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:

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.

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Every student of Hindustani music knows the name of Acharya Bharat. He is the father of all fathers of music, the great grandfather. It is said that Acharya Bharat learned the performing arts from Brahma himself. He was the author of Natyashastar, the most referenced source in both Indian Music systems (Hindustani and Carnatic). The depth of musical theories explained in Natyashastar gives us some hints that by the time Bharat came along, Indian music was already a fully developed art form.

Unfortunately, not many really know what is in Natyashastar.

There are two reasons for misinterpretation of Bharat’s music theory. First, Natyashastar is not available. Everything we know about Natyashastar is through other books that refer to it. Second, many writers especially in the 20th century wrote things that do not represent Bharat’s concepts. They used what they found in one place and without searching for the rest, filled the blanks on their own.

In April 1957, Acharya Brihaspati became the first man after Sarang Dev (13th century) to demonstrate Bharat’s Sharuties and Grams to an enlightened audience in Bombay. Since then a new wave of undoing the damage has started. Justifying the Thaat system with Bharat’s Grams and Moorshanas had made Indian music theory opaque. Everyone who was looking for the roots of their twelve notes in Bharat’s Grams had complicated the matter.

The explanations of Grams and Sharutis in my blog are based on Acharya Brihaspati’s research and demonstrations and my own ongoing research.

Bharat’s theory is based on three concepts:

1. Gram
2. Moorshana
3. Sharuti

In practice, a performer only uses Grams and Moorshanas. The knowledge of Sharuties is not needed to establish the Grams, it is only needed to understand them.
Here is Bharat’s Shudh Ashtak (octave):

As you can see, if one’s ears can perceive perfect third, fourth and fifth, one can tune any instrument to this Gram without the knowledge of Sharuties.

When Bharat Muni achieved this Gram, perhaps the following two questions came to his mind:
1. Why Re and Pa are not in Samvad (perfect fourth)?
2. What is the difference between current Pa (fifth in the above scale) and the Pa in Fourth Samvad with Rishav (2-5 = 1-4)?

Acharya Bharat’s Veena was an instrument not much different from modern Swar Mandal. He probably had many students and other music Acharyas in his ashram. Together they established that the difference between both of these fifths is the same difference that shows up on the ‘octave note’ when an octave is based on fifths or fourths (based on fifths, the octave notes is sharper, where based on fourths the octave notes is lower). When Pa (fifth in Shadaj Gram) was lowered to bring in the perfect fourth position with second (Rishav), it suddenly appeared to have the same relation with Ma (fourth) as Re did to Sa. In essence, the octave just shifted to the fourth. The difference between these two tunings of the fifth (pancham) was considered the most crucial in achieving a harmonic scale. Bharat Muni called it Parman Sharuti (sharuti of proof) as it was the Parman of difference between two identical scales sitting a perfect fourth apart from each other.

As he named his original scale Shadaj Gram, he named the new scale Madhyam Gram. Madhyam or Ma was the beginning note of this scale.

There are three types of Sharuties in Ancient Indian music:
1. Parman Sharuti
2. Sub-mehti Sharuti
3. Mehti Sharuti

According to Savart system devised by the French acoustician Joseph Sauveur (1653-1716) (named after the French physicist and doctor Félix Savart), if we divide the octave into approximately 301 equal parts (actually near 301.03), the approximate value of the above Sharuties is as follows:

1. Parman Sharuti = 5 Savarts
2. Sub-mehti Sharuti = 18 Savarts
3. Mehti Sharuti = sum of first and second sharuties or (18+5) = 23 Savarts

Now you can see that the Sharuties are not just unequal, their values are quite bit apart.

There are 22 sharuties in an octave. As I described earlier, sharutis are not Jananis (mothers) of notes, they are merely a way to measure and explain the phenomenon of physics of music. They are one of the ways to see how the pleasant sounding musical intervals relate to each other. In the end, it is all about pleasure.

Next time we will see how these Sharuties explain the harmonic position of notes in an octave.

sangtar.com > Music Theory > Advanced Theory

Music is an aural art. Any tone, which has a fixed frequency, can be used as a musical note. However, we sing and play music using more than one note. The difference between frequencies of any two notes is known as interval.

Long ago, a question popped in ancient artists’ mind.
What is the biggest or smallest note interval?
A never ending quest started. The Sharutis were their first yardsticks to map the intervals between notes, nothing more and nothing less.

We do not know the origin of music, but we do know that the theory of music is not the mother of music. The grammar of a language is defined after a language has been established. Also, a child learns to speak the language and then learns to read and write.

In the development of music, the things went like this (from a Natyashaster verse):
First songs, then notes, then Grams, Sharutis and then the Jaties (raags)

When we say that the songs must have developed after humans were civilized, we are forgetting something. Look around you. Birds sing, so do the other mammals. There are songs everywhere.

It is certain that as humans got civilized, their songs got complicated. With the development of language, the songs became more meaningful. The primal screams evolved into poems of love, separation, nature, beauty and other things that affected us emotionally. When something said through conversation does not capture the essence of our feelings, a song erupts in us. That is a primal instinct. It is not something that is impossible to do without the knowledge of Sharuties and Grams. A villager in India or a Gypsy in Europe cannot stop singing just because they do not know the difference between Just intonation and Chromatic intonation. These are afterthoughts.

When the enlightened artists of the ancient world sang their songs, the beauty of changing pitch compelled them to find more about it. What is it that changing the pitch up and down in certain ways sounds so…musical!

The first known theory of music in Indian Vedas (Samveda) contains four notes. Nowadays notes are always mentioned in ascending (such as C D E or Sa Re Ga) order. In Vedic tradition, the notes are mentioned in Avrohatmic order (in descending). The first four the Vedic artists knew were:
Madhyam (ma), Gandhar (ga), Rishav and Shadaj.
These were known as the first, second, third and fourth Svaras.

When I say they ‘knew’ about four notes, that doesn’t mean that they were unaware of higher and lower pitches. As described above, this was purely theoretical classification that explained the notes used in popular hymns and songs.

Then another note was found below all other known notes. They called it Mandar. A musicologist Tambru named it Dhaivat (the note that only enlightened one can hear, as it is the first note that has perfect third relation to the first note). This was the fifth note. Then Tambru established another note (Nishad) between Dhaivat and Shadaj. It was called the sixth. Later, below all other notes another note was found. It was named the ‘seventh.’ As it completed the septave, this note was also established above the first (Madhaym).

So in Samveda, M, G, R, S, D, N, P became the first, second, third, fourth, fifth, sixth and seventh. These notes were not the same as our modern notes with same names.

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