Sruthi
A sruti is a note of minute pitch which a refined and trained ear can distinguish. It is the smallest audible difference of pitch. It is a fraction of a semi- tone.
In the history of world music, Indian music is one of the earliest to use quarter tones. It is the use of quarter tones and micro tones that imports a peculiar charm, color and flavor to Indian music. 22 such notes are, 10 notes in addition to the universal 12 notes of the gamete having in use for centuries. Many ancient Tamil works refer to the 22 srutis as the foundation of Indian music. There is a universal statement commonly accepted that “the swaras are 7, swarasthanas are 12 and the srutis are 22”. Even though there existed differences in views regarding the number of srutis as 22, 24, 66, 32, 48, 27, 53, 96, etc. as put forth by various scholars, the number 22 has now been universally accepted due to many aspects.
The existence of 22 srutis in an octave was established and invented by Bharatha Muni. He proved this with the help of an experiment called “Dhruva Veena – Chala Veena experiment.”
A few of the 22 srutis figure in rare ragas, they give only through these ragas. Musicians are not conscious of the precise frequency values of these srutis but keeping the naadatmarupa or the melodic picture of the raga in their minds they are able to sing or play the srutis accurately.
The subject of 22 srutis is one of the most difficult branches of the science in Indian music. It can be understood only by the persons with many years of musical training. In fact, those janya ragas which can possibly claim more than one janaka mela are put under particular melakarthas based on their sruti values only. The melodic individuality of a raga is revealed only when its characteristic srutis are sounded.
In the history of world music, Indian music is one of the earliest to use quarter tones. It is the use of quarter tones and micro tones that imports a peculiar charm, color and flavor to Indian music. 22 such notes are, 10 notes in addition to the universal 12 notes of the gamete having in use for centuries. Many ancient Tamil works refer to the 22 srutis as the foundation of Indian music. There is a universal statement commonly accepted that “the swaras are 7, swarasthanas are 12 and the srutis are 22”. Even though there existed differences in views regarding the number of srutis as 22, 24, 66, 32, 48, 27, 53, 96, etc. as put forth by various scholars, the number 22 has now been universally accepted due to many aspects.
The existence of 22 srutis in an octave was established and invented by Bharatha Muni. He proved this with the help of an experiment called “Dhruva Veena – Chala Veena experiment.”
A few of the 22 srutis figure in rare ragas, they give only through these ragas. Musicians are not conscious of the precise frequency values of these srutis but keeping the naadatmarupa or the melodic picture of the raga in their minds they are able to sing or play the srutis accurately.
The subject of 22 srutis is one of the most difficult branches of the science in Indian music. It can be understood only by the persons with many years of musical training. In fact, those janya ragas which can possibly claim more than one janaka mela are put under particular melakarthas based on their sruti values only. The melodic individuality of a raga is revealed only when its characteristic srutis are sounded.
Sruti Intervals
The 22 srutis are derived from 12 swarasthanas. As Sa and Pa are Achala swara – they took one sruti each. The remaining 10 swarasthanas took two srutis each. Totally (10 x 2) + 2 = 22 srutis.
Based on the sruti interval between 2 swaras, they can be called as follows:
Eka sruti interval or Quarter tone: One sruti interval between 2 swaras. Frequency value: 256/243
Dvisruti interval or Semitone: Two sruti interval between 2 swaras. Frequency value: 16/ 15
Trisruti interval or Minor tone: Three sruti interval between 2 swaras. Frequency value: 10/9
Chatursruti interval or Major tone: Four sruti interval between 2 swaras. Frequency value: 9/8
Eka sruti interval is classified into 3 types:
The 22 srutis are derived from 12 swarasthanas. As Sa and Pa are Achala swara – they took one sruti each. The remaining 10 swarasthanas took two srutis each. Totally (10 x 2) + 2 = 22 srutis.
Based on the sruti interval between 2 swaras, they can be called as follows:
Eka sruti interval or Quarter tone: One sruti interval between 2 swaras. Frequency value: 256/243
Dvisruti interval or Semitone: Two sruti interval between 2 swaras. Frequency value: 16/ 15
Trisruti interval or Minor tone: Three sruti interval between 2 swaras. Frequency value: 10/9
Chatursruti interval or Major tone: Four sruti interval between 2 swaras. Frequency value: 9/8
Eka sruti interval is classified into 3 types:
{ A cent is a unit of measure for the ratio between two frequencies.}
Dvisruti interval is classified into 2 types:
Dvisruti interval is classified into 2 types:
Trisruti interval and Chatursruti interval has constant frequency values as mentioned above.
[ A Purna eka sruti and a Pramana eka sruti makes a Dvisruti interval.
256/243 x 81/80 = 16/15 (90+22 = 112 cents).
A Purna eka sruti, a Pramana eka sruti and a Nyuna eka sruti makes a Trisruti interval.
256/243 x 81/80 x 25/24 = 10/9 (90+22+70 = 183 cents).
A Purna eka sruti, a Pramana eka sruti, a Nyuna eka sruti and again a Pramana eka sruti makes a Chatursruti interval. 256/243 x 81/80 x 25/24 x 81/80 = 9/8 (90+22+70+22 = 204 cents). ]
The above said four sruti intervals are seen in the swaras Rishaba, Gandhara, Madhyama, Dhaivata and Nishada. So Shadja has one sruti, Panchama has one sruti, and the rest has four srutis each.
But according to Bharatha Muni, the distribution of sruti intervals are as follows:
Shadja has 4 srutis, Rishaba has 3 srutis, Gandhara has 2 srutis, Madhyama has 4 srutis, Panchama has 4 srutis, Dhaivata has 3 srutis and Nishada has 2 srutis.
[ A Purna eka sruti and a Pramana eka sruti makes a Dvisruti interval.
256/243 x 81/80 = 16/15 (90+22 = 112 cents).
A Purna eka sruti, a Pramana eka sruti and a Nyuna eka sruti makes a Trisruti interval.
256/243 x 81/80 x 25/24 = 10/9 (90+22+70 = 183 cents).
A Purna eka sruti, a Pramana eka sruti, a Nyuna eka sruti and again a Pramana eka sruti makes a Chatursruti interval. 256/243 x 81/80 x 25/24 x 81/80 = 9/8 (90+22+70+22 = 204 cents). ]
The above said four sruti intervals are seen in the swaras Rishaba, Gandhara, Madhyama, Dhaivata and Nishada. So Shadja has one sruti, Panchama has one sruti, and the rest has four srutis each.
But according to Bharatha Muni, the distribution of sruti intervals are as follows:
Shadja has 4 srutis, Rishaba has 3 srutis, Gandhara has 2 srutis, Madhyama has 4 srutis, Panchama has 4 srutis, Dhaivata has 3 srutis and Nishada has 2 srutis.
Bharatha Muni’s apporoach
Bharata Muni’s experimental tuning procedure to establish the srutis on two identical harp-like veenas, as related in the ancient Natyasastra took place more than two thousand years ago.
The veena was not only used as a concert instrument from early times, but was also used for studying and verifying the various musical laws and phenomena. Both the harp type and the lute type of veenas have been in existence from the vedic times. The emergence of the fretted veena with its immense possibilities for playing subtle gamakas, naturally forced the harp type of veena into oblivion.
A study of the notes obtained in the cycles of fifths and fourths enabled the ancient scholars to perceive the different musical intervals. They were already familiar with the Chatussruti interval (9/8 or 204 cents), Trisruti interval (10/9 or 182 cents) and the Dvisruti interval (16/15 or 112 cents) in the Sa grama. The Ma grama helped them to appreciate the interval of a pramana sruti, 22 cents. When the notes of the cycles of fifths and fourths, worked up to the 12th cycle in each case, were reduced to one octave and studied, it was found that there were 13 twins of notes, inclusive of the octave shadja, the notes constituting each twin being separated by the interval of a pramana sruti (81/80 or 22 cents). It was also noticed that in each twin, the lower note belonged to the cycle of fourths and the higher note to the cycle of fifths. The same study helped them to realize that in addition to the pramana sruti, there were two other types of ekasruti intervals : 25/24 or 70 cents and 256/243 or 90 cents.
In Bharatha Muni’s Natya Sastra (4th cent. B.C.), he has suggested an interesting experiment to get a clear grasp of these three types of Ekasruti intervals. These three types of ekasruti intervals are in the increasing order of magnitude respectively termed Pramana, Nyuna and Purna sruti intervals or the srutis of minimum, medium and maximum values.
Bharata Muni’s experimental tuning procedure to establish the srutis on two identical harp-like veenas, as related in the ancient Natyasastra took place more than two thousand years ago.
The veena was not only used as a concert instrument from early times, but was also used for studying and verifying the various musical laws and phenomena. Both the harp type and the lute type of veenas have been in existence from the vedic times. The emergence of the fretted veena with its immense possibilities for playing subtle gamakas, naturally forced the harp type of veena into oblivion.
A study of the notes obtained in the cycles of fifths and fourths enabled the ancient scholars to perceive the different musical intervals. They were already familiar with the Chatussruti interval (9/8 or 204 cents), Trisruti interval (10/9 or 182 cents) and the Dvisruti interval (16/15 or 112 cents) in the Sa grama. The Ma grama helped them to appreciate the interval of a pramana sruti, 22 cents. When the notes of the cycles of fifths and fourths, worked up to the 12th cycle in each case, were reduced to one octave and studied, it was found that there were 13 twins of notes, inclusive of the octave shadja, the notes constituting each twin being separated by the interval of a pramana sruti (81/80 or 22 cents). It was also noticed that in each twin, the lower note belonged to the cycle of fourths and the higher note to the cycle of fifths. The same study helped them to realize that in addition to the pramana sruti, there were two other types of ekasruti intervals : 25/24 or 70 cents and 256/243 or 90 cents.
In Bharatha Muni’s Natya Sastra (4th cent. B.C.), he has suggested an interesting experiment to get a clear grasp of these three types of Ekasruti intervals. These three types of ekasruti intervals are in the increasing order of magnitude respectively termed Pramana, Nyuna and Purna sruti intervals or the srutis of minimum, medium and maximum values.
DHRUVA VEENA : CHALA VEENA EXPERIMENT
Two veenas which were exactly identical in all respects including the timbre of their notes were chosen and tuned to the scale of Sa grama. That is seven strings of each veena were tuned to the notes of the following frequencies : –
Two veenas which were exactly identical in all respects including the timbre of their notes were chosen and tuned to the scale of Sa grama. That is seven strings of each veena were tuned to the notes of the following frequencies : –
These two seven-stringed veenas were of the harp type and were played on open strings, the seven strings of the two veenas were tuned to identical pitch. Of the two veenas, the pitch of one was kept constant and this was called the Dhruva veena or AChala veena. This stationary veena (A) was used for reference. The other veena called Chala veena, (B) was subjected to progressive reduction in pitch in four successive stages. At each stage, the reduction effected was by an interval of one sruti. Although the phrase ‘reduction by an interval of one sruti’ might lead to the inference that the reduction effected in each case was equal, still the rider added by Bharata at the end of each stage, that such and such a note of the Chala veena will now be equal to such and such a note of the Dhruva veena, conclusively proves that the reduction in pitch, effected at each stage, though within the limits of an Ekasruti interval was still not the same.
Now to the experiment described by Bharata : –
Stage 1. Let the Pa string of the Chala veena be reduced by one sruti. The scale of the Chala veena will now be that of Ma grama.
Note : The frequency of this reduced Panchama was only 40/27 or 680 cents and not any other pitch, since between this note and the Dhaivata above there was a Chatursruti interval. The Panchama string was thus reduced by an interval of a comma or a pramana sruti.
Now convert the scale of this Chala veena into one of Sa grama, by lowering the pitches of the remaining six strings by the same interval of a pramana sruti. The strings were reduced in pitch by slightly decreasing the tension i.e., by loosening the strings to the required extent. Both the veenas became now Sa grama veenas, but the tonic note of the Chala veena was a comma lower down, compared to the pitch of the Achala veena, this clearly shows how each string of the Chala veena is a pramana sruti lower than that of the corresponding string of the Dhruva veena.
Stage 2. Reduce the panchama of the Chala veena again by one sruti and afterwards reduce the other six strings also by the same interval. The Gandhara and Nishada of the Chala veena will now be found to coincide in pitch with the Rishabha and Dhaivata of the Achala veena.
This means that the extent of the reduction was such as to make this coincidence of notes possible. The sum total of the reduction made in the two stages was thus equal to an interval of a diatonic semitone, 16/15 or 112 cents. Since the first reduction was by an interval of a comma, it is evident that the reduction in stage 2 was by an interval of a purna sruti 256/243 or 90 cents. It is clearly seen that each string of the Chala veena is a purna dvisruti interval below the corresponding string of the Dhruva veena.
Stage 3. Reduce the Panchama of the Chala veena again by one sruti and follow this up by reducing the pitch of the other six strings similarly. The Dhaivata and Rishabha of the Chala veena will now be found to coincide with the Panchama and Shadja of the Dhruva veena.
This means that the extent of the reduction was such as to make this coincidence possible. The sum total of the reduction made in all three stages was equal to an interval of a minor tone, 10/9 or 182 cents. Since the total reduction made at the end of the second stage was a diatonic semitone it follows that the reduction made in the third stage was by an interval of a nyuna sruti, 25/24 or 70 cents. It is thus seen that the pitch of each string of the Chala veena is now less than that of the corresponding string of the Dhruva veena by the interval of a trisruti or 10/9.
Stage 4. Reduce the Panchama of the Chala veena again by one sruti and carry out this process for the other six strings as well. It will now be found that the Pa, Ma and Sa of the Chala veena coincide with the Ma, Ga and Ni of the Chala veena.
It is clear that the reduction effected in this last case was by a pramana sruti, since the notes of the pairs: Pa and Ma; and Ma and Ga; and Sa and Ni have between them a chatussruti interval. We thus find that the pitch of each string of the Chala veena is less than that of the Dhruva veena by a major tone, 9/8 or 204 cents.
Thus, the effective reduction in pitch made in Stage 1 was a pramana sruti 81/80, Stage 2 was a purna sruti 256/243, Stage 3 was a nyuna sruti 25/24 and Stage 4 was a pramana sruti 81/80. In other words, the reduction has been respectively by the intervals of a minimum sruti, maximum sruti, medium sruti and minimum sruti. In terms of the Shadja of the Dhruva veena, the frequencies of the Panchama string of the Chala veena at the four respective stages were: 40/27, 45/32, 27/20 and 4/3. It should be remembered that the scale of the Chala veena at the conclusion of each change of pitch of the seven 4 strings was one of Sa grama, the value of the Adhara Shadja progressively decreasing in each case. One interesting point in Bharata’s experiment is, he asks us to start the reduction in each case with the Panchama string. As a practical musician, he knew and fully realized the value of initiating the change from the string which gave the strong consonant note.
Now to the experiment described by Bharata : –
Stage 1. Let the Pa string of the Chala veena be reduced by one sruti. The scale of the Chala veena will now be that of Ma grama.
Note : The frequency of this reduced Panchama was only 40/27 or 680 cents and not any other pitch, since between this note and the Dhaivata above there was a Chatursruti interval. The Panchama string was thus reduced by an interval of a comma or a pramana sruti.
Now convert the scale of this Chala veena into one of Sa grama, by lowering the pitches of the remaining six strings by the same interval of a pramana sruti. The strings were reduced in pitch by slightly decreasing the tension i.e., by loosening the strings to the required extent. Both the veenas became now Sa grama veenas, but the tonic note of the Chala veena was a comma lower down, compared to the pitch of the Achala veena, this clearly shows how each string of the Chala veena is a pramana sruti lower than that of the corresponding string of the Dhruva veena.
Stage 2. Reduce the panchama of the Chala veena again by one sruti and afterwards reduce the other six strings also by the same interval. The Gandhara and Nishada of the Chala veena will now be found to coincide in pitch with the Rishabha and Dhaivata of the Achala veena.
This means that the extent of the reduction was such as to make this coincidence of notes possible. The sum total of the reduction made in the two stages was thus equal to an interval of a diatonic semitone, 16/15 or 112 cents. Since the first reduction was by an interval of a comma, it is evident that the reduction in stage 2 was by an interval of a purna sruti 256/243 or 90 cents. It is clearly seen that each string of the Chala veena is a purna dvisruti interval below the corresponding string of the Dhruva veena.
Stage 3. Reduce the Panchama of the Chala veena again by one sruti and follow this up by reducing the pitch of the other six strings similarly. The Dhaivata and Rishabha of the Chala veena will now be found to coincide with the Panchama and Shadja of the Dhruva veena.
This means that the extent of the reduction was such as to make this coincidence possible. The sum total of the reduction made in all three stages was equal to an interval of a minor tone, 10/9 or 182 cents. Since the total reduction made at the end of the second stage was a diatonic semitone it follows that the reduction made in the third stage was by an interval of a nyuna sruti, 25/24 or 70 cents. It is thus seen that the pitch of each string of the Chala veena is now less than that of the corresponding string of the Dhruva veena by the interval of a trisruti or 10/9.
Stage 4. Reduce the Panchama of the Chala veena again by one sruti and carry out this process for the other six strings as well. It will now be found that the Pa, Ma and Sa of the Chala veena coincide with the Ma, Ga and Ni of the Chala veena.
It is clear that the reduction effected in this last case was by a pramana sruti, since the notes of the pairs: Pa and Ma; and Ma and Ga; and Sa and Ni have between them a chatussruti interval. We thus find that the pitch of each string of the Chala veena is less than that of the Dhruva veena by a major tone, 9/8 or 204 cents.
Thus, the effective reduction in pitch made in Stage 1 was a pramana sruti 81/80, Stage 2 was a purna sruti 256/243, Stage 3 was a nyuna sruti 25/24 and Stage 4 was a pramana sruti 81/80. In other words, the reduction has been respectively by the intervals of a minimum sruti, maximum sruti, medium sruti and minimum sruti. In terms of the Shadja of the Dhruva veena, the frequencies of the Panchama string of the Chala veena at the four respective stages were: 40/27, 45/32, 27/20 and 4/3. It should be remembered that the scale of the Chala veena at the conclusion of each change of pitch of the seven 4 strings was one of Sa grama, the value of the Adhara Shadja progressively decreasing in each case. One interesting point in Bharata’s experiment is, he asks us to start the reduction in each case with the Panchama string. As a practical musician, he knew and fully realized the value of initiating the change from the string which gave the strong consonant note.
The object of Bharata in devising this experiment was : – (I)To demonstrate the three types of ekasruti intervals that occurred in the Indian musical scale. (II) To familiarize musicians with the idea of inversion of intervals. Thus the Begada madhyama is an inverted minor tone from the Panchama. (III) To impress the distinction between absolute pitch and relative pitch. (IV) To illustrate the 22 srutis. The 22 are easily the possible notes that can be used in a melodic system of music. It is useful to remember that in ancient times, all musical instruments were tuned to absolute pitch as is the case with European musical instruments even now and the middle octave Shadja was a note of a precise frequency just like the international philharmonic pitch. With the emergence of the concept of Adhara Shadja in the post-Bharata period, all ragas came to be sung to a common tonic note. Again, the emergence of the concept of Shadja and Panchama as Avikrita swaras made the pramana sruti intervals around these two notes pale into insignificance. The note of frequency 40/27 so prominent in the Ma grama fell into desuetude along with the Ma grama and gradually gave way to the note 64/45 which came to be called by various names as Kaisiki Panchama, Mridu Panchama and Varali Madhyama. Bharata in his experiment missed the note 64/45 because he was proceeding downwards from Panchama. If he had proceeded upwards from Suddha Ma, he would have hit upon the note 64/45. He adopted the downward course since he wanted in the first instance to illustrate practically the Ma grama and hence the note 40/27 had to be touched. The other notes got in successive reductions were only 45/32, 27/20 and 4/3. This is clear from the rider which he has given at each stage, i.e. that such and such a note of the Chala veena coincides with such and such a note of the Dhruva veena. Further, musicians at that time were already familiar with the downward progression. The murchanas of Sa grama were enumerated in the downward order. The progression of sama gana music was in the downward order. Those who perform this experiment will incidentally get training in the reduction of pitch by such delicate intervals as pramana, nyuna and purna srutis.
In the experiment, Bharata has not mentioned the equivalents of the notes given by all the strings of the Chala veena in relation to the notes given by the strings of the Dhruva veena. He has referred to the notes of only those strings of the Chala veena whose pitches exactly coincided with those of the Dhruva veena. He refrained from doing so, since the srutis of the particular strings of the Chala veena after reduction, were either close to the other correct srutis or were useless.
The Dhruva veena - Chala veena experiment can be performed in the reverse order starting from the Madhyama string and proceeding in the Arohana krama by tightening the string to the desired pitch in each case and the results verified. It is possible that the four stages of reduction mentioned by Bharata for each of the Sapta swaras might have suggested to Mahendra Varman, the author of the Kudumiyamalai inscription the four sruti varieties, ra, ri, ru, re, ga, gi, gu, ge, etc. for the sapta svaras.
In the experiment, Bharata has not mentioned the equivalents of the notes given by all the strings of the Chala veena in relation to the notes given by the strings of the Dhruva veena. He has referred to the notes of only those strings of the Chala veena whose pitches exactly coincided with those of the Dhruva veena. He refrained from doing so, since the srutis of the particular strings of the Chala veena after reduction, were either close to the other correct srutis or were useless.
The Dhruva veena - Chala veena experiment can be performed in the reverse order starting from the Madhyama string and proceeding in the Arohana krama by tightening the string to the desired pitch in each case and the results verified. It is possible that the four stages of reduction mentioned by Bharata for each of the Sapta swaras might have suggested to Mahendra Varman, the author of the Kudumiyamalai inscription the four sruti varieties, ra, ri, ru, re, ga, gi, gu, ge, etc. for the sapta svaras.
Cycle of 5th ( Sa - Pa Cycle )
In the cycle of fifths, we first consider the note Panchama whose relative frequency is 3/2. Now the Panchama of this Panchama has the relative frequency of (3/2) x (3/2) which is equal to 9/4. This number may be identified as the relative frequency of the note Chatusruti Rishabha in the Tara sthayi. Again, considering the Panchama of this note we get the number (9/4) x (3/2) which is equal to 27/8. This number may be identified as the relative frequency of Chatusruti Dhaivata of Tara sthayi. In this way one can build a series of numbers. Whenever the number exceeds 2, we divide it by 2 (or a suitable power of 2) so that the resultant number is always less than 2 and hence represents a sruti in the Madhya sthayi. The sequence of numbers so obtained constitutes the srutis of the cycle of fifths. Note that the sruti of Suddha Madhyama does not appear in this cycle.
The srutis belonging to the cycle of fifths may also be derived easily using the cents scale. The starting note is the Panchama whose relative frequency is 702 cents. The next note in the sequence is the Panchama of this Panchama, which is obtained by simply adding 702 to this, which gives 1404 cents. The procedure may be repeated by successive addition of 702 cents to the numbers previously obtained. Whenever the number exceeds 1200 cents it is brought back to the Madhya sthayi by subtracting 1200 (or a suitable multiple of this). The cycle of fifths is shown below. In this table, the cycle of fifths is shown up to the 22nd cycle. Note that this cycle can be continued indefinitely.
In the cycle of fifths, we first consider the note Panchama whose relative frequency is 3/2. Now the Panchama of this Panchama has the relative frequency of (3/2) x (3/2) which is equal to 9/4. This number may be identified as the relative frequency of the note Chatusruti Rishabha in the Tara sthayi. Again, considering the Panchama of this note we get the number (9/4) x (3/2) which is equal to 27/8. This number may be identified as the relative frequency of Chatusruti Dhaivata of Tara sthayi. In this way one can build a series of numbers. Whenever the number exceeds 2, we divide it by 2 (or a suitable power of 2) so that the resultant number is always less than 2 and hence represents a sruti in the Madhya sthayi. The sequence of numbers so obtained constitutes the srutis of the cycle of fifths. Note that the sruti of Suddha Madhyama does not appear in this cycle.
The srutis belonging to the cycle of fifths may also be derived easily using the cents scale. The starting note is the Panchama whose relative frequency is 702 cents. The next note in the sequence is the Panchama of this Panchama, which is obtained by simply adding 702 to this, which gives 1404 cents. The procedure may be repeated by successive addition of 702 cents to the numbers previously obtained. Whenever the number exceeds 1200 cents it is brought back to the Madhya sthayi by subtracting 1200 (or a suitable multiple of this). The cycle of fifths is shown below. In this table, the cycle of fifths is shown up to the 22nd cycle. Note that this cycle can be continued indefinitely.
Cycle of 4th ( Sa – Ma Cycle )
The process of the cycle of fourths is analogous to the cycle of fifths except that the note Suddha Madhyama is used in place of Panchama. Again, we first consider the note Suddha Madhyama whose relative frequency is 4/3. Now the Suddha Madhyama of this Suddha Madhyama has the relative frequency of (4/3) x (4/3) which is equal to 16/9. This number may be identified as the relative frequency of the note Kaishiki Nishada. Again, considering the Suddha Madhyama of this note we get the number (16/9) x (4/3) which is equal to 64/27. This number may be identified as the relative frequency of Sadharana Gandhara of Tara sthayi. In this way one can build a series of numbers. Whenever the number exceeds 2, we divide it by 2 (or a suitable power of 2) so that the resultant number is always less than 2 and hence represents a sruti in the Madhya sthayi. The sequence of numbers so obtained constitutes the srutis of the cycle of fourths. Note that the sruti of Panchama does appear in this cycle.
The srutis belonging to the cycle of fourths may also be derived easily using the cents scale. The starting note is the note Suddha Madhyama whose relative frequency is 498 cents. The next note in the sequence is the Suddha Madhyama of this Suddha Madhyama, which is obtained by simply adding 498 to this which gives 996 cents. The procedure may be repeated by successive addition of 498 cents to the numbers previously obtained. Whenever the number exceeds 1200 cents it is brought back to the Madhya sthayi by subtracting 1200 (or a suitable multiple of this). The cycle of fourths is shown below. In this table also, the cycle of fourths is shown up to the 22nd cycle. Note that this cycle can be continued indefinitely.
Cycle of 3rd ( Sa – Ga Cycle )
The process of the cycle of thirds is analogous to the cycle of fifths except that the note Antara Gandhara is used in place of Panchama. Again, we first consider Antara Gandhara the note whose relative frequency is 5/4. Now the Antara Gandhara of this Antara Gandhara has the relative frequency of (5/4) x (5/4) which is equal to 25/16. This number may be identified as the relative frequency of the note Panchama. Again, considering the Antara Gandhara of this note we get the number (25/16) x (5/4) which is equal to 125/64. In this way one can build a series of numbers. Whenever the number exceeds 2, we divide it by 2 (or a suitable power of 2) so that the resultant number is always less than 2 and hence represents a sruti in the Madhya sthayi. The sequence of numbers so obtained constitutes the srutis of the cycle of thirds. Note that the sruti of Panchama does appear in this cycle.
Palkuruki Somanathakavi gives the number of srutis as 22. Bhavabhatta in his Anupasangita Vilasa also defines a different set of 22 srutis. In addition to this, there is a system of 24 srutis mentioned by the author of Meladhikara lakshana.
In some ragas the frequencies may change in their sancharas or in arohana and avarohana.
Eg. Gandhara in Todi
The process of the cycle of thirds is analogous to the cycle of fifths except that the note Antara Gandhara is used in place of Panchama. Again, we first consider Antara Gandhara the note whose relative frequency is 5/4. Now the Antara Gandhara of this Antara Gandhara has the relative frequency of (5/4) x (5/4) which is equal to 25/16. This number may be identified as the relative frequency of the note Panchama. Again, considering the Antara Gandhara of this note we get the number (25/16) x (5/4) which is equal to 125/64. In this way one can build a series of numbers. Whenever the number exceeds 2, we divide it by 2 (or a suitable power of 2) so that the resultant number is always less than 2 and hence represents a sruti in the Madhya sthayi. The sequence of numbers so obtained constitutes the srutis of the cycle of thirds. Note that the sruti of Panchama does appear in this cycle.
Palkuruki Somanathakavi gives the number of srutis as 22. Bhavabhatta in his Anupasangita Vilasa also defines a different set of 22 srutis. In addition to this, there is a system of 24 srutis mentioned by the author of Meladhikara lakshana.
In some ragas the frequencies may change in their sancharas or in arohana and avarohana.
Eg. Gandhara in Todi
Sruti Jatis
Five jatis are mentioned for the 22 srutis.
1. Dipta: They are the brilliant or bright notes. Srutis coming under this category are Tivra, Raudri, Vajrika and Ugra. Eg: Gandhara in Atana and Kanada.
2. Ayatam: They are the streached notes. Srutis coming under this category are Kumudvati, Krodha, Prasarini, Sandipini and Rohini. Eg. Nishada in Kapi, Madhyamavati and Kedaragoula.
3. Karuna: They are the notes that give a pathetic feeling. Srutis coming under this category are Dayavathi, Alapini and Mandanti. Eg: Swaras of Subhapantuvarali and Ga in Asaveri.
4. Mridu: These swaras are rendered very softly. Srutis coming under this category are Manda, Ratika, Priti and Kshiti. Eg: Ga in the phrases ‘ g m g r s ‘ in Todi and ‘ r g r s ‘ in Sriraga.
5. Madhya: These swaras do not show any expression. Srutis coming under this category are Chandovati, Ranjani, Marjani, Rakta, Ramya and Kshobini. Eg: Ma in the phrase ‘ g m p ‘ in Sankarabharanam and ‘ s m p ‘ in Kutalavarali.
Five jatis are mentioned for the 22 srutis.
1. Dipta: They are the brilliant or bright notes. Srutis coming under this category are Tivra, Raudri, Vajrika and Ugra. Eg: Gandhara in Atana and Kanada.
2. Ayatam: They are the streached notes. Srutis coming under this category are Kumudvati, Krodha, Prasarini, Sandipini and Rohini. Eg. Nishada in Kapi, Madhyamavati and Kedaragoula.
3. Karuna: They are the notes that give a pathetic feeling. Srutis coming under this category are Dayavathi, Alapini and Mandanti. Eg: Swaras of Subhapantuvarali and Ga in Asaveri.
4. Mridu: These swaras are rendered very softly. Srutis coming under this category are Manda, Ratika, Priti and Kshiti. Eg: Ga in the phrases ‘ g m g r s ‘ in Todi and ‘ r g r s ‘ in Sriraga.
5. Madhya: These swaras do not show any expression. Srutis coming under this category are Chandovati, Ranjani, Marjani, Rakta, Ramya and Kshobini. Eg: Ma in the phrase ‘ g m p ‘ in Sankarabharanam and ‘ s m p ‘ in Kutalavarali.
From each grama are derived a number of secondary scales (murchana). The names of the Shadja grama murchanas are: uttaramandra, rajani, uttarayata, suddhasadja, matsarikrita, asvakrianta, abhirudgata. The first is the original scale, the remaining are the permutations. Thus, rajani is Ni Sa Ri Ga Ma Pa Dha.
The names of the Madhyama grama murchanas are: sauviri, harin. asva, kalopanata, suddhamadhya, margi, pauravi, hrsyaka.
Sarangadeva describes the rare use of the Gandhara grama by saying that it is used in the heaven, and not in this world. There is no unanimity regarding the assignment of the srutis in the Gandhara grama.
The Gandhara grama murchanas are: nandi, alapa, sukha, citravati, citra, sumukhi, visala.
Each grama is the foundation for pentatonic and hexatonic series of notes (tana), melodic line (varna), figuration and ornamentation (alankara) and mode (jati).
The names of the Madhyama grama murchanas are: sauviri, harin. asva, kalopanata, suddhamadhya, margi, pauravi, hrsyaka.
Sarangadeva describes the rare use of the Gandhara grama by saying that it is used in the heaven, and not in this world. There is no unanimity regarding the assignment of the srutis in the Gandhara grama.
The Gandhara grama murchanas are: nandi, alapa, sukha, citravati, citra, sumukhi, visala.
Each grama is the foundation for pentatonic and hexatonic series of notes (tana), melodic line (varna), figuration and ornamentation (alankara) and mode (jati).
Dviguna Relationship
It is clearly mentioned in ancient works that the octave bears a Dviguna relationship with the frequencies of a note and its octave, a ratio of 1:2. When a stretched string is plucked consecutively, it will be found that the shorter and longer segments give the notes Tara Panchama and Madhyama Panchama respectively. It is then the frequency of Panchama as fixed as 3/2 and the other srutis were calculated.
It is clearly mentioned in ancient works that the octave bears a Dviguna relationship with the frequencies of a note and its octave, a ratio of 1:2. When a stretched string is plucked consecutively, it will be found that the shorter and longer segments give the notes Tara Panchama and Madhyama Panchama respectively. It is then the frequency of Panchama as fixed as 3/2 and the other srutis were calculated.
Septimal Ratios
The srutis bearing septimal ratios possibly occur in a few ragas. The note of frequency 7/6 which occurs between Chatursruti Rishabha and Komal Sadarana Gandhara, the frequency 7/5 which occurs between Tivra Sudha Madhyama and Prati Madhyama and the frequency 7/4 which occurs between Chatursruti Dhaivata and Komal Kaishiki Nishada are examples.
The srutis bearing septimal ratios possibly occur in a few ragas. The note of frequency 7/6 which occurs between Chatursruti Rishabha and Komal Sadarana Gandhara, the frequency 7/5 which occurs between Tivra Sudha Madhyama and Prati Madhyama and the frequency 7/4 which occurs between Chatursruti Dhaivata and Komal Kaishiki Nishada are examples.
Complimentary intervals
An octave can be viewed as the sum of 2 intervals. The frequencies of these 2 notes will be different but their sum will be equal to 2. The following features can be noted amongst the sets of notes forming a complementary interval.
An octave can be viewed as the sum of 2 intervals. The frequencies of these 2 notes will be different but their sum will be equal to 2. The following features can be noted amongst the sets of notes forming a complementary interval.
- If of 2 intervals constituting an octave, one is a Samvadi interval, the other is also a Samvadi interval.
- If of 2 intervals constituting an octave, one is an Anuvadi interval, the other is also an Anuvadi interval.
- If of 2 intervals constituting an octave, one is a Vivadi interval, the other is also a Vivadi interval.
Each note not only represents that particular frequency but also the interval from the preceding note up to that note. Thus, Sa represents the entire interval from Ni to Sa. The notes that form the basic scale are called Suddha, notes lowered by a sruti are called Cyuta or Komala (soft), and those raised by a sruti or two are called Tivra (sharp), Sadharana or Kaisika (for one sruti) or Antara or Kakali (for two srutis). The altered notes are called Vikrita. Thus the 19 notes consist of 7 Suddha and 12 Vikrita notes.
Table containing 22 srutis name, their frequency value, vibrations per second, cent and ragas pertaining this sruti:
