How we test headphones: distortion

Have you listened to your own voice on a video, over a loudspeaker, or over the echo of a Skype chat? It probably sounds pretty different in all three circumstances. The reasons for this are twofold: Signal distortion, and Frequency Response (FR).

FR is one of the most important aspects of our testing, but signal distortion also has a profound effect on how your voice sounds when played on a given device. And like all distortion, it has to do with altering something from its original form. In this case, the things being altered are the digitally rendered sound waves that live inside your music player.

Getting Started

sine wave
The equation for a sine wave. "A" is the amplitude, "f" is the frequency in Hz, "t" is the time in seconds, "ϕ" is the phase offset, and "B" is the offset in the y direction.

Each pure tone you hear in a piece of music corresponds to a frequency. For instance, Middle C is represented by a sine wave with a frequency of 261.6 Hz, or 261.6 cycles per second.

In a recording studio, an artist or musician plays Middle C. In the following video, you will be able to hear Middle C, as well as see its equation and shape through time on a plot. Note the different time scales in each video:

When a recording artist or musician plays that note, the sine wave is one signal that gets rolled in with all of the other signals representing other notes and sounds that are being played at the same time. The sine wave is saved inside your music device, and when you click “play”, the sine wave is summoned by your headphones.

However, it turns out that your headphones cannot perfectly reproduce the original sine wave that was recorded in the studio. This occurs for two reasons: The first is that we do not live in a perfect world where signals are perfectly transmitted all the time, and the second is that the omnipresence of electronics with non-linear loads (i.e. your music device/headphones) means that the digital signal response of a device, when it draws a current, can be flawed and unpredictable.


While your headphones cannot exactly replicate that original sine wave, they do their best to reproduce it.

For example, let’s say your headphones were aiming for Middle C:

But came out with this instead:

The two sine waves don’t look terribly different, but if you listen closely to the two sound clips, you can hear the difference.

Our headphone tests quantify how your headphones distort the original music signal at each individual frequency. In SoundCheck, our headphone testing software, we measure distortion with a frequency sweep that starts with a pure tone at a subset of frequencies from 20 Hz (increase your volume to hear this one):

to 10 kHz (lower your volume for this one):

Knowing the original frequency and height (= amplitude) of the pure tone, we can analyze the sine wave that is actually output by the headphones and quantify how different the two sine waves are.


The summation of different sine waves can create a square wave.

So how do we analyze the resulting digital wave produced by your headphones? SoundCheck uses a method called Fast Fourier Transform, or FFT. With FFT, a wave is broken down into a finite number of sine waves with different frequencies and amplitudes. The best way to understand FFT is to imagine the process in reverse. You can take a finite number of sine waves, with known frequencies and amplitudes, and add them together to create a new wave of any shape or size. This process is known as superposition.

At a given point in time, some of those sine waves will cancel one another out to some extent by having opposing high and low values (destructive interference). At other points, some sine waves will add together by having similarly high or low values (constructive interference).

With a Fast Fourier Transform, SoundCheck takes the final digital wave and reduces it into the component sine waves. In this particular case, SoundCheck is only looking for component sine waves that represent harmonics of the original (or “fundamental”) tone.

Harmonic waves are simply waves that have frequencies that are integer multiples of the fundamental frequency. For instance, if the fundamental tone has a frequency of 20 Hz (=20*1), then the first harmonic tone would have a frequency of 40 Hz (=20*2), the second harmonic tone would have a frequency of 60 Hz (=20*3), all the way up the nth harmonic (=20*(n+1)), and so on.

Total Harmonic Distortion

There are many different types of distortion that can be measured in headphones. Total Harmonic Distortion, or THD, is the most basic kind of distortion. We'll be talking about THD in this post, but if you're curious about other kinds of distortion, check out this link for more information.

After identifying the harmonic tones that add together to create the imperfect fundamental tone, we calculate the THD using the equation shown below. Here the THD is presented as a percentage of the original amplitude of the fundamental sine wave, where Vn represents the amplitudes of the sine waves.

IEC equation for Total Harmonic Distortion
The IEC equation for Total Harmonic Distortion (THD)

For n > 1, Vn is the amplitude of the nth-1 harmonic sine wave, and for n=1, Vn is the amplitude of the fundamental sine wave.

If the amplitudes of the harmonic sine waves are very close to the amplitude of the fundamental sine wave (high THD percentage values), then the resulting wave will be significantly distorted from the original sine wave. If, on the other hand, the amplitudes of the harmonic sine waves are very small (low THD percentage values), then the fundamental sine wave is better preserved.

Let’s take another look at our distorted wave. In this video, you will first see the shape of the distorted version of Middle C, then the three waveforms that make up that distorted wave: the original fundamental frequency sine wave and two harmonic frequency sine waves. This waveform has a THD of 20%.

Here is a second wave that has also been distorted from the original Middle C fundamental tone. This distorted wave has a THD of 40%.

Distortion at different frequencies

The human ear tends to have an easier time hearing higher frequency tones. Consequently, the human ear can more easily perceive distortion of higher frequency tones than of lower frequency ones.

For example, listen to a sine wave with a fundamental frequency of 40 Hz (increase your volume for this one):

And here is a version of that sine wave with a THD value of 20%:

By contrast, this is a sine wave with a fundamental frequency of 1000 Hz (=1 kHz) (lower your volume for this one):

Here is a version of that sine wave with a THD value of 20%:

The distorted version of the low frequency tone is practically indistinguishable from the original fundamental tone. With the high frequency tone, the difference is immediately obvious.

Ideally, headphones would not distort the original fundamental tone at any frequency. Headphone manufacturers know that our sensitivity to distortion increases with higher frequencies, so they do their best to minimize the perceivable distortion at higher frequencies, while being somewhat less strict when it comes to THD at lower frequencies. We take this into account when we run our distortion test on a pair of headphones.

Our headphone testing

When developing our testing, we built an empirical THD curve that mimics the human ear’s sensitivity to distortion. This empirical curve (the shaded blue curve shown below) was defined by previous distortion data from 70+ products we’ve tested over the past few years. (Note the logarithmic, rather than linear scale in the chart.)

Empirical distortion curve
Our empirical distortion curve was built using data from over 70 headphone products that we tested previously.

In our distortion test, we do a sweep of original fundamental tones with frequencies from 20 Hz to 10,000 Hz. SoundCheck breaks the resulting distorted signals down into their component harmonic sine waves, and calculates the THD for each individual frequency. We plot that THD data (red line), and compare it to our empirical data curve (blue shaded area).

Product with distortion
A product's distortion score is determined by how much the THD values surpass those of our empirical curve at each frequency.

Any part of the product’s THD curve that lies above our empirical data curve results in a point deduction from a perfect score. The more a product’s THD curve resides above our empirical data curve, the more noticeable the distortion is to the listener, resulting in a lower overall distortion score.

Product with high distortion
This product would have a low distortion score because it has many THD values that are larger than those of our empirical curve.

Conversely, if a product’s THD curve resides entirely below our empirical data curve, then the distortion score for that product is a perfect ten.

Product with very little distortion
This product would have a perfect distortion score because it has THD values that are always lower than those of our empirical curve.

To make a long story short, the less the red line goes above the blue line, the less noticeable any distortion will be to the listener, and the better the product will score.

Our best scoring products have low distortion across the entire range of frequencies. To find out more about distortion in individual headphone products, be sure to check out our ever-updating library of headphone reviews. Click on the "Test Results" tabs in individual product reviews for the greatest detail.


TAGS: Headphones Testing Science Distortion THD How We Test Video

Credit: / Julia MacDougall

How we test headphones: frequency response

Have you ever wondered why your music sounds different, depending on what pair of headphones you're wearing?

For example, listening to the iconic Jaws theme will be a very different experience on a pair of Beyerdynamic over-ear headphones, compared to a pair of Beats in-ear headphones.

The dramatic difference between two pairs of headphones, other than the style and design, is which notes they choose to enhance or downplay. This is called frequency response, which is the most important performance metric that we assess in our headphone testing.

All headphones can be divided into two camps, frequency-wise: those trying to most closely reproduce the sounds as they were recorded, and those trying to ensure that each note sounds equally loud to the listener. But before we jump into the difference between those two ideals, let's break down the definition of "frequency response".


The frequency of any wave is defined as the number of cycles per second (aka “hertz” or “Hz”). When I say “cycles”, I refer to the fact that some waves have a structure or wave shape that repeats over and over throughout the lifespan of the wave. Here are some examples of those types of waves:

Waves with the same frequency but different wave structures.

As you can see, there are many different types of waves with repeating shapes, but we're going to focus on the so-called “sinusoidal” waves ("sine" in the image above)—waves that have peaks and valleys with curving characteristics.

Because these shapes are identical and repeat throughout the wave, we can isolate one wave shape and look at how long it lasts over a period of time. If a wave repeats many times in one second, that wave is said to be “high frequency.” If a wave repeats very few times per second, it is said to be “low frequency.”

Waves with different frequencies (or numbers of cycles per second)

In music, we deal mostly (but not exclusively) with sinusoidal waves. The note middle C—whether it is played on the clarinet, the piano, or the saxophone—is made up of waves that always have the same frequency: 261.6 Hz, or 261.6 cycles of the repeated wave structure in one second.


The "response" of a given frequency refers to its corresponding decibel level. Decibels define the intensity (or the amount of energy transmitted over time over an area) of the frequency wave carrying a given sound.

Decibels (dB) are tricky to understand because they're logarithmic in nature. That means an increase of 10 dB (say, from 25 dB to 35 dB) represents a ten-fold increase in intensity. More confusingly, the intensity of a frequency wave doesn't directly translate into the "volume" that we hear in our ears. In order to change the volume setting on your radio from "1" to "2", the radio has to increase the intensity of that frequency wave by 6-10 dB.

The strange relationship between numerical decibels and the loudness (i.e. the volume) was first quantified by Harvey Fletcher and Wilden A. Munson, in the early 1930s. They asked volunteers to listen to single notes at a range of frequencies and intensities. At each frequency, they adjusted the intensity of the wave until the listeners believed that the loudness matched that of a reference frequency wave with a set decibel level.

In this way, Fletcher and Munson built empirical curves that represented a constant loudness, as perceived by the human ear and defined by a range of frequencies and decibel values. These curves, which have since been revised and updated, are called "equal loudness" (EL) curves. Today, they're a key part of our frequency response testing.

"Frequency Response"

Sounds that have lower pitches have low frequencies. The rumble of traffic or the thrum of an air-conditioning unit are sound waves with fewer cycles per second and lower dB values. They're difficult to perceive because, with fewer cycles, the wave shape (and the sound produced) change very gradually, making it more difficult to observe and recognize the wave.

Conversely, sounds with high pitches have high frequencies. Fire alarms and nails on a chalkboard create sounds that have high frequencies and high dB values. High frequency sounds are more easily distinguished with the human ear because many cycles occur in one second. Our ears more easily pick up on the rapidly changing wave than those with lower frequencies.

With all of this background information, it is perhaps unsurprising that when we discuss the “lows,” “mids,” and “highs” of a piece of music, we are referring to the frequencies of the sound waves. A single note represents a sound wave with a specific frequency; a note with a low frequency of ~100 Hz may be produced by a bass drum, a note with a mid frequency of ~1,000 Hz may be made by an alto saxophone, and a note with a high frequency of ~10,000 Hz may be made by a piccolo.

Our Frequency Response Test

In our frequency response test, we use SoundCheck software to send a range of sound waves with known frequencies through headphones and measure the decibel level the headphones reproduce. When we look at the data for the frequency response test, we're plotting frequency vs. response in decibels.

The frequency response data for a pair of headphones.

In general, headphone manufacturers are trying to match one of two popular frequency profiles: the “consumer” response or the “studio” response.

The consumer response is defined by the equal loudness curves mentioned above, which attempt to achieve a constant loudness across a range of frequencies. Because it is easier for us to hear mid- and high-frequency notes than low-frequency notes, EL curves increase the intensity of lower-frequency waves and limit the intensity of mid- and high-frequency waves. With this type of frequency response, you'll hear the hum of an upright bass at the same loudness as the blare of a trumpet.

Different Equal Loudness (EL) curves.

We call this the “consumer” frequency response because most headphones on the market aim for this frequency profile. It allows you to hear all parts of your music with equal emphasis on the different sounds, vocals, and instruments.

The frequency response data of a pair of headphones compared to the best-fitting equal loudness curve.

The studio frequency response is the opposite: the manufacturer seeks to reproduce all of the notes, both at high and low frequencies, at the same decibel level.

This doesn’t correlate to the volume as perceived by the human ear; doing so requires a curve, as you saw earlier. On the frequency vs. response in decibels plot, the ideal studio response is a flat horizontal line at any given decibel level. This is appealing to listeners who want to hear the music as it was mixed in the studio. There's no artificial emphasis or de-emphasis on certain notes.

We call this the studio response because these headphones are often used in a studio setting, where producers can clearly hear the sound as it was recorded, and then choose to boost or reduce certain frequencies to achieve the exact sound they want.

The frequency response data of a pair of headphones compared to the best-fitting ideal studio response.

The "consumer" and "studio" profiles represent two distinct philosophies, so when we test a pair of headphones, we look at the frequency response and judge it based on which of the two frequency profiles it was seeking to reproduce. As most headphones on the market have a consumer profile, it would be unfair to compare that rapidly changing sound to a studio profile. Similarly, a flat studio profile would be a poor match for an ideal EL curve. Some companies will aim to produce their own "signature sound," but those tend not to deviate very far from either of the two previously mentioned philosophies.

Using our methodology, each pair of headphones is scored on how well it actually mimics the frequency profile that it most closely resembles. The reviewers can then take this information and tell you categorically that, with a given pair of headphones, the violins in the shower scene of Psycho are so muted that all sense of suspense is lost, or that the roar of the waterfall at the dam in The Fugitive will be so loud that you'll feel like you're being pursued by Tommy Lee Jones.

Only you can decide which sound profile you prefer, and that desire has to be balanced with the price tag and the look of a given pair of headphones. For the products that top our list, be sure to check out the Best Right Now: Headphones article, or our constantly updated library of headphone reviews.


TAGS: Headphones Testing Science Frequency Decibel

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