There are 22 Sharuties in one octave.
To find the intervals between notes, first a base note is established.
This note is our Shadaj (Sa). The intervals are counted upwards starting from this note.
Shadaj Gram has the following intervals:
Rishav or Re= 3 sharuties
Gandhar or Ga = 2 sharuites
Madhyam or Ma = 4 Sharuties
Pancham or Pa= 4 Sharuties
Dhaivat or Dha = 3 Sharuties
Nishad or Ni = 2 Sharuties
Shadaj or Sa = 4 Sharuties
As I described earlier that all Sharuties are not equal, they are not arbitrary either. There are three types of Sharuties :
1. Mehti Interval
2. Sub-mehti Interval
3. Parman Interval
Let’s call them A, B and C intervals.
The following rules of sharuti distribution dictate the harmonic relation of notes to each other:
1. Every interval must have at least 1 Parman Sharuti (C).
2. Every Interval of two Sharuties, ( such as Ga (modern komal!) from Re and Ni (modern Komal!) from Dha), is made of A+C (mehti+parman).
3. Every Interval of three Sharuties, must have one of each Sharuties (A+B+C).
4. All intervals that are 4 Sharuties apart, must have 2 Parman Sharuties (C+A+B+C).
If we use the Savarts system (dividing an octave into 301 Savarts, more here), we can say that:
1. All 4 Sharuti notes are:5+23+18+5 = 51 Savarts
2. All three Sharuti notes are: 23+18+5 = 46 Savarts
3. All two Sharuti Notes are: 23+5= 28 Savarts
Therefore, the Shadaj gram is:
| Notes: |
S
|
R
|
G
|
M
|
P
|
D
|
N
|
S
|
| Sharuties: |
–
|
3
|
5
|
9
|
13
|
16
|
18
|
22
|
| Savarts |
–
|
46
|
28
|
51
|
51
|
46
|
28
|
51
|
When tuning a scale, Shadaj is the first note to be established. All other notes are created with their relation to this note. However, when we are measuring the intervals, the four Sharuties of Shadaj sit on top of the Suptak, so we normally mention it in the end, completing an octave.
The word ‘Shadaj’ has two meanings:
1. The creator of six notes
2. The creation of six notes
Without the knowledge of Sharuties, the above meanings may seem metaphorical, a grand status given to the keynote. However, after the Sharuti Darshan (establishing Sharuties) it is apparent that the meaning is quite literal. Shadaj creates all notes, as it is the first note, but the Shadaj Sharuti count cannot be determined without establishing all six notes. Therefore, it becomes the creation of other six notes.
Here is the decisive verse from Natayshastar:
Triso Davaich chat-sarshach , chat-sarshach eva ‘ch.
Davai chat-sarshach shadajakhaye gramay sharuti-ni-darshanam.
Meaning: The order of Sharuties in Shadaj Gram is 3-2-4-4-3-2-4.
It means that notes look something like this:
The main question asked by modern musicologists (i.e. Hon. Pundit V.N. Bhatkhande, Hon. Raja Nawab Ali.) is that can it be proven? Can one establish a harmonic or playable Suptak (scale) based on the formula above? The answer is yes, we can.
How?
That is next.
Dear Sangtar,
I enjoy reading your blog very much. I became interested in Indian music theory, because my sister brought me a bansuri from India, which I’m now trying to learn.
While writing this, I have approached the chapter “Grams of Natyashastar” and hopefully understood most of it correctly. But concerning the Sharuti theory, I figured that the mehti sharuti is slightly bigger than the sum of two other sharuties..
When you compute the frequency ratios in the scale constructed by Bharat’s schema and check the division 3-2-4-4-3-2-4 according to the rules it does not exactly match with the condition that Mehti Interval (A) is the same as Sub-mehti Interval (B) and Parman Intervall (C) together:
The conditions derived from scale ratios and Sharuti rules
9/8=C*A*B*C
10/9=C*A*B
16/15=C*A
give values
A=81/80 B=75/72 C=256/243
which do not obey A=B*C, while the numbers differ on the third decimal.
Thus this equates that Parman and Sub-mehti taken together are slightly sharper than Mehti alone: p*s=1,054…>1,053…=m.