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.

Hindustani Classical Music - My little understanding - Part 1

I have been trying to read  about and understand the Hindustani Classical Music for some time. Note that I am not trying to learn to sing Hindustani Classical Music. I am not quarter of the fraction talented for that. I aspire to understand the finer points of the art and identify them when I listen to the great singers of the art. I will try to keep it as simple as possible here at the beginning. Please pardon me for any mistakes. I am just a beginner willing to learn and understand the art. Please feel free to "beat and bash me" for the mistakes I make here.

So, with the disclaimer and clarification over, let us start.

Classical music in our country is divided into two forms, Hindustani and Carnatic. Hindustani Classical is dominant in the North and Carnatic in the South. There are lots of similarities and dis-similarities between the two. I am not dwelling into them in this post. However, whatever I mention here is specific to Hindustani classical.

The basic thing to keep in mind in our music (Hindustani or Carnatic) is that it is very analogue in nature. This is the main reason we sense a sense of continuity in our music when we listen to it, unlike western music.

We all know that our Music is made of the 7 swars (surs, or notes). They are
"Sa", "Re", "Ga", "ma", "Pa", "Dha" & "Ni".
These are the "Shudh" (pure) form of the notes. (All of the above have a long name version too, for example "Sa" is actually the short of "Shadja", "Re" is "Rishabh" and so on.) Note when you sing the 7 swars, you tend to "raise your pitch" a little higher when you sing the next in the sequence. Meaning, you sing "Re" at a higher frequency than "Sa"... which means the sequence of the notes matter. Each of the notes in the above sequence is at a higher frequency that than the one preceding it.

As I  said that our music is analogue, we divide this scale a bit more by adding more notes in between so that our music does not seem to jump from one note to another. (Remember, the sampling theorem?) So let us  introduce  more notes in the sequence above. The new sequence of 12 notes now looks like this:
"Sa", "re", "Re", "ga", "Ga", "ma", "Ma", "Pa", "dha", "Dha", "ni" and "Ni"

The new notes: "re", "ga", "dha" and "ni" are the "Komal" (softer, lower frequency) version of their "Shudh" (pure) forms. Whereas the note "Ma" is the "Tivra" (sharper, higher frequency) version of the "Shudh" "ma". So note that all "shudh" notes are written with capital letters, except "ma". This is to indicate that for "ma" there exists no "komal ma" but a "tivra Ma". This is the convention I follow to denote the notes.

One more important consequence of the above is that the notes "Sa" and "Pa" exist only as "shudh" and are never "komal" or "tivra". They are thus "fixed" notes. (Ever wondered what the disciples play on the "Tanpura" behind the performing artist? They generally play a combination of "Sa"-"Pa"-"Sa" and of course it is not without a reason. More on that in a later post)

It is said that our forefathers (and foremothers) further divided the scale above to define more notes in between to give even smoother transitions from one note to another. So in all they came up with 22 "shrutis" (or 22 notes). Though of much importance, we will not tend to divide our scale further than the one done above with 12 notes.

We now come to the last topic of the post. And that is the "Saptak" definition. So in school when we were taught music, we always sang "Sa Re ....Ni and ended in Sa".... what is this "Sa" after the "Ni"? This is the "Sa" of the next saptak or the "taar saptak". This is twice the frequency of the "Sa" you sang at the beginning. Like wise you can have a "Ni" before your first "Sa", and that would be the "Ni" of the "mandra saptak" which would be half the frequency of the "Ni" in your original "Ni".

So, now we have something like:

(Mandra Saptak): .S .r .R .g .G .m .M .P .d .D .n .N        (Your voice's natural (or middle) saptak): S r R g G m M P d D n N      (Taar Saptak): S. r. R. g. G. m. M. P. d. D. n. N. (Ati taar saptak) S.. r.. and so on

Note that, I define the notes in Mandra Saptak with a dot (.) before the note letter, and after the note for Taar Saptak notes. One can stretch the scale on either side "as much as possible" .

"As much as possible" is the next point. In our music, the frequency of  "Sa" in the natural saptak is not fixed. It is determined and selected by the performing artist (vocal or instrumental) as per his or her convenience. So the frequency of my "Sa" for me may be the frequency of "Ga" for you. So if you and I are to sing together, we have to tune ourselves, so that when we sing together and we do not sound out of tune. Our system is thus very fluid (again analogue). This is in contrast to western music. They have sort of standardized their scales, in that they have a one-to-one mapping between their note and frequency. So, for instance in one of their standards, A#4 is fixed at 440 Hz and everything follows thereafter. Check here. Of course there are general conventions in our system, so singers generally choose the frequency of C4 or C#4 as their "Sa". However, note this only an easy convention. There are lots and lots of performers who simply chose a frequency of their choice and convenience as "Sa". Generally, vocal artists train their voices so that their voices span across one "saptak" above and one "saptak" below their natural "saptak", and this what I meant by "as much as possible".

Since the "Sa" in our music is not fixed (in terms of frequency), whenever a classical piece begins the performer will make every effort to establish the "Sa" first. He or she will do so by singing the notes around "Sa", the "Sa" itself or some characteristic phrases, so that the listener (and the performer too) have the "Sa" fixed in their minds. It is also required to periodically refresh the "Sa" during the performance, and hence the use of Tanpura playing the two fixed notes, "Sa" and "Pa" throughout. (Note there is more to the drone instruments, will post later)

Well, that's all for today. In the next post I will discuss a little about the "gap in frequencies" between each note and  a little mathematics around it!