Most sounds are not pure sounds of a single wavelength and frequency. Other frequencies are mixed in with the sound, creating the particular texture and tone of an individual voice or instrument. These frequencies are called harmonics.
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 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!
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 worries if that come 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.
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