The proof of 22 Shrutis

CHATUH-SAARANA

The cornerstone of the theory of Hindustani Classical music is the concept of ‘shruti’. The theory that the natural Saptak (or octave) comprises of 22 shrutis is, in a way, a natural corollary to the ancient theory that one can perceive the natural sound produced by the human body, that is referred to as ‘Naad’ in twenty-two frequencies[1] and hence (is believed) to be generated from the 22 naadis (energy-channels) that spring out of the Oordhvanaadi (or Sushumna naadi) which passes through the human body to culminate into the cerebrum.

In a strict musical sense, however, it is necessary to locate and ascertain the measure and position of the 22 shrutis in the Saptak in a systematic and scientific manner. The Chatuh Saarana procedure was first suggested by Bharat Muni for this very purpose, which was further clarified subsequently by Sharangdev, with some modifications.

Before we move on to the procedure, one must remember that the experiment is to be conducted on the veena. While Bharat prescribed the procedure to be carried out on a 7-stringed veena, Sharangdev employs two veenas of 22 strings each. The logic behind using two twenty two-stringed veenas is;

firstly, that Sharangdev reserves a separate string each for all the 22 shrutis, which makes the process of measuring and quantifying the shrutis obtained in the course of the experiment very simple;

secondly, that while it is impossible to test or verify the results of each step in the procedure without a fixed reference in Bharat’s experiment, the veena with fixed frets (or Dhruv veena) in Sharangdev’s experiment facilitates this process by playing the role of a standard measure[2]. All the changes to be made during the experiment are carried out on the Chal veena (the veena with moveable frets) and are tested and verified on the Dhruv veena. Also, it is possible to perceive all twenty-two shrutis on the 22-stringed Dhruv Veena[3].

We ought to note that this procedure can be successfully carried out on an instrument, and not through the human voice. Although the sound that both Bharat Muni or Sharangdeva refer to is the sound that manifests in the human body from the throat, the twenty-two shrutis that comprise the musical sound are not easily discernible in the human voice. It is difficult to perceive the subtle difference between each microtone in the human voice. Besides, the voice can only produce each shruti progressively, in succession. It is not possible to study the Samvaad between more than one notes, brought out by the differences in the shrutis, simultaneously, in the singing voice. One requires two sounds to operate at once, which is eminently possible if one makes use of two veenas. Also, the sound of the strings is more discernible than the voice. It is also very convenient to repeat the procedure in order to verify one’s findings, on an instrument. Therefore, the ancient musicians have prescribed the veena as a means to prove the validity of the twenty-two shruti theory.

While the word ‘Saarana’ literally means ‘to move’ (downwards) or to lower, it must imply in this context,the process of establishing the notes by adjusting the strings suitably. One may note that in order that the notes of one veena merge into those of the other, one may also have to tighten certain strings.

The reader will notice the ‘/’ symbol in certain Sanskrit words transliterated to English. This is for the convenience of the reader, to break a particularly long compound-word while reading. This has not been done on the basis of the strict rules of Sanstkrit grammar, but is merely for the convenience of the reader unfamiliar with the Sanskrit language.

Finally, may it please the interested reader to refer to the original text of the treatise for sharpening one’s understanding of such a crucial subject. This is a translation from the scholarly commentary on the Sangeetratnakar, by Smt. Subhadra Chowdhury. Any discrepancies in this paper may be attributed to the limitations of the translator.

Saarana Chatushtay (The four rounds of Saarana)

सारणाचतुष्टयेन श्रुतिनिदर्शनम्

Saarana Chatushtayena Shrutinidarshanam

Establishing the twenty-two shrutis through the procedure of Chatuh-Saarana

VERSE Nos. 10 (PART 10) & 11 (PART 1)

व्यक्तये कुर्महे तासां वीणाद्वन्द्वे निदर्शनम् ॥१०॥

Vaktaye Kurmahe Taasaam Veenadwandwe Nidarshanam

द्वे वीणे सदृशौ कार्ये यथा नाद: समो भवेत्

तयोर्द्वाविंशतिस्तन्त्र्य: प्रत्येकम्,

Dwe Veene Sadrushou Kaarye Yathaa Naadah Samo Bhavet

Tayordwavinshati/stantryah Pratyekam,

Translation:(We require) two veenas in order to ascertain the (twenty-two) shrutis. Both the veenas must be made identical, in order that they produce the same (quality of) sound. The two veenas must have twenty-two strings each.

VERSE Nos. 11 (PART 1) &12

तासु चादिमा ॥११॥

Taasu Chaadimaa

कार्या मन्द्रतमध्वाना द्वितीयोच्चध्वनिर्मनाक्

स्यान्निरन्तरता श्रुत्योर्मध्ये ध्वन्यन्तराश्रुते: ॥१२॥

Kaaryaa Mandratamadhwaanaa Dwiteeyochcha/dhwanirmanaak

Syaannirantarataa Shrutyormadhye Dhwanyantaraa/shruteh

Translation: The very first string of both the veenas ought to be tuned to the lowest possible pitch (sound). The second string (of both the veenas) must be tuned to the sound that is only a little higher than the preceding one. This (arrangement of sound) makes sure that there is a continuous (unbroken thread) between both the sounds (of the two strings), since no sound other than the one produced by each of the strings respectively, can exist between the two (established on the first two strings) of the veenas.

Note-

In the first stage of preparation of the veenas, before commencing the Saarana procedure, one must remember that the author does not refer to ‘tuning’ in the strict musical sense. By ‘sound’ or ‘shruti’, the author refers to a ‘tangible and audible sound’. The first string is therefore tuned in such a manner that it shall cease to resonate if it is loosened further. The tightness of the string should be only so much that it procduces a discernible sound. Similarly, the next string ought to be only so tuned that it is a shade higher than the previous one, meaning thereby, that if it is loosened even a little, the sound it shall then produce shall be the same as that of the preceding string. The two strings do not produce ‘samvaad’, nor are they expected to do so.

VERSE- 13 (PART 1)

अधराधरतीव्रास्तास्तज्जो नाद: श्रुतिर्मत:

Adharaadharateevraa/staastajjo Naadah Shrutirmatah

Translation: (Thus), the strings of the veena are tuned, respectively, to a progressively increasing frequency of sound, (as we proceed) downwards (along the veenas). We regard the sound that is generated (by the strings) as ‘shruti’ (or discernible sound).

Note-

The ‘first string’ mentioned in the preceding verses refers to the first string from the side of the veena-player. Thus, the author refers to the strings ‘proceeding downwards’ along the veenas. It is interesting to note that the sound produced in singing increases in frequency as it travels upwards, through the human body. This is opposite to the case in veena. Also, it is necessary to remind ourselves that the author, in the first limb of verse no. 13, has still not referred to ‘shruti’ in the musically relevant sense. He still talks about shruti as a tangible sound.

The following verses prescribe the procedure of establishing the twenty-two musical shrutis on the veenas.

VERSE NO. 13 TO 16

स्वरस्थापनम्

Swarasthaapanam (establishing the notes)

वीणाद्वये स्वरा: स्थाप्यास्तत्र षड्जश्चतु:श्रुति:।।१३।।

Veenadwaye Swaraah Sthaapyaastatra Shadjash/chatuhshrutih

स्थाप्यस्तन्त्र्यां तुरीयायामृषभस्त्रिश्रुतिस्तत:

पंतमीतस्तृतीयायां, गान्धारो द्विश्रुतिस्तत: ॥१४॥

Sthaapyas/tantryaan Tureeyaayaam/rushabhas/trishrutistatah

Panchameetas/truteeyaayaam, Gaandhaaro/dwishrutistatah

अष्टमीतो द्वितीयायां, मध्यमोS चतु:श्रुति:

दशमीतश्चतुर्थ्यां स्यात्पंचमोS चतु:श्रुति: ॥१५॥

Ashtameeto Dwiteeyaayaam, Madhyamotha Chatuhshrutih

Dashameetash/chaturthyaam Syaatpanchamotha/chatuhshrutih

चतुर्दशीतस्तुर्यायां, धैवतस्त्रिश्रुतिस्तत:

अष्टादश्यास्तृतीयायां निषादो, द्विश्रुतिस्तत: ॥१६॥

Chaturdasheetas/turyaayaam, Dhaiwatas/trishrutistatah

Ashtaadashyaas/truteeyaayaam Nishaado, Dwishrutistatah

एकविंश्या द्वितीयायां,

Ekavinshyaa Dwiteeyaayaam

Translation-Both veenas ought to be tuned first. The Chatuhshruti Shadja must be established (tuned) on the fourth string (of both the veenas). Consequently, the Trishruti Rishabh must be established on the third string from the fifth one (i.e., the seventh string). Then, the Dwishruti Gandhar must be established on the string next to the eighth string (i.e., the ninth string). As a consequence, the Chatushruti Madhyam shall lie on the fourth string from the tenth (i.e., the fourteenth string). Now, the Chatushruti Pancham will be established on the fourth string from the fourteenth (i.e., the seventeenth string), the Chatuhshruti Dhaivat on the third string from the eighteenth (i.e., the twentieth string)and (finally), the Dwishruti Nishad (must be established) on the string next to the twenty-first (i.e., the twenty-second string).

Note-

The above cluster of verses are indicative of the fact that the process of establishing musical notes (and their determinative shrutis) shall be commenced from this stage onwards. The author (Sharangdeva) does not mention that the notes tuned on the veenas must be those of the ‘Shadja Gram’. However, the arrangement of the notes, determined by the prescribed distances of the shrutis (as established on the strings in the previous stage) indicates that Sharangdeva intended that the veenas must be tuned to Shadja Gram. Bharat Muni, on the other hand, mentions this explicitly in his treatise, the Natyashastra[4].

Neither does the author mention howthe notes are to be determined and placed in this step, nor do any of the (old) commentators of this work (or the works of Bharat) throw light on this problem. The most plausible explanation to this seemingly significant lapse is that the trained musicians or experts of Sharangdeva’s or Bharat’s times must be expected to have been extremely well-grounded in their knowledge of the placement of notes in the Shadja Gram, and therefore the authors must not have found it necessary to explain the same. Since the modern musicians conceive the Saptak (the musical octave) in a manner quite different from that in the ancient times, the lack of sufficient information on this poses a problem in conducting this procedure now.

(The commentator Smt. Subhadra Chowdhury seeks to resolve this problem by ascertaining the exact location of the notes of the Shadja Gram with the help of the established theory of ‘Samvaad’ between particular notes of the Saptak of Shadja Gram. The Sa-Pa, Re-Dha and Ga-Ni of the Shadja Gram create the Shadja-Pancham samvaad, while Ma-Ni make Shadja-Madhyam Samvaad. The commentator uses these particular details, alongwith other established intricacies, to locate the notes on the veenas by calculating the shruti-distance between the said notes that is required to create the said effect. The shruti distance is suggestive of which string on which we ought to start the procedure. The interested reader may refer to the original commentary of this book for a detailed study of the subject)[5].

VERSE NOs. 16 (PART 2) &17 (PART 1)

वीणाकाSत्र ध्रुवा भवेत्

Veenakaatra Dhruvaa Bhavet

चलवीणा द्वितीया तु तस्यां तन्त्रीस्तु सारयेत् ॥१७॥

Chalaveena Dwiteeyaa Tu Tasyaan Tantreestu Saarayet

Translation:Among the two veenas, one must be ‘fixed’ or ‘Achal/Dhruv’(the frets of the veena should be fixed). The other veena must be ‘moving’ (or adjustable- ‘Chal’ veena). The strings (frets) of this (second) veena must be moved (or adjusted).

प्रथमा सारणा

PRATHAMAASAARANA

VERSE NOs. 18 & 19 (PART 1)

स्वोपान्त्यतन्त्रीमानेयास्तस्यां सप्तस्वराबुधै:

धृववीणास्वरेभ्योSस्यांचलायांतेस्वरास्तदा॥१८॥

Swopaantya/tantree/maaneyaas/tasyaam Sapta Swaraa Budhaih

Dhruvaveena/swarebhyo-/syaam Chalaayaam Te Swaraastadaa

एकश्रुत्यपकृष्टा: स्यु:,

Ekashruty/apakrushtaah Syuh

Translation: (In the first round of Saarana) all seven notes of the Chal veena must be brought to their penultimate string (i.e., the string immediately preceding the one on which they were originally established), by the experts (experimenter). By doing so, the notes on the Chal veena get lowered by one shruti, in comparison to (the position of) the notes on the Dhruv veena.

Note-

The first Saarana brings out certain facts that have been described below. We must note some points:

  1. 1. Procedure:

Sharangdeva does not indicate how and where one must start the shifting (adjustment) of notes in the first Saarana.  However, Bharat has shed some light on this point[6] .The first limb of the Chatuh Saarana procedure must begin with Pancham. Pancham is the point that distinguishes Shadja Gram from Madhyam Gram. Since both the veenas are tuned to Shadja Gram, the Pancham in both the veenas makes ‘samvaad’(or is in-sync) with the Shadja (sa) and not with Rishabh (Re). In this first Saarana, if we lower the Pancham of the Chal veena to make samvaad with the Re of the Dhruv veena, the Chal veena will be, as a consequence, tuned to Madhyam Gram. With reference to verse no. 16, therefore, we lower the 16th string of the Chal veena to make samvaad with the 7th string of the Dhruv veena. Having thus obtained the new Pancham, we use it as a reference-note to re-adjust the strings of the Chal veena, so that it is re-tuned to Shadja Gram once again. Therefore, the seven notes Sa, Re, Ga, Ma, Pa, Dha, and Ni get tuned, respectively, on the 3rd, 6th, 8th, 12th 16th, 19th and 21st strings of the Chal veena.

  1. 2. This brings home certain points, viz.

a)      We get the measure of the first shruti of all the notes, in descending order, which is the same as that of the shruti we obtain in this round of the procedure (It refers to the difference in the Shrutis of the newly established notes from the notes in the original Saptak).

b)      The difference in the shruti-distance between the Pancham of the Shadja Gram and that of the Madhyam Gram is referred to as the ‘Pramaan Shruti’ (the shruti of reference). The Pramaan shruti is the one that determines the Gram. The other notes are lowered by the same measure[7].

c) Each note stands on the last shruti of the group of shrutis comprising it:

The word ‘Swopaantya’ used to qualify the string to be changed (in the Chal veena) in the 18th verse is self-explanatory. ‘Upaantya’ means ‘one that is immediately next to’ the subject. If the author had used only ‘upaantya’ as a qualification to describe the position of the string in his description, it could also have meant the one immediately followingthe original string. Now, the string that follows the original, represents the shruti of the next note, and not the note that is to be adjusted. The prefix ‘Swa’, however, dispels the possibility of such an ambiguity. Swa means ‘self’, and here it refers to the shruti of the note that is intended to be changed and brought down. The word ‘swopaantya’, therefore, means the penultimate shruti of the same note. This also makes it evident that the notes stand on the last shruti of the group of shrutis that constitute the note.

द्वितीया सारणा

DWITEEYAA SAARANA

VERSE NO. 19 (PART 2) & 20 (PART 1)

एवमन्यापि सारणा।

श्रुतिद्वयलयादस्यां चलवीणागतौ गनी ॥१९॥

Evamanyaapi Saarana

Shrutidwaya/layadasyaam Chalaveenagatou Gani

ध्रुववीणोपगतयो रिधयोर्विशत: क्रमात्

Dhruvaveenopagatayo Ridhayorvishatah Kramaat

Translation: The second Saarana must also be carried out in the same way. In this Saarana, since there will be a ‘lapse’ of two shrutis, the Ga-Ni (tuned) on the Chal veena will respectively lapse into (or merge with) the established Re-Dha of the Dhruv veena.

Note-

  1. 1. Procedure:

The second round of Saarana is similar to the first one, inasmuch as the notes in this round are also lowered by one shruti each. However, this round begins with either Gandhaar or Nishaad. This has also been indicated in the Natya Shastra[8]. The author lays down that the Saarana should be carried out in a manner whereby the Ga-Ni of the Chal Veena shall merge into Re-Dha of the Dhruv veena, and therefore the Saarana must begin from one of these points. Therefore, (with reference to verse nos. 16 and 18), the notes on the 7th and the 20thstrings of the Chal veena should be so lowered as to merge with the notes on the 7th and the 20th strings of the Dhruv veena respectively, thereby establishing Ga-Ni on the Chal veena. The remaining notes on the Chal veena must then be lowered according to the new Ga-Ni. It therefore follows that, Sa, Re, Ga, Ma, Pa, Dha and Ni on the Chal veena shall lie on the 2nd, 5th, 7th, 11th, 15th, 18th and 20th strings respectively.

  1. 2. We get the following results from the second phase of the Chatuh Saarana procedure:

a) Four shrutis.

Matanga brings to our notice the proof of the existence of four shrutis in the second Saarana. The fact that Ga-Ni of the Chal veena merge with the Re-Dha of the Dhruv veena establishes the extistence of four shrutis.

b) Measure of the shruti obtained.

The shruti obtained in the second Saarana is of a much larger measure than the one obtained in the first Saarana. This is evident from the fact that the Pancham obtained on the Chal veena in the first Saarana creates samvaad with the Rishabh of the Dhruv veena. However, the Pancham that we get on the Chal veena after lowering the notes in the second Saarana sounds very much low to be compatible with the Rishabh of the Dhruv veena. Also, we find that the second shruti of each note respectively, in the descending order, is of the same measure as the difference of the shrutis obtainedin this Saarana.

c) The two shrutis of Ga and Ni

We also find that Ga and Ni are both comprised of two shrutis each.

d) Antar Gandhaar and Kaakali Nishad

It is very important to note that the Ma and Sa that we get on the 11th and 2nd string of the Chal veena respectively, correspond to the Antar Gandhaar and Kaakali Nishaad of the original Saptak. The second round of Saarana therefore leads to the discovery of the Antar Gandhaar and the Kaakali Nishaad. Also, we find that both the Antar Gandhaar and the Kaakali Nishad lie on the second shruti immediately preceding the next notes respectively.

तृतीया सारणा

TRITEEYAA SAARANA

VERSE NO. 20 (PART 2)

तृतीयस्यां सारणायां विशत: सपयो रिधौ ॥२०॥

Truteeyasyaam Saaranaayaam Vishatah Sapayo Ridhou

Translation: The Re (and) Dha (of the Chal veena) merge with the Sa (and) Pa of the Dhruv veena, in the third Saarana.

Note-

  1. 1. Procedure:

It has been suggested by Bharat Muni[9] that the procedure in the third round of Saarana should begin with Re. The Re-Dha of the Chal veena must be so tuned as to correspond with the Sa and Pa of the Dhruv veena. This means that Re and Dha must be established on the Chal veena by tuning the 4th and the 17th strings of the Chal veena respectively to merge with the Sa and Pa of the Dhruv veena. This will be followed by lowering the remaining strings of the Chal veena to be compatible with the newly established Re and Dha. Consequently, Sa, Re, Ga, Ma, Pa, Dha and Ni on the Chal veena shall now lie on the 1st, 4th, 6th, 10th, 14th, 17th and 19th strings respectively.

  1. 2. The results of this procedure are:

a)      The number of shrutis obtained

This part of the procedure establishes the fact that Rishabh and Dhaivat are comprised of three shrutis each. We therefore obtain 6 shrutis in all, in the third Saarana.

b) The measure of the third shruti in descending order

The measure of the third shruti of all the notes except the ‘Dwi-shruti’ swaras (notes comprised of only two shrutis) is the same as that of the difference in the shrutis of the notes on the Chal veena from the notes of the original Saptak (i.e. the shruti-distance we moved), that we obtain in this Saarana.

c) The measure of the Shruti obtained in the third Saarana

The shruti we get in this Saarana is of a much larger measure than the one we get in the first Saarana. This is evident from the fact that in order to establish Ga and Ni on the 19th and the 6th string of the Chal veena respectively, to correspond with the Madhyam on the 10th string of the Chal veena, one has to lower the 19th and the 6th string considerably.

चतुर्थी सारणा

CHATURTHI SAARANA

VERSE 21 (PART 1)

निगमेषु चतुर्थ्यां तु विशन्ति समपा: क्रमात्

Nigameshu Chaturthyan Tu Vishanti Samapah Kramaat

Translation:In the fourth Saarana, the Sa, Ma and Pa (of the Chal veena) merge with the Ni, Ga and Ma (of the Dhruv veena), respectively.

Note-

1) Procedure

a) Difficulty in tuning Sa

The notes of the Chal veena shall be lowered by one shruti each in the fourth round of Saarana also. This procedure must begin with Sa (on the Chal veena). Now, we had lowered the Sa to the first string of the Chal veena in the previous round. Thus, we no longer have a string to lower the Sa further on the Chal veena. This problem can be overcome in two ways;

  • The Ni of the  (original) Madhya Saptak or the middle octave, which lies on the 22nd string, can be the point where we merge (or establish) the Sa of the Chal veena, since the Madhya Saptak Ni is the same as the Mandra Ni for this purpose-except that it is double the frequency of the Mandra Ni.
  • Or, we may presume the existence of a string for the Taar Shadja (upper Sa) of the original Saptak. Now, Ni (of the original Saptak) lies on the 22nd string. To merge the Sa of the Chal veena with Ni, we must therefore merge the Sa with the 22nd string, in this Saarana.

Either way, the Sa in this Saarana will be established on the 22nd string.

b) Merging Ma and Pa

Once we establish the Sa, the Ma and Pa of the Chal veena which merge with the ‘Ga’ and ‘Ma’ of the Dhruv veena, lie on the 9th and 13th string (of the Dhruv veena) respectively. Therefore, we establish Sa, Ma and Pa on the Chal veena, on the 22nd, 9th and 13th strings respectively. The remaining notes shall thus be established on the 5th, 16th and 18th strings.

2) Re and Dha

It is important to note that the Re and Dha in this Saarana get established on the 3rd and the 16th strings (of the Chal veena) in the same way as Sa and Pa were established on the same strings respectively, in the first round of Saarana. We are not required to change the tuning of the strings- as the measure of the shruti we get in the Saarana is the same as that we get in the first Saarana.

3) Important results

In this Saarana, therefore, we find that

a)      The notes Sa, Ma and Pa are comprised of four shrutis each.

b)      The fourth Shruti of the Chatuh-shrutik Swaras (notes comprising of fourt shrutis) is also the ‘Pramaan shruti’ (with reference to the Note under Pratham Saarana). In other words, the measure of the first and the fourth shrutis of the Chatuh-shrutik notes is the same. This can be proved by observing the findings of the first, third and fourth Saaranas- the Re of the third Saarana creates samvaad with the Pa of the fourth Saarana, in the same way as the Re of the original Saptak creates Samvaad with the Pa of the first Saarana.

The Chatuh Saarana experiment, thus, establishes four important facts:

  1. The number of shrutis i.e. that the Saptak comprises of 22 shrutis;
  2. The measure of the 22 shrutis;
  3. The order in which we find the shrutis, as comprising the notes in the Saptak;
  4. The Antar and Kaakali Swaras.

VERSE Nos. 21 (PART 1) & 22

श्रुतिद्वाविंशतावेवं सारणानां चतुष्टयात् ॥२१॥

Shruti/dwaavinshtaavevam Saaranaanaam Chatushtayaat

धृवाश्रुतीषु लीनायामियत्ता ज्ञायते स्फुटम्

अत: परं तु रक्तिघ्नंन कार्यमपकर्षणम् ॥२२॥

Dhruvaa/shruteeshu Leenaayaam/iyattaa Dnyaayate Sphutam

Atah Paran Tu Raktighnam Na Kaaryamapakarshanam

Translation- And therefore, by the merger of 22 shrutis with (the notes of the) Dhruv veena, it comes to our knowledge distinctly (and therefore we prove) that the number of shrutis is the same (i.e. 22). However, since lowering (the notes on the strings) further will destroy the resonance (of the strings), we must not lower (them) any more.

Note-

The author lays down that the one must stop after the fourth Saarana and not lower the notes any further. The reasons why the fourth Saarana concludes this experiment are-

  1. The first string of the veenas was initially tuned to the lowest possible frequency. If the string is lowered further, it will cease to resonate and thus defeat the purpose of the experiment.
  2. We will enter the Mandra Saptak (lower octave) if we proceed lower, and therefore the notes we find here will only be the duplicates of the notes in the previous octave. We will not find any new note or shruti.
  3. The largest shruti distance between two notes is that of 4 shrutis. An additional round of Saarana will therefore not yield a new shruti.

[1]Sharangdevkrut Sangeetratnakar by Subhadra Chowdhury, Chapter (prakaran) 3, pg no. 60, verse nos. 8, 9

[2]ibid, appendix- pg. no. 263

[3]ibid, appendix- pg no. 261

[4] Bharata’s Natyashastra (28)

[5] Sharangdevkrut Sangeetratnakar by Subhadra Chowdhury; appendix (k), pg 257-259.

[6]Natyashastra  - मध्यमग्रामे तु पंचम: श्रुत्यपकृष्ट: कार्य:, तयोरन्यतरस्यां पंचमस्यापकर्षे श्रुतिं मध्यमग्रामिकींकृत्वा (28), संवादो मध्यमग्रामे पंचमस्यर्षभस्य च (15)

[7]Abhinav interprets the term ‘pramaan’ as the first instance wherein we experience the frequencies (on which a note is located) to be on the higher side or lower side; and this first instance becomes the basis on which we determine the measure of the shrutis we subsequently obtain during this experiment-( Abhinavbharati); ibid- appendix, pg no. 264.

[8]पुनरपि तद्वदेवापकर्षेत् यथा गान्धारनिषादवन्तावितरस्यामृषभधैवतौ प्रवेक्ष्यत: द्विश्रुत्यधिकत्वात् (28)

[9]पुनरपि तद्वदेवापकृष्टायां धैवतर्षभावितरस्यां पंचमषड्जौ प्रवेक्ष्यत: त्रिश्रुत्यधिकत्वात् (28)