[MUSIC] Notice today I'm not playing the piano but the violin. Haha, actually just kidding. I don't really play the violin. This is my daughter's violin. But I did go to a lot of violin lessons during the 12 years that she studied it. I am holding the violin because this session is devoted to tone color. Primarily, the colors or sounds of the instruments of the Western symphony orchestra. The music we will be listening to and indeed music that we just heard, was by Rossini, his William Tell Overture. There are trumpet and french horns, and then violins. Ever wonder why one instrument sounds differently than another? Okay sure, they're made from different materials and have different shapes, and that really is the answer. But the sound coming out of these instruments is actually different. It has to do with the acoustics of music, and that's what I'd like to explore for a moment. Let's go back to a topic that we broached in our first session, the overtone series. Remember, when a column of air is vibrating within the chamber of a musical instrument, inside a flute or trumpet, or a string is vibrating, as on a violin, many subparts of that column or that string are also vibrating, as we see in this diagram. This shows the whole string vibrating in red, halves of the string vibrating in blue, and thirds of it vibrating in green. Now let's look at these same subsections in a different way, standing them upright. The lowest pitch is on the left, that we call the fundamental. That's the one that we actually hear, it's basic sound. And the successively smaller sections of the string are to the right. They're the overtones. We hear them, but only very, very faintly, almost subconsciously. Okay. Freeze that idea. Because we're going to go, work in another concept, and that is volume. All musical sounds have a pitch. Also, sounds have a tone color, or timbre as it's called. And they also have a volume, or loudness. Let's think of pitch as sound waves operating horizontally, you have big sound waves, which create low pitches, and you have small ones that create high pitches. But let's focus on volume for just a moment. We have these loud sounds and we have soft sounds. These are usually displayed vertically. Loud ones go way up or down. Soft ones up or down just a little bit. To see this, let's return to our Beethoven's Symphony Number Five, and to the active listening guide that accompanies it at the website that you may choose to accompany this course. Here, we see a scale of amplitude, as it's called. Amplitude is simply the measure of loudness, louds spike. With soft sound, the needle doesn't move very much. [MUSIC] So watch the amplitude bars begin growing here, begin to expand. [MUSIC] Then control. Expand with the loud sections. Contract. Low volume, but it's beginning to grow. And you can hear this crescendo. And you can indeed see this crescendo, because the amplitude bars increase. [MUSIC] Driving the final point of loudness and sudden disappearance of sound. Okay, now let's combine these two ideas, pitch and volume. But before we did do that, I need to say one more thing. All musical instruments generate the same overtone series. All overtones are halves of the fundamental thirds of the fundamental fourths of the fundamental on down the line. Again, we hear them only faintly, but each instrument, the trumpet, the violin, the oboe, whatever, generates a different amplitude for each of the overtones within the series. The instruments have different patterns of amplitude and these different patterns determine the difference in tone color of the instruments. On the screen you see the diagram of a violin. Shows the overtones for the violin. Now, the vertical bars not only reflect the overtones moving left to right, but also the loudness, the amplitude for the instrument of each overtone. Notice as we proceed down through the overtones it's not a straight line decent. Some of the overtones pop up quite loudly, and others are very quiet. And it's this mixing of loud overtones and soft overtones, yet all these are very, very quiet, mind you. It's this mixing that creates a particular tone color or timbre for the instrument, just like at Starbucks. The coffee meister will mix a different blend of coffees from different regions of the world to form a holiday blend or a bold, or whatever it might be. So to here, we have different amplitudes of the different overtones creating a distinctive tone color, or timbre. Lets compare the overtone chart of a violin to that of a trumpet. You can see that's different, again here, violin is on top, trumpet is on the bottom. Now watch a demonstration of how overtones work on a trumpet as they are added in. My friend Ed Doering at the Rose Hulman Institute of Technology in Terre Haute, Indiana created this and has allowed us to make use of it. Remember, in the discussion here, frequency here refers to pitch, amplitude to volume, and here, he uses the word partial to refer to overtone. Musicians and scientists use the terms partial, a part of a string or part of a column of air vibrating, and overtone, partial and overtone, interchangeably. On this demonstration, zero is the fundamental, that's the sound we hear. One the first overtone, two the second and so on. Watch as this scientist creates the sound of a trumpet in the lab by building up the overtone series. >> Here's an illustration of this technique applied to a short burst on a trumpet. I'm indicating the frequency and amplitude trajectories, and then I can by using the slider, add or subtract partials to build up the sound. >> First [INAUDIBLE]? >> This is only with the first partial. And then we can see the corresponding amplitude of our sine domain signal quite nicely. Here we see that the frequency has a little bit of a, a jump at the beginning transient, but it's mostly [SOUND] the same frequency throughout. So now I'm adding the next partials at a higher frequency. [SOUND]. This is the next one yet, even higher frequency and as you look at the amplitude you notice that the onset of the higher frequency partial is a little bit delayed. [SOUND]. >> Now is he adding in all the overtones? >> So again you see each of these higher frequency partials has a little bit of a late entrance but then they also decay faster as well. >> Pretty cool. The more the engineer adds in overtones, the more we come to realize the instrument in question is, in fact, a trumpet. If he put them in using other proportions of loudness, he could make this sound like a clarinet or an oboe, and that's what an electronic synthesizer does. And that's what we have here. On a synthesizer you can push a button and program a particular amplitude series to set up the sound of the strings, for example, and then hit a key and you get the sound of the instrument that you've chosen, whatever instrument you want to have produced. You have in effect the entire orchestra at your disposal. Now let's see what I've got over here at the moment. [MUSIC] Okay, that's programmed with the overtone series of a modern grand piano. Let's see if I push this button over ,here what do I get? Who knows? [MUSIC] Some kind of electronic organ. Let's try this one. [MUSIC] That's a string sound. String orchestra. To sum up, in music it's the amplitude or loudness of the various overtones created by an instrument that produces a particular blend of sound, and thus the distinctive tone color or the timbre of that instrument. Miraculously our brain processes all of this complicated information about overtones and amplitudes and tells us in a split second hey, that's the sounds of a trumpet, or hey, that's the sound of a violin.