Making the next 16 Thaats with 8 Tetrachords:
In the last post, we put together our 8 Tetrachords and figured that there are 16 available combinations. That made our first 16 Thaats. Now to make the next 16, we will have to make only one change in each, that is the position of the fourth or Madhyam.
All Thaats in the last post, had a natural Madhyam, now we are going to use Tivar Madhyam or sharp fourth. Here in a simple table, I am going to write each Thaat’s Tivar Madhyam counterpart Thaat right in front of it. I will present all 32 Thaats in a flash movie in the next post:

	Natural Madhyam Thaat	Vikrat			Tivar Madhyam Thaat	Vikrat
1.	Bilaval	none		17..	Kalian	M’
2.	Sarsangi	d,		18.	Latangi	M’, d,
3.	Khamaj	n,		19.	Vachaspati	M’, n,
4.	Charukeshi	d, n,		20.	Rishavpirya	M’, d, n,
5.	Suryakant	r,		21.	Gamanpirya	M’, r,
6.	Bhairav	r, d,		22.	Pooravi	M’, r, d,
7.	Chakarvak	r, n,		23.	Rampirya	M’, r, n,
8.	Bakulabharan	r, d, n,		24.	NamNarayani	M’, r, d, n,
9.	Gauri Manohari	g,		25.	Dharamvati	M’, g,
10.	Kirvani	g, d,		26.	SahinderMadhyam	M’, g, d,
11.	Kafi	g, n,		27.	Hemvati	M’, g, n,
12.	Asavari	g, d, n,		28.	ShanMukhPirya	M’, g, d, n,
13.	Kokilpirya	r, g,		29.	Svaranangi	M’, r, g,
14.	Dhenuka	r, g, d,		30.	Todi	M’, r, g, d,
15.	Natakpirya	r, g, n,		31.	ShadvidhMargani	M’, r, g, n,
16.	Bhairavi	r, g, d, n,		32.	Bhavpirya	M’, r, g, d, n,

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Making The First 16 Thaats with 8 Tetrachords:

In the last post we saw that there are 4 poorvang Tetrachords and 4 Utrang Tetrachords.

By combining the upper and the lower Tetrachords, we can get 16 (4×4) unique scales.

The scale structure will be as shown below:

		Tetrachord Number
		Poorvang		Utrang
Thaat Names					Vikrat
1. Bilaval		1	+	1	none
2. Sarsangi		1	+	2	‘d’
3. Khamaj		1	+	3	‘n’
4. Charukeshi		1	+	4	‘d’, ‘n’
5. Suryakant		2	+	1	‘r’
6. Bhairav		2	+	2	‘r’,’d’
7. Chakarvak		2	+	3	‘r’,’n’
8. Bakulabharan		2	+	4	‘r’, ‘d’, ‘n’
9. Gauri Manohari		3	+	1	‘g’
10. Kirvani		3	+	2	‘g’,’d’
11. Kafi		3	+	3	‘g’,’n’
12. Asavari		3	+	4	‘g’, ‘d’, ‘n’
13. Kokilpirya		4	+	1	‘r’, ‘g’
14. Dhenuka		4	+	2	‘r’, ‘g’,’d’
15. Natakpirya		4	+	3	‘r’, ‘g’, ‘n’
16. Bhairavi		4	+	4	‘r’, ‘g’, ‘d’, ‘n’

The scales will look as shown below:

1. Bilaval:

Bilaval is the combination of Bilaval Tetrachords from the both sides (1+1).

	1. S R G m	+1. P D N S*

2. Sarsangi:

Sarsangi is the combination of Bilaval & Sarsangi Tetrachords (1+2).

	1. S R G m	+2. P d N S*

3. Khamaj:

Khamaj is the combination of Bilaval & Khamaj Tetrachords (1+3).

	1. S R G m	+3. P D n S*

4. Charukeshi:

Charukeshi is the combination of Bilaval & Charukeshi Tetrachords (1+4).

	1. S R G m	+4. P d n S*

5. Suryakant:

Sutyakant is the combination of Surykant & Bilaval Tetrachords (2+1). Suryakant is also known as Anand Bhairav.

	2. S r G m	+1. P D N S*

6. Bhairav:

Bhairav is the combination of Surykant & Sarsangi Tetrachords (2+2).

	2. S r G m	+2. P d N S*

7. Chakarvak:

Chakarvak is the combination of Surykant & Khamaj Tetrachords (2+3). Chakarvak is also known as Ahir Bhairav.

	2. S r G m	+3. P D n S*

8. Bakulabharan:

Bakulabharan is the combination of Surykant & Charukeshi Tetrachords (2+4).

	2. S r G m	+4. P d n S*

9. Gauri Manohari:

Gauri Manohari is the combination of Gauri Manohari & Bilaval Tetrachords (3+1).

	3. S R g m	+1. P D N S*

10. Kirvani:

Kirvani is the combination of Gauri Manohari & Sarsangi Tetrachords (3+2).

	3. S R g m	+2. P d N S*

11. Kafi:

Kafi is the combination of Gauri Manohari & Khamaj Tetrachords (3+3).

	3. S R g m	+3. P D n S*

12. Asavari:

Asavari is the combination of Gauri Manohari & Charukeshi Tetrachords (3+4).

	3. S R g m	+4. P d n S*

13. Kokilpirya:

Kokilpirya is the combination of Kokilpirya & Bilaval Tetrachords (4+1).

	4. S r g m	+1. P D N S*

14. Dhenuka:

Dhenuka is the combination of Kokilpirya & Sarsangi Tetrachords (4+2). Dhenuka is also known as Pilu.

	4. S r g m	+2. P d N S*

15. Natakpirya:

Natakpirya is the combination of Kokilpirya & Khamaj Tetrachords (4+3).

	4. S r g m	+3. P D n S*

16. Bhairavi:

Bhairavi is the combination of Kokilpirya & Charukeshi Tetrachords (4+4).

	4. S r g m	+4. P d n S*

Please note that all these Thaats have ‘Komal Madhyam’. Which is also know as Natural Fourth or Shudh Madhyam.
Making the rest of the 16 Thaats is easy now. Just change the Madhyam to Tivar in all the above. We will talk about those in the next post.

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In the last post, we looked at eight Tetrachords. As I mentioned in that post, these Tetrachords are holding the key to all musical scales. How easy is it? Just memorize eight groups of four notes and construct 32 Thaats on the fly. Review the Tetrachords once more here before proceeding.

Now let’s name these Tetrachords:

Natural scale “C D E F – G A B C” is ‘Bilaval’ in Indian music, and these notes are:

S R G m – P D N S*

When we assign a name to a Tetrachord, we assume that its counterpart is natural. So when we are naming Poorvang Tetrachords, we assume that Utrang is “P D N S*” or “G A B C;” and when we are naming the Utrang Tetrachord, we assume that the Poorvang is “S R G m” or “C D E F.”

Later we will cross match them to build different scales.Now have a look at these images along with the assigned names:

Poorvang Tetrachords:

1. Bilaval		2. Suryakant
3. Gauri Manohari		4. Kokilpirya

1. S R G m is Bilaval
2. S r G m is Suryakant
3. S R g m is Gauri Manohari
4. S r g m is Kokilpirya

Utrang Tetrachords:

1. Bilaval		2. Sarsangi
3. Khamaj		4. Charukeshi

1. P D N S* is Bilaval
2. P d N S* is Sarsangi
3. P D n S* is Khamaj
4. P d n S* is Charukeshi

Complete the scales by adding upper or lower natural (Bilaval) Tetrachord as needed.

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In essence, a Tetrachord is a series of four tones filling in the interval of a ‘perfect fourth’, a 4:3 frequency ratio. In modern Persian music, two Tetrachords come together to construct an octave. When Persian musicians came to India, they also brought the Tetrachord theory with them. In Indian music, these are known as the Poorvang and the Utrang (lower and upper half of octave).
Two Tetrachords of any octave are:

1. C D E F
2. G A B C

In Indian music, these will become:

1. S R G m
2. P D N S*

Here C and F in the lower, and, G and C in the upper Tetrachord are sitting at a 4:3. The positions of the middle notes are variable.
Now, let’s talk about the variables. Take the Poorvang, or the lower Tetrachord first.

S R G m

We know, that S and M (1st and fourth) have to stay permanently at an interval of fourth to make it a Tetrachord. So the only variables are the middle notes, R and G. These both notes can move freely between their two positions (Komal and Tivar). Knowing that, it is very simple to find that there are only four ways to write this Tetrachord:

1. S R G m
2. S r G m
3. S R g m
4. S r g m

If your Sa is on C, then these four variations are:

1. C D E F
2. C Db E F
3. C D Eb F
4. C Db Eb F

Here are four illustrations showing four variations of the ‘Poorvang’ or the lower Tetrachord.

1.		2.
3.		4.

The Utrang or the upper Tetrachord also has four similar (or identical, technically speaking) variations:

1. P D N S*
2. P d N S*
3. P D n S*
4. P d n S*

If your Sa is on C, then the ‘Utrang’ variations are:

1. G A B C
2. G Ab B C
3. G A Bb C
4. G Ab Bb C

Here are four illustrations showing the four possible variations of the ‘Utrang’ or the upper Tetrachord.

1.		2.
3.		4.

Study them well. It seems so simple. However, thousands of scales (All possible Thaats and Raags) are hidden in the eight illustrations above.

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