 This beautiful song sounds even more beautiful when it's accompanied by harmonium. Of course I didn't play the harmonium because I do know how to play the harmonium. I was afraid to record it and then I voiced over that recording. But I want to talk about these white and black keys. What are these keys? You know they correspond to notes A, B, C, D, E, F or Sari, Amaka as they are calling Indian classical music. But what are these notes? What is the physics of these notes? And what is the physics of music? The word harmonium is reminiscent of the English word harmonic which we see in physics, in simple harmonic motion. And this word is also related to the word harmony which we use in general to refer to different parts of the society working together to create something. In all these senses, harmony refers to one thing and that is fitting together. If we have a rectangle at several small squares, if all these squares are together exactly fit inside the rectangle, we say that the rectangle and the squares are harmonium. And if there is some part of rectangle or square left over, we say that they are not harmonic with each other. What does this have to do with simple harmonic motion? You see, simple harmonic motion is a sine or a cos function of time. And sine and cos are called circular harmonics. Why aren't they called circular harmonics? You must have seen the diagram where sine is represented as the length of the chord of a circle, half chord length of a circle. Now this chord length increases and decreases sometimes positive, sometimes negative. But overall, it completes one cycle or one loop along with the circle. In other words, a circle, the completion of a circle and the completion of one period of sine and cos fit together. That is why they are called harmonics, therefore circular harmonics. Because the nature of the function is in harmony with the circle. When you complete a whole circle, the function begins to repeat itself. In college level physics, we have spherical harmonics, which are harmonics over a sphere. These are polynomials in terms of force theta, which are synchronized with the sphere. As you complete a closed loop on the sphere, these harmonic functions also complete one cycle of their matrix. Therefore, circular harmonics and the word harmony of fitting together and working together are closely related. So now that you know that harmonics are used in society or harmony in the sense of fitting in of different people together. And they are using physics to represent a function that fits into the shape of a circle, by completing one period of values every time the circle completes one rotation. We now look at why harmonics are used in music. Why is this instrument called the harmonium? What exactly fits in into the different parts of the harmony? You see, first I will give you the physical fitting in sense, in terms of what you can hear. And then I will tell you what is the physics behind it, what exactly fits in mathematically to develop this harmony. I am going to press a note that represents the classical note sum. This will play a harmonium sound of sum, but I am going to match that sum with my voice. And you will notice that if I match it properly, then you will be able to hear a certain resonance between my voice and the speaker. However, I will be able to match my voice to this note of sum in two different ways. So, way one, here we go. Voice to this music in two different ways. Just to give you an illustration of matching, I will now show you a note that does not match with sum. You can see that my voice does not fit in with this and it feels weird. But when I matched my voice to the note, it was clearly audible as a result of resonance between the speaker and my voice. So, harmony is a fitting in of sound notes. So far, what I have demonstrated to you is a sense, an intuition of how it feels when two notes fit together. But what exactly is fitting in this note? In order to know that, we need to look at strength. Practically, we need to generate waves, these waves on a string. When you take a string, this traveling motion of the string is called a wave. What waves and strings have to do with sound and music? You see, sound also is a wave. And strings are a great analogy to understand how sound waves work. Look at this string. I can move this string around in such a way that it forms a groove, something like this. You can see my hands at the end of the string are not yet moving much and the center of the string is moving a lot. I can do the same thing. I can move the string without moving my hands very much. But I can generate two loops of the string. You can see that the ends of the string are largely constantly in place. And the center of the string is also constantly in place. And the string is actually moving in two loops. Now, what is happening to the string as we increase the number of loops? You see, when I rotate the string in one loop, one exact rotation, one exact bit of string that is vibrating is fitting inside the loop. When I rotate the string in two loops, two exact segments of the string vibrating are fitting in the total distance between my hands. So strings vibrating in loops are related to fitting in of harmonics. The word harmonic is related to fitting in and strings vibrating in loops are required to vibrate in such a way that the ends are fixed and there is a fitted number of loops in between those ends. In other words, I can vibrate the string in one loop. I can vibrate it in two loops, three loops or four loops. But I cannot vibrate a string in one and a half loop. And therefore the number of loops in the string would have to fit exactly in the distance between my hands. That is why strings are related to harmonics. Because vibration of a string or rotation of a string is a harmonic process where loops are supposed to fit exactly into the distance between my hands. My hands are called nodes and the points that are stationary in between the string are also nodes. Therefore movement of the string is the fitting of a fixed number of loops, a whole number of loops in between the end nodes which represent my hands. Now we address the question of how sound ties into all of this. You see sound also can be represented mathematically as something akin to the vibrating string which I just showed you. If this y-axis represents the pressure of air and the horizontal line represents the position in the column of a flute or in the blow of a harmonium, the position in a musical instrument, then the graph of pressure versus position is going to look just like the string where these are end points of the instrument. The vibrating pressure of air inside the musical instrument can form two loops like I have found here. It may form three loops, it may form a single loop or it may form any number of loops. But it will have to form a fixed number of loops because the treasured at the two ends are fixed. You see this end is open to the atmosphere which means it must be at a fixed pressure, the atmospheric pressure. This act is open to our lungs and this must be fixed at the pressure at which we are insulating air. Therefore the pressure cannot move at these two positions and it is in this intermediate position that the pressure is allowed to form loops and these loops must fit in, a whole number of these loops must fit in to the gap between these two end points. That is why sound is similar to the vibration of a string which I just showed you. You see each number of loops fitting into the distance between the end points, each number of loops is called a harmonic because it is a particular way to fit in the loops into the distance. Different harmonics vibrate at different frequencies while frequency is the number of vibrations per second. Different harmonics vibrate at different frequencies and these different frequencies are called notes. The musical note's different pitch and the quality of a wave which causes us to experience different pitches for different waves is frequency. Frequency is dependent on the number of loops fitting in between two fixed points and therefore changing the number of loops or changing the harmonic of the musical instrument of the air vibrating inside the musical instrument gives us a change in the pitch which we perceive as musical notes. And what was I doing earlier? Singing the same note in two different ways to match my voice with that of the harmonium. You see initially I was singing my note and perhaps there were 50 loops vibrating in my open pots between my lungs and my mouth. When I sang the note again this number was changed by a certain fixed percent, maybe it was 75 loops more and that gave me the next note, the next pitch or the next frequency which is a fixed number of loops between the same two points. And that is why I was able to match my voice in two different ways with the sound of the harmonium.