Total Harmonic Distortion Score and Tests
Distortion is any change to the original signal by a system. Harmonic distortion is an unintended generated frequency which is an integer multiple of an intended frequency fed to the system. It is also worth noting that distortion differs from noise by being dependent/related to the original signal, whereas noise is a random external/unrelated signal added to the original signal. In sound reproduction, harmonic distortion is considered a flaw since it reduces the accuracy of reproduction by generating frequencies that were not included in the original content. This colors the sound and could make the music sound impure, harsh, or muddy.
We perform harmonic distortion tests at 90 dB SPL and at 100 dB SPL. From these results, we calculate the weighted total harmonic distortion (weighted THD) of the headphone for the mentioned sound pressure levels.
When it matters
It is important to have a headphone that produces low amounts of harmonic distortion when a clean and pure sound reproduction is desired. For example, in audio mastering applications or critical listening, and especially when there is a preference for a clean and uncolored reproduction, like in classical music.
However, since moderate - and even in some cases - high amounts of harmonic distortion is not very audible to humans, most headphones should be considered good-enough in this regard. Except for extreme cases, their harmonic distortion performance shouldn't be a deciding factor. Audible levels of harmonic distortion tend to deteriorate the sound reproduction by making it muddy, colored, or harsh, especially at higher volumes since harmonic distortion tends to rise as the volume is increased.
Total Harmonic Distortion
Harmonic distortion is an overtone that is a whole number multiple of a fundamental frequency. Inharmonic distortion differs from harmonic distortion by being an overtone that is not an integer multiple of the fundamental frequency. For example, if the original signal is a 100Hz sine wave, a system with second order harmonic distortion would output a 200Hz tone in addition to the original 100Hz signal, and a system with inharmonic distortion would output a non-integer multiple, like 273Hz, in addition to the input. A noisy system would produce a random signal even in the absence of an input. Total harmonic distortion (THD) refers to the ratio of the sum of the powers (RMS amplitude) of all the harmonics to the power (RMS amplitude) of the fundamental frequency.
The test signal for our THD measurements is the same as our frequency response test signal. It is a 16-bit/48KHz 10-second sine wave swept at -6dB FS (RMS) between 10Hz and 22KHz. The headphones are placed on a Head Acoustics HMS (Head Measurement System), which is connected to an RME UFX audio interface. For passive headphones, the headphones are driven by a Schiit Ragnarok amplifier, and for active headphones, the headphone's own amplifier is used. The signal level is calibrated post-compensation (i.e. after being flattened by applying the target response) using a periodic pink noise limited between 250Hz and 2KHz. The resulting sound pressure level is measured and calibrated with the SPL meter in Room EQ Wizard (REW), which is set to C-weighting and Slow.
The measurements are performed at two different intensity levels; 90dB SPL and 100dB SPL. Due to the sample-rate of 48KHz and the test signal being limited to 22KHz, the THD results are capped at 10KHz, since harmonics of higher frequencies would fall outside of the test bandwidth.
Weighted THD @ 90
The THD (total harmonic distortion) of the 90dB SPL pass is calculated by our test software (Room EQ Wizard) as a percentage of the fundamental frequency's power. Since speakers and headphones tend to produce more distortion in lower frequencies and human hearing is less sensitive to low frequency harmonic distortion, a perceptual weighting filter is applied to the THD calculations which gives as much as 20x less weight to the lower frequencies compared to the higher frequencies. The final THD value is derived by calculating the variance of the weighted THD response between 20Hz and 10KHz.
Weighted THD @ 100
The THD (total harmonic distortion) of the 100dB SPL pass is measured in the same way as the 90dB SPL one described above, but with the volume set to 100dB SPL instead.
Although THD generally increases as the volume increases, some headphones show a decrease in THD in certain frequency bands as the volume goes up. In some cases this may be due to the high self-noise of the device which is masked by the louder test signal. But in some other cases this could be due to the increased flexibility of the diaphragm under heavier loads1.
As mentioned before, humans are quite tolerant of high levels of THD, especially in the bass range, and as you can see below some of the well-reputed and sought after headphones produce seemingly significant amounts of THD.
One of the factors that affects the audibility of THD is masking. Auditory masking occurs when the perception of one sound is affected by the presence of another sound. In the case of spectral masking, when two tones that are near in frequency are produced, the louder tone drowns out the quieter one. Therefore, lower order harmonic distortion tends to be less audible since it has a better chance of being masked by the fundamental frequency. This also means that spikes in THD tend to be more audible than a constant elevation in THD.
Although THD has been a staple of audio measurements and specifications, studies have shown that there is only a moderate correlation between the THD response of a device and its perceived audio fidelity2, 3. Depending on the ratios between the different harmonics produced by a device, auditory masking, and other psychoacoustic effects, it is possible for a headphone with high levels of THD to produce very little audible effects. It is also possible for a headphone with audible levels of distortion to have a typical THD curve. This could also be due to the fact that harmonic distortion is measured with a single tone sweep, which may not be able to put headphones under as much load as a full-spectrum, bass-heavy piece of music.
Other methods for measuring distortion such as inter-modulation distortion (IMD), multi-tone distortion, and non-coherent distortion have been proposed and studied and among these, non-coherent distortion has significantly outperformed THD. There have also been new methods developed for interpreting THD, such as the GedLee metric, which incorporate auditory masking and other psychoacoustic phenomena into their calculations. We have plans for adding such measurements to our distortion tests in the future.
Questions & Answers
Thanks for your message. We are familiar with Olive-Welti's paper, and have even discussed improving our measurements with them. As part of our new test bench, which will be rolled-out slowly over the next few months, we have an improved THD weight curve and have also added IMD measurements. But measuring non-coherent musical distortion may be a bit more difficult for us to implement at the moment.
The GedLee metric seems quite interesting! We've been thinking of something along the same line for a while, and are definitely open to incorporating it into our reviews, but it won't be a high priority at the moment. We have just finalized our new test bench, and based on the papers out there, we should first make sure we're getting our Frequency Response, Soundstage and Imaging right, before worrying about distortion! ;-)
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