THD+N Audibility Calculator

Will the THD+N Produced by My System be Audible?

It is very easy to calculate how loud a source of distortion will be in your listening space. It is far more difficult to determine if this distortion can be detected by the human ear. Music can hide some of the distortion produced by playback system components. However, if the distortion never exceeds 0 dB SPL at the listening position, we can safely say that it is "absolutely inaudible". Let's explore this concept using the THD+N Audibility Calculator.

Masking

The distortion produced by electronics may be hidden by similar harmonic content that is naturally produced by musical instruments (including the human voice). However, if the distortion level is too high, the musical instruments will begin to sound different than they do live. The distortion threshold, where an instrument begins to sound different, will vary significantly depending on the instrument, and on the complexity of the musical performance. The best that we can say is that the system distortion may be masked by music.

If the masking is partial, the distortion can change the sound of the instruments, change the apparent EQ of the recording, blur the stereo image, or add clutter and confusion to the overall presentation.

When Masking Fails

Certain instruments are very difficult to reproduce because the overtones produced by the instrument are not exactly the same frequency as the harmonic distortion produced by electronics. These electronically produced harmonics are poorly masked when they beat against the overtones produced by the instrument.

The piano is particularly difficult to reproduce since the overtones are stretched slightly above integer ratios to the fundamental tone. These stretched overtones beat against the exact integer ratios produced by electronic systems. Making fails when two tones are very close in frequency. For this reason, a piano can easily expose distortion in our signal chain.

Music is also much less effective at masking non-harmonic distortion. IMD, jitter-induced sidebands, and digital aliasing are common examples of non-harmonic distortion. These non-harmonic non-musical distortion components have no correlation to the overtones that are naturally produced by musical instruments. Consequently, these forms of distortion are much easier to hear when playing music.

Music Cannot Mask Idle Channel Noise

Music has absolutely no ability to mask idle channel noise, because this is noise that is present when the music is not playing. If a hiss or hum can be heard coming from the speakers, this will be noticeable every time the music is paused. It may also be noticeable while the music is playing softly.

Audible Noise may Partially Mask the Music

System noise may not be noticeable while the music is playing, but it may still obscure some of the low-level details in the recording. In other words, the system noise can partially mask the music if this noise is easily audible while the system is idle.

Absolute Inaudibility - 0 dB SPL - No Masking Required!

There is a threshold at which noise and distortion are absolutely inaudible. This occurs when the noise plus distortion is reproduced at a level that is below the threshold of hearing at the listening position. The threshold of normal hearing is about 0 dB SPL. Therefore, if we can reduce the system noise and distortion to these levels, we are no longer dependent on masking. In other words it would be impossible to hear the distortion plus noise, even if we could play these while the music is off.

Achieving THD+N below 0 dB SPL is Possible!

Reducing the electronically-generated THD+N to levels below 0 dB SPL is entirely possible with today's technology. In fact, all Benchmark electronic audio products are specifically designed to keep the electronically-produced THD+N at or below 0 dB SPL. The combined THD+N contribution of the DAC, preamplifier, and power amplifier will be less than 0 dB SPL at the listening position. This calculator can be used to confirm this fact. It can also be used to determine how low the THD+N needs to be in order to achieve absolute inaudibility.

The Music Should not be Expected to Hide System Defects

Our playback electronics should deliver the music without adding distortion that exceeds the threshold of hearing. If we allow higher levels of distortion and noise, then we are choosing to use the music to hide the defects in the electronics. This compromise is completely unnecessary with today's technology.

THD+N that we Cannot Control

In a state-of-the art system, the only remaining distortion will be the distortion produced by the loudspeakers (definitely audible) and the distortion plus noise in the recording (often audible). When the playback electronics are clean, variations in recording quality are quite noticeable. Likewise, the differences between speakers become very noticeable.

Using the Calculator

Enter the rated output power of your amplifier.
Enter the THD+N of the worst electronic component in your signal chain.
Enter the voltage sensitivity of your speakers.
Select the number of speakers
Choose your room configuration.
View the result!
If the result is less than 0 dB SPL, the THD+N produced by your electronics will be absolutely inaudible.

Advanced Use

Enter SNR (as a negative number) instead of THD+N to see if your system will generate audible idle channel noise.
Enter THD instead of THD+N to see if your system will generate distortion that exceeds 0 dB SPL.
Enter the THD of your speakers to see how loud this will be at your listening position. This number will not make you happy.

Video Tutorial

Our calculators were featured in a video at Erin's Audio Corner. Erin discovered one of our other calculators (Peak SPL) and liked it so well that he discussed it in the following YouTube video. The calculator above is very similar, but this calculator adds an input field for THD+N. This extra input field allows the calculation of peak THD+N, while simultaneously calculating peak SPL. Erin was just calculating the peak SPL.