instrument. I tuned the Baj strings of both Sitars in unison with each other. Normally these strings are tuned in Mandra Madhyam, but for the sake of determination of Shadja gram I assumed the Mandra Madhyam of the unfettered or free string to be Shadja. So under the temporary arrangement, consider that the free strings produce Shadja. Before proceeding further I once again ascertained that the two strings are in perfect accord. Then, in one of the Sitar-s I tuned the Pancham fret with the free string of the other. The fret we normally consider to be Madhya Shadja would become the Pancham fret, but is necessary to see whether it is in place of Pancham in relation to the free chord of the first Sitar. For an astute artiste it is not difficult to set the Pancham fret while listening to the free chord of the other Sitar. Now on the basis of this Pancham the fret of the first Sitar is set to Pancham. Now Shadja and Pancham of the two Sitar-s sound the same.

Shadja and Madhyam

We shall play the free string of the first Sitar presumed as Shadja and fix the fret of Madhyam in the second Sitar on its basis. Playing the second Sitar with corrected Madhyam, we shall set the Madhyam fret on the first Sitar as well. Thus we obtain, ShadjaPancham and Madhyam on both Sitar-s.


Playing this corrected Madhyam fret on the first Sitar we temporarily assume it to be Shadja. On the basis of Madhyam-incarnated Shadja playing on the first we determined the Madhyam to Shadja on the second Sitar, playing the two notes as if they were actual ShadjaMadhyam. On the basis of corrected Madhyam fret on the second Sitar we corrected the fret on the first Sitar as well. Thus on assuming Madhyam to be Shadja the Madhyam we obtained was actually Bharat’s Nishad which is situated nine Shruti-s away from Madhyam and five Shruti-s from Pancham.


Once again we assume the Nishad fret on the first Sitar to be Shadja and determine the place of Madhyam in the descending order on the second Sitar. When we fix the Madhyam fret on the second Sitar in descending order to Nishad-incarnated Shadja on the first, we resolve the Gandhar of Bharat. On the basis of Madhyam established on second the fret of the first also suitably positioned.

Before proceeding any further is necessary to check the two instruments. It is quite common for string instruments to get out of tune after being played for some time. So the two Sitar-s should once again be brought in tune, confirming that no fret is out of tune.


Through the above process, so far Shadja, Gandhar, Madhyam, Pancham and Nishad have been obtained; we have to obtain Dhaivat and Rishabh. For this we shall have to seek recourse to Shadja, Shadja-Pancham consonance and Shadja-antar consonance. All astute artistes are conversant with the fact that while strumming the mandra-Shadja on Tambura or atimandra-Shadja on Sitar, one can distinctly hear the Gandhar, situated seven Shruti-s away from Shadja. As the note arises out of sympathetic vibration, it is called Swayambhoo (self-evolved) Gandhar. This Swaymbhoo Gandhar lies at the core of Shadja-antar consonance. Due to its fixed and pleasant interaction, The Gandhar or Shadja-antar consonance is universally acclaimed. It is said that through this Tumbru Rishi was the first to see Dhaivat. Hence, the Shadja-antar consonance shall be used in resolving Dhaivat.

We can use this in two ways. First is to consider Madhyam to be Shadja and find Swaymbhoo Gandhar that shall be Dhaivat. Else we can determine the true Gandhar with actual Shadja and then considering Gandhar as Shadja, we resolve its Madhyam that shall become Dhaivat.

Both methods yield the same note, the difference lying in the method of resolution alone. So, I preferred the first and playing the Madhyam fret of the first Sitar repeatedly, obtained the Gandhar on the second and fixed the Dhaivat fret on it. One can obtain Gandhar on the second Sitar on the basis of thus resolved Dhaivat on the first. Now, we have Bharat’s Dhaivat on both the Sitar-s.


It is not much of a problem to obtain Rishabh now. Playing Dhaivat on the first Sitar repeatedly, assuming it to be Shadja, Madhyam is determined in descending order on the second Sitar. With Dhaivat-incarnate Shadja, the Madhyam obtained in descending order is Bharat’s Rishabh. In accordance with Rishabh obtained on the second, the first Sitar too is matched with Rishabh fret in position. In this manner the two Sitar-s are now tuned in accordance with Bharat’s Shadja gram.

That both the Sitar-s are properly tuned in Bharat’s Shadja gram should be confirmed before proceeding further. Careful evaluation on two counts expounded by Bharat would ease the process. Bharat ordains that interval between Shadja and Rishabh is of 3 Shruti-s, between Rishabh and Gandhar 2 Shruti-s, 4 Shruti-s between Gandhar and Madhyam, 4 between Madhyam and Pancham, 3 between Pancham and Dhaivat, 2 Shruti-s between Dhaivat and Nishad and 4 between Nishad and TarShadja. Secondly, Shadja-Pancham consonance is at interval of 13 Shruti-s, Shadja-Madhyam consonance at 9 Shruti-s and Shadja-antar consonance at interval of 7 Shruti-s.

Now, the Shadja-Pancham and Shadja-Madhyam we obtained are at intervals of 13 and 9 shruti-s respectively. Applying Shadja-Madhyam consonance to Madhyam-incarnate-Shadja, the Nishad we obtained is at an interval of 9 shruti-s from Madhyam. Interval between TarShadja and Madhyam is 13 shruti-s, hence it is evident that interval between obtained Nishad and TarShadja being 4 shruti-s as given by Bharat, our process has retained mathematical integrity. Examining from various possible angles, one can conclude that the Nishad above is of Bharat gram.

In the descending order the interval between Shadja and Madhyam is of 13 shruti-s. To wit, the interval between Shadja-Pancham in the ascending order is the interval between Shadja-Madhyam in the descending order. Similarly in the descending order Nishad is 13 shruti-s from Gandhar and this Gandhar is 5 shruti-s beyond primary Shadja and 4 shruti-s prior to Madhyam. In this way too is it is situated as given by Bharat.

After this we considered Madhyam to be Shadja and obtained Dhaivat through Shadja-antar consonance. This consonance occurring at interval of 7 shruti-s, the Dhaivat obtained was situated 7 shruti-s beyond Madhyam. Thus its interval from Madhyam is 7, from Pancham 3 and from Nishad is 2 shruti-s, which was what Bharat decreed.

Rishabh obtained through Dhaivat-incarnate Shadja is spaced at 13 shruti-s from Dhaivat, like Nishad above is from Gandhar. The interval of this Rishabh, from primary Shadja is 3 and from Gandhar is of 2 shruti-s.

It is evident that there lies an interval of 13 shruti-s between Shadja-Pancham, Rishabh-Dhaivat, Gandhar-Nishad and between Madhyam to TarShadja.

There can be no doubt that the two Sitar-s tuned through above process carry Bharat’s Shadja gram. I have demonstrated this on Sitar to many leading instrumentalists, artistes and scholars of the country and they have agreed with my hypothesis. A Sitar tuned in this manner can be played and it is interesting to observe the difference between modern chatuh-shrutik Rishabh and Bharat’s tri-shrutik Rishabh; how panch-shrutik Gandhar sounds different from shashth-shrutik Gandhar and which notes in a particular Raga sound more natural and obvious than others.

Chatuh Sarana

After establishing the notes of Bharat’s Shadja gram in the manner described above, I modified the North Indian RudraVeena and carrying out the chatuh-Sarana established the Shadja gram as well as twenty two shruti-s on this instrument.

The author then gives a detailed description by which Rudra Veena is modified into Shruti Veena and demonstrates how instead of two Sitars the strings on this single instrument are capable of establishing first Bharat’s Shadja gram and then obtains all 22 shruti-s. This part is not being given here lest it seem a repetition to less keen readers.

1 G.H. Ranande, Hindustani Music. p.34

2 Lalit Kishor Singh, “Sangeet ka Vikas” in Janvani




Details of Shruti Veena

References :

Excerpts from Bharatiya Sangeet Vadya -- Dr. Lalmani Misra

Time Theory of Raga-s  -- Dr. Lalmani Misra

Points to Ponder: Some Do’s for Musicians -- Dr. Lalmani Misra

Dr. Misra and I -- Nancy Nalbandian

Contemporary Problems for Indian Music -- Dr. Lalmani Misra

Dr. Lalmani Misra on Wikipedia डॉ लालमणि मिश्र विकीपीडिया पर

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