 Hello, and 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 Mathematics. In our last lesson, we learned about frequency and timbre, the unique sound that each instrument makes. In this lesson, we will be learning about harmonics and the relationship between harmonics and the music that we listen to every day. In order to do this, let's begin by looking at the notes that make up a major scale. A major scale has eight tones. Much of the music that we listen to every day is based on a major scale. All styles of music, from pop to folk to classical and even rock and roll, use the major scale as the foundation for their melodies and harmonies. For today's lesson, we will be using the A major scale. This is because in the past two lessons, we focused on the note A. However, all of the concepts that we cover in today's lesson relate to all of the major scales. An A major scale has eight tones. They are... These can be represented with a number as we consider each step of the scale. Now, let's consider some of the important parts of a scale. Certainly, the two As, number one and eight, are the most important notes of the scale. They are known as the tonic and they bear the name of the scale, in this case, A major. The next note of importance is the fifth note of the scale. It is known as the dominant of the scale and is generally considered to be the second most important note in the major scale. Next, we have the third note of the major scale. This note is known as the mediant and it is the tone that makes a scale major. Lastly, the tonic, mediant and dominant or the first, third and fifth notes of the scale all work together to form a major triad or a chord. Again, we hear major chords every day in music. Let's take a look at frequencies and harmonics and how they relate to major chords. Think back to our last lesson on frequencies and timbre. When the cello sounded an A220, other frequencies showed up in the wave that we studied. Those frequencies are 440, 660 and 880 hertz. Note that the numbers representing the frequencies are all related. They are all multiples of 220 hertz, the fundamental frequency. Multiple of 220 include the following numbers. 220 times 2 equals 440. 220 times 3 equals 660. 220 times 4 equals 880. 220 times 5 equals 1100. 220 times 6 equals 1320. 220 times 7 equals 1,540. 220 times 8 equals 1,760. Look again at the 3D representation of the cellos A220. Can you see the wave at each of these frequencies? We know that A, the tonic note, is 220 hertz. What other frequencies that are shown are the note A? As you can see, there are four As represented in these numbers. 220, 440, 880 and 1760. But what about the other numbers? First, there's the frequency 660. It is the pitch E. 220, 440, 660, 880. Note that E is the fifth or dominant note in the A major scale. So, clearly the first three harmonics are closely related to the A major scale. They are the tonic, dominant and tonic notes. Now, let's look at the fourth, fifth and sixth harmonics. Using what we know about octaves and doubling, we can name another one of the harmonics. What is 660 times 2? The answer, of course, is 1320. What is the name of that pitch? If you answered E, you are correct. Now, let's use some reasoning to figure out the fourth harmonic, 1100 hertz. If you guessed C sharp, you are correct. Remember that C sharp is the mediant of the A major scale or the third note of the scale. The fourth harmonic or fourth multiple of a fundamental is always the third note of the major scale. Finally, the seventh harmonic is a G natural. Now, this may not seem to fit into the pattern of the A major scale. A major has a G sharp. G sharp is the seventh note of the scale. And while it would take more time than we have today to fully explain the presence of a G natural in this series, I would like you to hear what it sounds like within the chord. A, C sharp, E, G natural. The G natural makes the chord dominant. A dominant chord feels like it should be moving on to another chord. Now, let's listen to the fundamental and each of the harmonics in order. Let's review some of the material that we've covered in today's lesson. First, we discussed the major scale and the important notes in the major scale. We said that the first and eighth step of the scale are the most important tones. And that the fifth and third tone of the scale also serve very important roles. When these tones are played together, they form a major chord or triad. Next, our goal is for you to understand that there are many frequencies represented in each note that we hear. This group of frequencies, which are multiples of the fundamental frequency, are called harmonics. Next, we considered the numbers that would follow if we listed the fundamental and the first six multiples of A220. We then looked at the pitch names that are associated with those frequencies. Finally, we found a pattern in those pitches. The first six multiples of a fundamental are the first, third, fifth, and eighth notes in the major scale, beginning on the fundamental. We can draw a close comparison between the harmonics of a note and the major scale and chord associated with that note. Thank you for joining me today for where music meets science, frequencies, and harmonics. If today's topic was of particular interest to you, don't stop here. I encourage you to go to your school library or your community library and continue to learn about frequencies. There are a variety of careers that one might pursue if they're interested in this topic, from physicist to sound engineer to hearing specialist to acoustic architect. A sound engineer uses his knowledge of frequencies and sound to create good sounding recordings and pleasing live sound support in a variety of venues. Here at the School of Science and Math, we had a guest lecturer who uses her knowledge of frequencies to study and predict underwater earthquakes. Architects use their knowledge of frequency to choose materials for buildings. Architects want some rooms to be quite loud and reverberant, while others need to be very quiet. Finally, hearing specialists use their knowledge of frequencies to diagnose hearing problems and to accurately provide recommendations for solving those problems. It has been a pleasure working with you today, and I look forward to the next time we get together.