Natalie Savelyeva

Gandharva music - definition of grama

Grama, Murchana and Jati are technical terms that were used in such works like Natya Sastra of Bharata and Dattilam of Dattila. These two works were written between the 1st or the 4th century A.D. The musical tradition described in these works is called "gandharva".

Basic harmonics

In Natya Sastra Bharata Muni defines the gramas as follows:

"The gramas are two: Sadja grama and Madyama grama. Here there are 22 srutis. In the sadja grama there are three srutis in risabha, two in gandhara, four in madhyama, four in pancama, three in dhaivata, two in nisada, and four in sadja. In madhyama grama one sruti should be reduced of pancama."

(Slokas 24-26, Chapter XXVIII)

Thus, from Natya Sastra we get the following information:

  1. There are two scales starting from two different tonics (sadja and madhyama).
  2. An octave is divided into 22 intervals called srutis.
  3. Each scale comprises seven swarasthanas.
  4. Intervals between swarasthanas in sadja grama are: 4 3 2 4 4 3 2 and in madhyama grama: 4 3 2 4 3 2 4.
  5. Tuning of scales was fit for string instruments (Bharata Muni uses example of vina tuning to explain the difference between two gramas).

The question is what exactly Bharata Muni implies when speaks about intervals of 2, 3, 4 srutis and what are proportions of the swarasthanas. He uses example of string instrument (vina) tuning, thus, the principles of calculating ratios of particular swarasthanas should be simple and precise, to fit practical needs.

    Using principle of dichotomy we get the four basic harmonic swarasthanas of purvaranga (lower portion of the octave):

  1. 1 + 1/2 = 3/2 (pa or perfect fifth)
  2. 1 + 1/3 = 4/3 (ma or fourth)
  3. (1 + 3/2 )/2 = 5/4 (Ga or third)
  4. (1 + 5/4)/2 = 9/8 (Ri or second)
  5. Using Pancama interval (3/2) we get the following swarasthanas of uttararanga (upper portion of the octave):

  6. 1/1 * 3/2 = 3/2
  7. 9/8 * 3/2 = 27/16
  8. 5/4 * 3/2 = 15/8
  9. 4/3 * 3/2 = 2

Sadja Grama

Sadja Grama Intervals

The resulting Grama sounds as follows:

Madhyama Grama

We also can use Madyama interval (4/3) to derive swarasthanas of uttararanga:

  1. 1/1 * 4/3 = 4/3 (ma)
  2. 9/8 * 4/3 = 3/2 (pa)
  3. 5/4 * 4/3 = 5/3 (Da "major")
  4. 4/3 * 4/3 = 16/9 (ni "minor")
Madhyama Grama Intervals

The resulting Grama sounds as follows:

The difference between two Gramas are:

  1. Sruti intervals between adjacent swarasthanas (4 3 2 4 4 3 2 in Sandja grama and 4 3 2 4 3 4 2 in Madhyama grama).
  2. Intervals sa-pa, ri-da, ga-ni , ma-sa are all constant and equal to 3/2 in sadja grama (in madhyama grama those intervals are different), and intervals sa-ma, ri-pa, ga-da, ma-ni, pa-sa are all constant and equal 4/3 in madyama grama (in sadja grama those intervals are different).

Thus, Sadja grama is derived to keep constant intervals of perfect fifth between corresponding sthanas inside the grama, and Madhyama grama is derived to keep constant intervals of fourths between corresponding sthanas inside the grama.

Gandhara grama

Following the same logic, Gandharva grama should be based on keeping constant intervals of thirds (5/4 or 6/5) between every triplet of swarasthanas.

Gandhara Grama is not mentioned in Natya Sastra, but referred to in Dattilam.

In Dattilam too, there are no details regarding the murchana-s derived from it. But we get information about the names of the murchana-s and sruti intervals of svara-s from texts like Naradiyasiksa and Sangitaratnakara of Saringadeva.The structure of Gandharva grama as given in Sangitaratnakara is: -4-g-3- m-3- p-3- d-4- n-3- s-2-r, which gives us the following sruti pattern: 3-3-3-4-3-2-4.

In the table below analysis of intervals inside gandhara grama is presented. The is one violation of the order: interval between 3/2 (pa) and 16/9 (ni) is neither 5/4, nor 6/5. Correspondingly, interval between 6/5 (ga) and 16/9 (ni) is also different from 3/2. The reason lies in concept of sruti itself. Not all 22 srutis are equal. One sruti interval between different notes may be 256/243, 81/80 or 25/24. Thus, we cannot operate one sruti as constant and standard measure. We have to consider the context, the sthanas, and calculate intervals very carefully while proceeding from one sthana to another.

For instance, three sruti between 10/9 and 1/1 comprises three following sruti:

256/243 by 81/80 by 25/24 = 10/9

The interval between 10/9 and 6/5 comprises also three sruti, but values differ:

81/80 by 256/243 by 81/80 = 27/25.

Gandhara Grama Intervals (as given in Sangitaratnakara)

The resulting Grama sounds as follows:

The certain combinations of intervals are repeated in the scale (also see the picture below):

4 sruti 256/243 by 81/80 by 25/24 by 81/80 9/8
81/80 by 25/24 by 81/80 by 256/243 9/8
25/24 by 81/80 by 256/243 by 81/80 9/8
81/80 by 256/243 by 81/80 by 25/24 9/8
3 sruti 256/243 by 81/80 by 25/24 10/9
81/80 by 25/24 by 81/80 2127/2048
25/24 by 81/80 by 256/243 10/9
81/80 by 256/243 by 81/80 27/25
2 sruti 256/243 by 81/80 16/15
81/80 by 25/24 135/128
25/24 by 81/80 135/128
81/80 by 256/243 16/15

Every four consequent sruti gives interval of 9/8 (we have to multiply, not add as proportion of frequencies follow geometrical progression). Three consequent intervals give 10/9, 27/25 or 2127/2048 = 1.0386, and pair of consequent srutis give 16/15 or 135/128.

Intervals between 22 swarasthanas

Svara mandala comprising both major scales, Sadja and Madhyama grama

Conclusions

The question is if there is any difference for the listener if we use one grama or the other.

There is interesting feature of human perception of the sound. The experiments were carried out which showed that if two strings, tuned to different frequencies are plucked together, careful listener could notice not only two different notes, but also the third note, which frequency was equal to difference between the frequencies of the strings.

Thus, our perception is able to distinguish not only separate frequencies of two strings, but also the difference between those frequencies, which we hear as separate, third, sound.

The secret of gramas lies in that fact. Swarasthanas are numerous. Combinations of different swarasthanas are even more numerous. The grama defines particular harmony of intervals between swarasthanas. The constant intervals kept between different swarasthanas in the grama are perceived as special quality of this particular set when we listen to the flow of music composed in this grama. As if we "hear" the intervals hidden inside the grama itself. We do not realize it, but feel something like a flavor of grama, constantly present and implied in each combination of the notes.

References

  1. The Natyasastra. English translation with critical Notes by Adya Rangacharya, Munishiram Manoharlal Publishers Pvt. Ltd., New Delhi, 2010
  2. Dattilam by Mukund Lath, Motilal Banarsidass Pvt. Ltd., 1990
  3. Grama Murcchana Jati by Premalatha Nagarajan
  4. The Traditional Indian Theory and Practice of Music and Dance By Jonathan Katz (Editor), Publisher: brill academic publishers (Sep 1992)
  5. Influence of Sastra on prayoga: the svara system in the post-Sangitaratnakara period with special reference to south Indian music By N. Ramanathan
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