What are Harmonics? - Definition & Types

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  • 0:00 Harmonics Defined
  • 0:40 Frequency
  • 2:00 Harmonics
  • 2:54 Overtones
  • 3:22 Playing a Harmonic
  • 4:37 More on Harmonics
  • 6:05 Harmonic Series
  • 7:50 Lesson Summary
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Lesson Transcript
Instructor: Logan Wright

Logan is an active Jazz Guitarist, and classically trained composer with an affinity for contemporary musical styles.

Harmonics are a widely used musical technique, but where do they come from? This lesson will focus on what a harmonic is, where they come from, and how this all relates back to musical pitch.

Harmonics Defined

When a musical instrument is playing a note, what we are actually hearing is the fundamental pitch, which is the pitch being played by the instrument, accompanied by a series of frequencies that are usually heard as a single composite tone. Those frequencies that are integer multiples of the fundamental pitch's frequency are called harmonics. If a musician causes one of these harmonics to sound, without sounding its fundamental frequency, it is called playing a harmonic. This can be a little bit confusing, so let's backtrack for a second. First off, we need to understand frequency.

Frequency

Frequency is the rate at which a vibration occurs. This is measured in hertz (Hz), which is calculated by finding the number of vibrations per second. For example, a frequency that is vibrating 100 times per second would be described as having a frequency of 100Hz. When a pitch is produced, it creates a sound wave that vibrates at a specific frequency, the fundamental frequency, but it also causes a variety of other, higher frequencies to vibrate. These vibrations will be referred to as composite frequencies because they are a result of the vibrations of the fundamental frequency.

When the fundamental frequency and all of its composite frequencies are perceived by a listener, they are rarely heard as separate pitches. A listener will more likely perceive all of the frequencies wrapped together to form what we refer to as a composite tone. Any time an instrument produces a pitch, it will inherently produce a range of composite frequencies that add to the richness of the tone, and allow us to differentiate sound qualities, such as the difference between the way a violin sounds, and the way a guitar sounds. Ok, now that we've established a bit about how a pitch is heard, let's make it even more complicated!

Harmonics

In order to discuss harmonics, we need to add one more component to the mix . . . MATH! Mathematics plays a big part in discussing harmonics, but lucky for us, none of it will get overly complex. For a composite frequency to be considered a harmonic, its frequency must be an integer multiple of the fundamental frequency. Don't worry if that came on a little strong, we're going to elaborate a bit on it now.

Let's start with a hypothetical fundamental frequency of 100Hz. If we were to multiply it by any integer, our result would be considered an integer multiple of the fundamental frequency. In contrast, if we have a composite frequency, divide it by the fundamental frequency, and the result is an integer, then that composite frequency is an integer multiple. This is elaborated on a bit in the table.

Fundamental Frequency Hypothetical Composite Frequency Equation Is It an Integer Multiple?
100 Hz 200 Hz 200 / 100 = 2 YES
100 Hz 250 Hz 250 / 100 = 2.5 NO
100 Hz 100 Hz 100 / 100 = 1 YES

Overtones

An overtone is any composite frequency that vibrates at a higher frequency than the fundamental frequency regardless of whether or not it is a harmonic. Most of the time, all of the overtones an instrument will also be harmonics, and because of this, the two terms are often used interchangeably. There are however, some instruments that will produce overtones that are not harmonics, most notably, percussion instruments.

Playing a Harmonic

Don't worry if you didn't catch everything right away, these topics can be very confusing at first, and sometimes they require a bit of time to grasp. For now, let's talk about why, as musicians, we care about harmonics in the first place! Musicians have found ways to isolate certain overtones and make them sound without the use of a fundamental frequency. The resulting sound is called a harmonic. Wait a minute! I thought a harmonic was the frequency itself? Well, it's both! It's confusing at first, but just remember that anytime a pitch is produced, it comes with composite frequencies, some of which are harmonics. However, if a performer is isolating one of these harmonic frequencies without the fundamental, that is called playing a harmonic, and the sound heard is also referred to as a harmonic.

The technique used to play a harmonic varies greatly from instrument to instrument; however, they are much easier to produce, and thus much more commonly used on stringed instruments. When used tastefully, playing a harmonic can be a beautifully expressive technique in music. Their sound is so distinctly different that they tend to take on an almost 'other worldly' quality.

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