Hindustani Classical Music - My little understanding - Part 2 (Intonation)

In the previous article I gave a very basic introduction to Hindustani Classical Music. In this article I will talk about the "spacing" between the notes in Hindustani Classical music. "Spacing" means the difference of frequency between each successive notes. This is a bit complex to explain. I will keep it very simple. Let us begin!

"Intonation" is the word used to describe what I remarked above as "spacing". Intonation in music can be classified broadly as "equal tempered" or "just intonation". (This is a vast research topic. Just Google it!)

In equal tempered, the notes are spaced by a constant factor. That means, if say the constant is "1.059463", and the frequency of "Sa" is selected as 440 Hz, then the "Komal Re" will be (440 Hz *  1.059463 = 466.163 Hz). Similarly if I want to get "Shudha Re" then we multiply with a factor of  (1.059463 * 1.059463) to 440 Hz. Now, what is so special about "1.059463"? It is the 12th root of 2. There are 12 notes in an octave and the 13th note should be double the frequency of the 1st note. 440 Hz is what most western instruments tune to (as their note A4). Why the special treatment? You can read more about this here and here.

Please note, the notes in Hindustani Classical are not tuned (equally spaced) like how it is mentioned above. Though, if one uses a keyboard or (even a harmonium) they would "not" be playing the exact "re" if they played the key after the chosen "Sa" key. (There are other limitations of equal tempered instruments that do not adjust well with the Hindustani classical music. "Andolan (gentle oscillations around a note)", "Meend (slide from one note to another note)" cannot be performed in these instruments. More on these in a later post.) So how are the notes in Hindustani Classical spaced? Come, "just intonation".

Just Intonation, uses the concept of "ratios" between each notes. One broader way to define the ratios between each note in Hindustani Classsical is given below:

One possible ratios for Hindustani Classical notes

Please note that, there exists no single ratio system in Hindustani Classical listed in our texts that can be taken as final. In fact, in certain "Ragas" the ratios are definitely altered. But the above table does help us to get a working assumption (and a very closed assumption too). In fact, there is research done that specifies the ratios between all the 22 shrutis. Check here.

So assuming the above table, if we select 440Hz as our "Sa", then "re" would be 440 Hz * (16/15) =  469.333 Hz. "Re" would then be 440 Hz * (9/8) = 495 Hz. And "Pa" would be 440 Hz * (3/2) = 660 Hz. And "Sa." (of the next Saptak/octave) would be 440 Hz * (2/1) = 880 Hz.  Similarly, .Sa (of the lower octave) will be 440 Hz * (1/2) = 220 Hz. It should be noted that whatever be the ratios, "Pa" is always 1.5 times the frequency of "Sa" in an octave. There is some good reason too for the ratios in this fashion. You can read it here.

Enough of theory! Let us try something practical. So, below, I have an audio clip, where the singer sings all the 12  notes of the sargam in an octave. We will try to verify that the ratios that we have defined are actually true, when the performer performs. For this, I will use a software, called Sonic Visualiser.  The screen can be intimidating at first. So some explanation is required. Consider the figure below:

Right click and open the image in separate window to view the text

This is a screen grab from Sonic Visualiser. The screen above shows the fundamental frequency of the audio clip and its harmonics. We will concentrate only on the fundamental frequency spectrum here (The lowest frequency spectrum in the above graph, in orange). The X-axis is time an the Y-axis is the frequencies. As expected, since the singer is singing from "Sa" to "Ni" the frequency graph is seen in an ascending graph. I have written a software code that works upon this layer in S.V. and calculates the Hindustani Note using the ratios in the table above at any instance of time. This Hindustani note can be viewed in the lower right corner along with the corresponding western note. The "Sa" in this case is at 130 Hz.
Below presenting the video grab of the S.V. output. As you listen to the "AAaa"s of the singer, keep an eye on the lower right corner to check the Hindustani Note that is detected  based on the table of ratios I shared  above. My software code allows for a deviation from 2% in the frequencies. So with the above "Sa" at 130 Hz, I will report a "Sa" for any frequency between 127.4 Hz to 132.6 Hz. We need to allow a small deviation to take the human factor into consideration.

In the next post I will describe the concept of "Taal" in Hindustani Classical music.