Testing your ears and speakers for distortion

Test your ears and speakers for distortion

Testing your ears and loudspeakers for distortion

Colin Pykett

Posted: 25 February 2017

Revised: 25 February 2017

This article includes links to files containing various audio frequency test signals. Like all other music and audio files, they should only be listened to at safe volume levels. If you lack experience or understanding of these matters, or have any doubts about listening to these signals, then you should not do so.

Abstract. Discusses some sources of distortion encountered when listening to music. It considers distortion introduced by electronic items such as amplifiers and computer audio systems, as well as acoustic elements including loudspeakers, headphones and the ear itself. Audio test files are included which demonstrate intermodulation distortion in particular, and they also give some idea of the relative contributions of the distortion due to your listening system and your ears. They can also be used for identifying and troubleshooting a listening system which seems to have a poor distortion performance. The material might be of interest to those play digital organs as well as to those who listen to recorded music.

Introduction

Distortion introduced by the system you use to reproduce music is often discussed but seldom demonstrated, something which this article will remedy. In using the word 'system' I am including all elements of the reproducing chain, including purely electronic items such as amplifiers, as well as loudspeakers or headphones which are electro-mechanical. Therefore the article has relevance not only to those who play digital organs, but also to those who will have nothing to do with them and play only pipe organs. This is because even the latter will usually listen to pipe organ recordings from time to time.

What is distortion? There are various types, but in this article it means an unwanted alteration of the frequency spectrum of an audio signal as it passes through a system to reach our ears. But it must also consider the additional distortion introduced by the ears themselves, where the term 'ears' also includes the brain. We shall be discussing only those forms of distortion in which spurious frequencies (those which do not exist in the original signal) are introduced into the sounds which we perceive consciously. This type of distortion is called harmonic distortion when the spurious frequencies, the distortion products, are integer (whole-number) multiples of frequencies already present in the original signal. Thus in this case the distortion products are themselves harmonics, hence the name. A simple example of harmonic distortion is when a spurious tone at 2 kHz is also heard when a pure sine wave with a frequency of 1 kHz is input to the system - these frequencies are an octave apart and are therefore harmonically related (the higher is a harmonic of the lower). Although harmonic distortion is obviously undesirable, the fact that it results in harmonically related spurious frequencies means that its effects are not necessarily unpleasant, and in fact it can go undetected by uncritical listeners much of the time.

This is not true of another, more serious, form of spurious-frequency distortion called intermodulation (IM) distortion. This manifests itself when more than one input signal is present, which happens all the time in music of course. As an example, we might play two notes at once on a keyboard instrument. If significant IM distortion is present we will often hear spurious tones whose frequencies are the sum or difference of those in the original sounds. Taking an example, if we play treble C at 8 foot pitch (whose fundamental frequency is about 523 Hz) and the E above it (659 Hz), an audible difference tone might be heard growling away at a much lower frequency (136 Hz) if IM distortion is present, because 659 - 523 = 136. This is nearly two octaves further down the keyboard around tenor C sharp, and it has no harmonic relationship with either of the generating frequencies. This feature renders the overall sound unpleasantly discordant when IM distortion is present.

The distinction between harmonic and intermodulation distortion is to some extent artificial because both types are caused by the same deficiencies (called nonlinearities) in the reproducing chain and in our ears. However we shall not pursue this here, though it is explained in more detail elsewhere on this website [1]. More important as far as this article is concerned is the fact that IM distortion is often easier to hear than harmonic distortion because (as shown above) the frequencies of the spurious tones do not necessarily coincide with those present in the original signals, or with harmonics of them. This also makes IM distortion easier to demonstrate, as will be shown presently. The same reasoning also means that IM distortion is usually more objectionable than harmonic distortion because it inserts many non-harmonically-related frequencies right across the audible spectrum.

Some tests

Some short mp3 audio samples are included here, and a few words about how to listen to them are necessary. You need a computer set up to download and play audio in stereo (all recent and most older ones will do this), connected to a reasonably high quality amplifier and loudspeakers because there is little point in using poor quality ones. If you have a digital organ you might be able to play the signals through its sound system if there is a suitable socket or jack receptacle for this purpose, and this would be a good thing to do because then you will be testing a system which you actually use for music purposes. Alternatively or in addition, you could do the tests using your hi-fi system. Preferably you will also need headphones, again good quality ones, because some interesting differences between headphone and loudspeaker listening will also be demonstrated.

If you click on the following two links you should hear pure sine waves at the frequencies stated. Both samples play in monaural mode i.e. the same signal will come from both channels. To avoid damaging your equipment or your hearing you should have the volume at zero initially and then increase it slowly to a comfortable listening level. The duration of each sample is 15 seconds, giving you enough time to find the optimum volume setting.

Note C5 - 1046.5 Hz

Note D#5 - 1244.5 Hz

(C5 means the note 'C' which starts the fifth octave on an organ keyboard, and D#5 is the D sharp above that, making an interval of a minor third [2]. The frequencies stated above correspond to these notes played on an 8 foot stop tuned to equal temperament with middle A set to 440 Hz).

Not very interesting you might conclude, and you would be right. However it is useful to know about these tones because they form the basis of the subsequent more complicated listening tests, and it is also useful to prove that you can download and play them properly.

Now try this one:

C5 and D#5 added - mono - Test A

The tones in the first two samples have now been electronically combined (added together) in both the left and right channels, which are identical and therefore play monaurally. Start with the volume at zero as before and then slowly increase it. At low listening levels you should simply hear a rather weird high pitched sound which bears little resemblance to the smooth and pure tones which you heard originally. But if you now continue to turn up the volume slowly, you will probably hear a faint tone at a much lower frequency begin to appear in the mix at some point. This has a frequency of 198 Hz, which is the difference between the two sine wave frequencies. This frequency corresponds almost exactly to that of note G2 (the G below middle C) and it is an example of intermodulation distortion The effect should be heard when using both loudspeakers and headphones.

Note that it is important not to expose your ears to excessively loud sounds, especially when using phones, and your equipment will probably not like it much either. So if you do not hear the difference tone, do not just keep winding the volume ever higher to levels beyond those at which you normally listen to music. An absent difference tone probably means that your listening system and your ears are unusually linear and that they do not readily generate intermodulation distortion. For this you can be thankful. For what it is worth, I do not begin to hear a difference tone myself until the overall volume gets reasonably loud with the speakers and amplifiers used in my virtual pipe organ (Prog Organ) and various hi-fi setups.

To confirm that no vestige of a difference tone exists in the original composite signal comprising Test A, its measured frequency spectrum is shown below. Only the two tones at 1046.5 Hz and 1244.5 Hz can be seen as spectrum lines. There is no signal power visible at any other frequency, including the difference tone frequency of 198 Hz.

Spectrum of the 'Test A' signal showing only the two sine wave frequencies

But, assuming that you do hear a difference tone, how can you tell whether it is arising in your listening system or within your ears? To find out more, now play the following sample starting with the volume set to zero as before:

C5 and D#5 together - stereo - Test B

Here, the two original sine waves are not added together even though they still sound simultaneously. Instead, they are fed separately to the right and left channels of your listening system respectively (C5 should be heard in the left channel and D#5 in the right). If you have a balance control you can prove this for yourself by panning the sound from one extreme to the other (a virtual balance control should be available somewhere in the 'mixer' window of your computer sound system, or your hi-fi amplifier might also have a real physical one).

Subjectively, Test B will quite likely not sound much different to Test A when listening with loudspeakers in a room. And you will probably hear a difference tone if you carefully increase the volume as before, at least if you heard one in Test A. Again as before, do not increase the volume beyond your normal listening levels. However, and interestingly, a difference tone will quite probably NOT be heard if you now listen with headphones to Test B, whereas you probably heard it in Test A. So why the difference, and why only with headphones and not loudspeakers?

When listening with loudspeakers their sounds add acoustically in the room before reaching your ears, and therefore you are hearing much the same combined signal in Test B as you did before in Test A when the tones were added electronically. In other words, both ears hear both tones in both tests. But when using headphones, each ear is supplied with only one frequency in Test B, therefore there is no opportunity for intermodulation to occur (by definition) until the neural data streams from the two ears are combined (termed binaural fusion). Anatomically, this only occurs beyond the inner ears deep in the brain, and in my case I do not hear a difference tone at all under these conditions when using phones. However I have been in the audio game long enough to know that people differ in this respect, and some do seem to report the appearance of artefacts such as difference tones generated purely within the brain whereas others do not. So one cannot be too prescriptive at this point.

The subjective loudness of the difference tone is important because it can reveal further information. If a difference tone of about the same loudness is heard using loudspeakers in both tests when the overall sound levels are also comparable, this implies two things. Firstly, your ears are mainly responsible for the distortion you are hearing in both cases, and secondly (saying the same thing in a different way) that your listening system is not adding a significant amount of distortion to the signals passing through it. This is because the listening system cannot generate any intermodulation distortion at all in Test B because at no point are the two signals combined. And in Test A the system cannot be generating much distortion compared with that produced by your ears, otherwise the difference tone (the distortion product) would be louder in Test A than in Test B.

So far we have not been discussing particularly quiet sounds because difference tones are not usually detectable under these circumstances. Therefore what should we conclude if a difference tone does appear in Test A (using loudspeakers) when the volume of the overall signal in the room is indeed low? Firstly check, again using loudspeakers, whether it occurs in Test B at a similar overall volume level. If it does, this implies your hearing apparatus is significantly more nonlinear than mine, and I cannot say much more than that. This is because intermodulation distortion in Test B can only be occurring in your ears and brain because none can be generated by your listening system - the two tones never mix within the system in Test B. But if the difference tone does not appear in Test B when listening at low levels, but only in Test A, it implies that your listening system is probably defective regarding its distortion performance, because gross audible distortion products should not occur at low listening levels in any half-decent system. In this event it is possible that certain controls might be set incorrectly somewhere along the reproduction chain. A common culprit is within the mixer incorporated in the sound card (or onboard sound chip) software of your computer. Often, these have several intermediate virtual potentiometers or volume controls which might be set too high so that subsequent processing stages are overloaded, so try adjusting them. Another common problem is that your computer is outputting an analogue signal whose amplitude is too high for the input stages of the external amplifier driving your loudspeakers, and again this can be easily adjusted from within your computer.

So although it is difficult to assign numbers to the effects, these simple tests demonstrate qualitatively the effects of intermodulation distortion. They also give some idea of the relative contributions of the distortion due to your listening system and your ears. And they can also be used for identifying and troubleshooting a listening system which seems to have a poor distortion performance.

References

1. "Resultant Bass, Beats and Difference Tones - the facts", an article on this website, C E Pykett 2011.

2. For the benefit of musicians, yes, I realise C and D sharp do not technically form a minor third, and the interval should properly be written as C to E flat. But the frequencies of the notes played are the same (in equal temperament), and I am merely using the tuner's convention of referring to the 'white' notes as naturals and the 'black' ones as sharps.