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.
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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.
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Study them well. It seems so simple. However, thousands of scales (All possible Thaats and Raags) are hidden in the eight illustrations above.
Hello,
And thank you for the great series of articles covering such an important stuff!
The problem with the tetrachords which a faced is: what about the cases of sharp 4th (ma). It appears to be prohibited in Arabic music? Please cast some light on it.
Thank you again!
You have a very informative site. I have learned a great deal about eastern music and music in general, from your pages.
Your construction of scales from tetrachords building blocks is presented with great clarity and thus has been immensely helpful.
I have only been studying music for 2 years so forgive me if my question/comment seems elementary or erroneous.
I am a little confused about your assertion that there are only 4 ways to construct a basic tetrachord:
Using your orginal restrictions/limit/definition that the interval between the first and the 4th note be a perfect 4th, and then using C to F as the outer limits of the tetratchord, to my way of thinking we would have:
1. C D E F T T S *
2. C D Eb F T S T *
3. C Db Eb F S T T *
4 C Db E F S 3S S *
5. C D# E F 3S S S
6. C Db Ebb F S S 3S
Since you have included a combination in your list of 4 possibilities that includes a three semi-tone type interval, why not include the other two combinations (#5 & 6) that use a 3-semitone interval?
As I said, I am new to music & music theory but I really want to have a solid grip on the foundations. So any light you shed would be most appreciated.
Thank you,
Robyn