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.

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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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In Indian tradition, music is a combination of three separate art forms:
1. Singing
2. Playing and
3. Dancing

These art forms are learned and performed through Raag and Taal. ‘Raag’ is the dictator of melody and the ‘Taal’ is the dictator of Rhythm. In addition, melody is the product of sound and the rhythm is product of time. Therefore, ‘the music is the art of manipulating the ‘sound’ through ‘time’.

The time affects music in two different ways. First through rhythm is obvious. However, the time is also at work producing the musical sounds that are useful in melody. The universe is full of sounds, but every sound is not musical.

Therefore, the next question is, what is a musical sound?
Each sound can have two segments:


1. The strike and
2. The resonance

In Hindi, these are known as ‘Aghaat’ and ‘Kampan.’ The strike is not a musical sound, but its resonance is. Let’s explore that further. When an object is hit, the first movement it creates in the air is not musical. After the initial strike, the object either will resonate at a fixed frequency or will stand still. If the object creates a tone at a fixed frequency, that tone can be useful in music. Without that resonance the sound will be nothing more than a ‘tick.’

In Sanskrit, these are known as ‘RaNit’ and ‘AnuraNit.’ The ‘AnuraNit’ is the mother of Sharuties.

Now the question is, how long this resonance has to be?
Musically speaking, it has to be long enough so our brain can register it as a musical sound. With the damper on, you can run your hand on a piano keyboard as fast as you can and brain still registers the pitches. Therefore, the length has to be in mere milliseconds. Nowadays if you use a digital audio editor, keep cutting a wave file of a single note, eventually it loses its tone. At that point, it becomes an unmusical ‘strike’ or a click. All those who work with digital editors know that there is an annoying ‘tick’ hidden in the beginning of every pleasant sound. The minimum length of a note varies with the frequency. Naturally, higher the frequency, sooner the note is detected.

The sages of music knew these things without the help of DAWs thousands of years ago.

When more than one frequency is present in the air, they interact with each other. Their vibrations overlap. The sound changes. Some frequencies compliment each other and others do not. The intervals of notes in an octave are directly related to their power to influence the other frequencies.

The enlightened ones have recognized this effect equally all around the world. One way or the other, they set up the notes that share similar frequencies. In India, the practice of setting up the note intervals was based on Sharuties. We will start to explore the ‘Sharuti System’ in the next post.

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Somewhere between 3000 and 6000 years ago, an Indian sage Bharat Muni, wrote a book about the performing arts and forever tied the stage, dance and music together. The book is called ‘Natyashastar’ (Natya = performing Arts, Shastar = Science). It is said that the Brahma himself taught Bharat the secrets of performing arts and asked him to spread the knowledge in the world.

The book became the most important source in the development of art of music throughout the world. At that time, India was an important destination for knowledge seekers and travelers. Artists from all over the world went to Indian Ashrams and learned the secrets of Natyashastar. The seven main notes of music in Indian, Chinese, Persian and European music are not just a coincidence, we have to thank Bharat Muni for it. He proved that the note intervals are not arbitrary but (should) have a relation to the root.

Natayshastar is the first available source in the history of our civilization that explains the true nature of harmonics. This knowledge eventually arrived in Europe and a couple of millennia later, Pythagoras used some of Bharat Muni’s techniques to explain the musical phenomenon thorough math and physics. Unlike Bharat Muni, Pythagorus established a scale based on perfect fifths. I read somewhere that at Pythagoras’ time, the consonant of third was not known to Europeans. Yet it was a major part of Bharat’s scale. Bharat established his scale based on three types of harmonics:

Perfect fifth or 3/2,
Perfect fourth or 4/3 and
Perfect third or 5/4.

We will continue discussing these concepts in detail in other posts. Here I would like to give you a simple example of Bharat Muni’s Shudh (pure) Suptak on a Swar Mandal or a Harpsichord:
1. Establish Sa
2. Establish Pa with Sa-Pa (3/2, perfect fifth or Sa-Pa) relation
3. Establish Ma with Sa-Ma (4/3, perfect fourth or Sa-Ma) relation
4. Establish N with M-N (4/3, perfect fourth or Sa-Ma) relation
5. Establish Ga with Ni-Ga Avrohagatic (3/2, perfect fourth or Sa-Ma in descending) relation
6. Establish Dha with Ma-Dha (5/4, perfect third or Ma-Dha) relation
7. Establish Re with Re-Dha Avrohagatic (3/2, perfect fourth or Sa-Ma in descending) relation
8. Establish upper Sa with Pa-Sa (4/3, perfect fourth or Sa-Ma) relation

Compared with modern natural scales, Bharat’s Ga and Ni are komal (flat). Bharat used only nine notes in his music. The above seven are the pure notes and the following two are the Vikrats (moved):
1. Modern shudh Ga (natural third) or Bharat’s Antar Ga (Gandhar) = Sa- Ga (5/4, perfect third or Ma-Dha) relation
2. Modern shudh Ni (natural seventh) or Bharat’s kakali Ni (Nishad) = Pa-Ni (5/4, perfect third or Ma-Dha) relation

Bharat established his music system based on Gram and Moorshana. Gram is the system of establishing the interval of notes, where Moorshana is the system of making parent scales. The above Shudh scale is Bharat’s Shadaj Gram (the Gram of Sa).

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You may have read somewhere on this site that Indian Natural Scale is identical to Western Natural Scale.

tone-tone-semitone-tone-tone-tone-semitone

Now, as we discuss the advance theory of music, we have to find the true ‘Natural Scale’. There is no standard Western Natural Scale, so the comparison makes no practical sense. Although, if one does not wish to look into the soul of music, the comparison and the term itself (natural scale) need no further explanation.

Physics of music is a weird phenomenon. For centuries, musician tuned their instruments to each other. What they perceived natural, was natural. Without knowing the frequncies of various notes, everything was naturally in-tune. Now, when we are trying to tie the music to a fixed octave, the natural scale is mere a term. There is nothing natural about any scale played on an electronic keyboard or piano.

Music is an audible art, based on what we hear. To our ears, perfect harmonics sound pleasing. Thus the ancient musical scales were based on perfect harmonics. There are many ways to construct a harmonic scale. Although by doing so, based on the composition, sometimes a few temporary or permanent interval adjustments are required. That is what music is all about. A professional composer or performer knows how to make his composition sound ‘just right’.

Generally speaking, a scale based on ‘just intonation’ is a natural scale. The notes in this scale are established by multiplying the base note’s value with the following harmonic intervals:

Unison= 1 (starting note)
Major 2nd=9/8
Major 3rd=5/4
Perfect 4th=4/3
Perfect 5th=3/2
Major 6th=5/3
Major 7th=15/8
Octave=2

If a piano is tuned according to the above ratios starting from the middle ‘C’, and one wishes to play D major, the intervals will not work. Having said that however, you can change the ‘keynotes’ in C major to get seven different scales, and they all are perfectly natural (more on this later).

We will slowly explore the physics of music. The point is not to remember the frequencies of notes, the point is to understand the natural musical intervals. Indian musicologists explored these phenomenon long before the rest of world. Around 2000BC, The Indian scales based on harmonics had already established and explained in depth.

Nowadays, the natural scale is not derived from harmonics. It is derived from ‘the twelfth root of two’, which has a value of 1.059463 (approx). When this number is multiplied 12 times, the answer is “2”, that is the value of our octave notes (See the list above, the last ratio is 2:1). This system ignores all other harmonics to get a perfect octave. 12 notes of an octave are placed on equal intervals. Although, the values you get through this system are around the desired values, but these are not perfect. This system of dividing a scale into 12 equal intervals is called an “Equal Temperament Scale.”

A violin player cannot play this scale. Only a tuner can achieve these tunings. Humans (trained) naturally play a ‘just intonation’ scale. Yet many musicians think that ‘just intonation’ scales are outdated. Have a look at how one “music wizard” explains the ‘just intonation’ scale in ‘Google Answers’:

“The archaic natural scale uses whole number ratios multiplied by the base note of the octave to achieve the frequency of the other notes. This is an imperfect or dissonant method of composing scales and usually does not sound right.” Perhaps he is a DJ.

If you are interested in reading more about physics of music, the following website has a lot of correct information: Physics of music

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