Western instruments, such as the piano keyboard, are tuned to what is known as Equal Temperament. The idea here is pretty simple, divide the space between a note and its octave note (i.e. note with double the frequency of the original) into 12 equal parts. Each division is then set to a note. In fact, the space is divided artificially into 1200 parts. Each part is called a “cent”. A note is at every 100th cent. When musicians talk about a note being flatter or sharper than standard, they often talk in terms of cents (i.e. 2 cents flatter or 4 cents sharper etc.)
The logic behind equal temperament is pretty straight forward. A keyboard has no starting or ending note. The musician should be able start from any note. If notes are equally spaced, this becomes pretty easy.
The philosophy of Hindustani music is a bit different. The starting note is always considered to be Sa. To keep reference of the Sa, the musicians have the Tanpura tuned to it. When Tanpura strings interact with one another, they create harmonic frequencies. These harmonics are, by definition, multiples or ratios of the interacting frequencies. It follows then, that if a performer matches his notes to these harmonics, those notes will be complemented by the sound of the Tanpura. Conversely, if the musician hits notes that are not in tune with the harmonics (and equally spaced notes are not), he or she will not sound as good.
Therefore, Hindustani musicians play their instruments or sing in what is known as the Just Intonation. The table below shows the relationship between Just Intonation and Equal Temperament.
Relationship between equal temperament and just intonation is shown in the table below. It is not very important to remember the calculations as the offsets in the last column are used in the explanation on how to use chromatic tuner for Hindustani music.
Now that we know the theory of Hindustani scale and ear training, we would have a basic question in mind – how do we apply this theory. In other words, you know that you have to train your ear to be able to listen to the beats but in absence of immediate feedback from a teacher (which is how it has been taught traditionally), how will you know if you are hitting the right notes.
Fortunately, modern technology created a simple device called Chromatic Tuner. If you haven’t already read about it, please take a minute to read this.
Hindustani music teachers rarely use Chromatic tuner for several good reasons. First of all, the traditional way of teaching Hindustani music is from Guru (teacher) to Shishya (disciple) one on one. The teacher helps the student with all aspects of music including tuning and ear training.
Secondly, the Chromatic tuner shows tuning to the Equal Temperament scale and Hindustani music is not played to equal temperament scale. It is not only played to a scale based on integral ratios of frequencies but also the exact frequencies of notes sometimes vary depending on Raga.
However, if we know the positioning of the just temperament note relative to the indicator on chromatic tuner, we can use the chromatic tuner for our ear training. If you are interested in deeper discussion on how these offsets are calculated you can check here, but to keep it simple, simply open this page, print it, cut out the offsets table and stick it on your Chromatic tuner.
If we look at this table closely, we can think of making a creative use of calculations articulated in the table. We can use a Chromatic Tuner for verifying if we are hitting appropriate notes in Hindustani scale as long as we hit them with the offsets summarized in the table below. In other words, for getting the Hindustani Pa note, we must make sure that we strike it 2 cents higher from what the Chromatic tuner shows as the correct note.
Of course, modern iOS or Android based tuners are programmable and you can simply choose Just Intonation as option with base note as the Sa of your flute. Then you can just focus on hitting perfect tuning at zero setting without worrying about offsets.
Using this method has several benefits. It helps tremendously in ear training. Since getting the right note in Bansuri is a function of applying the correct blowing pressure and correct angle of blow, it is quite difficult for beginners to hit the note correctly. In such cases, Chromatic tuner can come very handy.
This of course, is no substitute for traditional Guru-Shishya training. As I mention before, sometimes notes are dependent on Raga. For example, the flattened second (komal re) note is used in both ragas – Bhairav and Marwa. However, the same note in Bhairav gravitates towards Sa, while in Marwa it gravitates towards Re (major second). Such nuances can only be taught by the teacher.
More Resources on this topic –
1. How Equal Temperament Ruined Harmony (and Why You Should Care). A wonderful, easy to read book that explains mathematical theory behind musical sound and its application in Western music.
2. Java Tuner – You can try out tuning with equal temperament and just intonation.