 Welcome to Where Music Meets Science. My name is Scott Laird and I'm a music instructor at the North Carolina School of Science and Math. In our last lesson, we learned about frequency and octave relationships. In this lesson, we will be focusing on the waves that are generated by a variety of instruments and their unique characteristics. In order to do this, let's begin by looking at a perfect wave. This diagram represents a sine wave. It is a perfect wave. Let's listen to it. Notice that there are no imperfections in the shape of the wave and it is not very pleasing to hear. This represents a pure, single frequency and really doesn't occur naturally on its own in our world. The sine wave was generated by a computer. It is the frequency 220 Hz, which we discussed in the previous lesson. I have chosen this frequency to use today because it's in the middle of the musical range and many instruments can play this pitch. Let's review the parts of the wave. The high point of the wave represents the place that air molecules are compressed together. The low point in the wave represents the place where they are spaced apart. The y-axis is air pressure. The height of a wave depicts how loud the sound is. Taller waves are louder. Shorter waves are quieter. The height or volume of a wave is known as its amplitude. This part of a wave will become very important as we look at the unique qualities of the waves generated by different instruments. If we look at this sine wave in 3D, we see that the only frequency that is represented is 220. There is no amplitude at any other frequency. Now, let's look at the wave that is generated by a cello. Notice that the wave has many more angles and changes than the sine wave. We can see the big portion of the wave moving is at 220, but there are many other changes. What do these represent? Let's take a look at the cello's wave in 3D. Note that there is amplitude represented at a variety of numerical values on the graph. Can you see which frequencies seem to be present? Can you name a few? Is their amplitude the same as the amplitude at 220? Or are they larger or smaller? Note that we are still hearing the pitch A220, but there seem to be other frequencies represented. This is what we call a complex wave. A complex wave is a sound that is made up of many different sine waves coming together to form the unique sound of, in this case, a cello. Notice that there seems to be a frequency at 440, 660, and 880 hertz. These numbers, which represent pitches, are very important and they certainly relate to the pitch A220. Do we know anything about any of these frequencies already? Think back to our last lesson on octave relationships. First, the sound is created by changes in air pressure. Second, these changes occur in a wave-like motion. Third, faster waves or frequencies represent high pitches. Slower waves or frequencies represent low pitches. Fourth, one complete vibration of a wave is a cycle. And frequency or pitch is measured in cycles per second. Finally, octave relationships between pitches are represented by a doubling relationship. In lesson one, we learned that 440 hertz and 880 hertz are higher octaves of the pitch A. Octave relationships are represented by a doubling of any frequency. It is important to note that we don't actually perceive these other frequencies that we see in the graph of the cello's note. But these other frequencies and their amplitudes or relative volumes all work together to create the unique sound of every instrument. The frequency that we actually hear is called the fundamental. Note that it is the tallest frequency and the lowest frequency. These other frequencies that show up in a sound wave are known as harmonics. This unique sound of an instrument is also known as its timbre. So the fundamental and the harmonics that an instrument makes all work together to create its unique sound or timbre. Let's take a look at the waves of some other instruments and compare their harmonics. Here is the graphic representation of a trombone playing A220. Notice the shape of the wave. Again, the big part of the wave appears to be similar to the cello and the sine wave. But the smaller inconsistencies of the wave are quite different. Let's look at it in 3D. What other frequencies are represented in the 3D image of the trombone? Are they the same as the cello or different? Are the amplitudes of the other frequencies similar to those of the cello or different? Is the fundamental frequency about the same amplitude? Which of the harmonics appear to have higher amplitudes? Which of the harmonics appear to have lower amplitudes? Note the clear differences between the cello and trombone waves. All of these differences contribute to the unique sound of the two instruments or their timbre. Now, let's look at the wave from another instrument. We can note again as we look at the graph of the wave and compare it to a sine wave, it is clearly not a sine wave. This complex wave again is not the same as the cello or the trombone. Let's take a look at these in 3D. Note the similarities between the harmonics in the cello and the trombone and the clarinet. Note the differences. Take a moment to write down one similarity and one difference that you can see. As you can see, each of these instruments has a unique set of harmonics that combine to form the timbre of that instrument. Even the human voice, in fact, every human voice has its own set of unique harmonics that come together to form its timbre. Let's take a look at the waves of two different human voices and compare the harmonics. As you can see, even while the singers were singing the same pitch, the waves look very different. Each voice has a unique timbre. So, let's review what we've learned in this lesson. First, we learned about sine waves, perfect waves that really don't occur by themselves in nature. These are pure sounds of a single frequency that are usually generated by a computer or some other tone generator. Next, we looked at the waves generated by a cello. We noted that the wave was much more inconsistent than the sine wave. There was definitely more happening in that wave. As we looked at the 3D representation of that wave, we noticed that there were certainly other frequencies in there, namely 440, 660, and 880. And those frequencies had very different amplitudes than the note or pitch that we hear, the fundamental. All sounds that we hear on a daily basis are made up of a variety of sine waves. These are known as complex waves. The note that we identify is known as the fundamental. And the other frequencies that are in the wave are known as the harmonics. These frequencies all work together to form the unique sound of an instrument known as its timbre. As we look at a variety of waves generated by instruments and voices, we can see that the harmonics all come in a variety of amplitudes. These amplitudes are different in every instrument that we studied. In fact, every voice has a unique set of harmonics that work together to give it a unique quality. In our next lesson, we will look at these harmonics and try to find some relationship between harmonics and the notes that we understand and work with on a daily basis as musicians. Thank you for joining me for where music meets science, timbre, and complex waves. I hope that you'll join me again soon for the third lesson of our series, Frequency and Harmonics. For now, so long from the North Carolina School of Science and Math.