Amplifier harmonics and load stability

[STHLS5]

Imo, think the graphs you are referring to tell quite a bit, regarding how well an amp is designed, the philosophy and discipline. The graphs show distortion levels as more power is required from it, where it peaks out (the “notch” -normally should correlate relatively closely with rated standard specs). It might also tell how much noise there is to begin with. In other words, we can observe where distortion of an amp. begins on the scale, how it travels and starts to deteriorate (close to rated ........

I still don't get you. If you look at THD+N graphs it gave some sort of curves. Why*were the measurements taken using different values? Why not all the amplifier measured using 100W? Why would the magazine use 100W to measure THD +N in one amplifier and a mere 1W in another amplifier? Naturally, the one with 1W looks neat. Whether that's relevant or not is beyond my limited knowledge.

In another forum, someone posted a graph promoting a certain product. On closer look, I noticed that the measurement for the selected product was given for every 100Hz for certain frequency range and in another graph for another product it was given for every 10Hz ( or something like that). Expectedly, the one with 10 Hz increments showed a wavy plot.

As a consumer, I want an apple to apple comparison.

ST

[A.S.]

Now we have some discussion about this you've motivated me to have a look at the curves in more detail.

There's not much we can learn from the basic frequency response curves. These amps all look great in that respect; far flatter than our ears and certainly as good as they need to be. But you're right: the (perhaps) tell-tale distortion plots are taken at different power levels, and as we know that amplifiers (just like speakers) exhibit more distortion the harder they are working (the more power they are generating). As you point out, we are indeed not comparing apples with apples. Not remotely so. Why?

It seems that now I've scanned the specs that amp C is by far the most powerful. Judging solely from the specs, the technical performance is really examplary: it was evidently designed by a master craftsman who had many tricks available to him to drive distortion down. There is a generation or more of technical skill revealed by these figures. It is not a amateur design. It certainly would have involved a very careful, intuitive positioning of all the components on the pcb, mm by mm consideration of the circuit board track layout, the dressing of the cable loom - let alone the actual circuit design and component values. It really is an exceptional piece of engineering. I have not read the review so I do not know how it was subjectively rated but I'd be very happy indeed to own one, based on reading the graphs alone.

Picking amp A (the first letter of the alphabet, I could have picked B) informs us that the distortion traces were, as noted, made at a much lower power of only 10W. I can only imagine that this low level was being kind to the amp, and that had it been worked harder, the distortion would have risen, perhaps dramatically. Perhaps there was some discussion between SP and the makers as to what power level represented a typical in-use level, relative to the maximum power available from the design. That would be an entirely reasonable approch: you wouldn't normally measure a cars 100-120mph acceleration; the 30-60mph figure would be much more relavant for the ordinary user in town.

But the distortion curves are indicative of two very different design approaches, much more than just a comparison of two very different power output capabilities. Let's look at just one type of measurement: the THD + Noise graph. THD is Total Harmonic Distortion, and in the old days using an analogue moving coil meter, some simple circuit would add together the total of all the harmonics and arrive at a number. For example, ignoring the single, precision fundamental test tone, if there was some second harmonic distortion generated in the amp + some third + some fourth + some fifth ...... the final amount would be lumped together into one nice convenient number. Say, "1.5% THD @ 10W into 4 ohms, 50Hz - 10kHz" or something like that. What that didn't tell us at all was how much of each harmonic was present in the 1.5%. And that really matters because odd harmonics like 3rd, 5th, 7th ... sound horrible when excessive to the ear, whereas even order harmonics can actually sound very pleasant. Yes, true: they can warm-up the sound as musical instrument designers have known for centuries.

Then along came the computer based audio spectrum analyser of the type used to make these graphs and we can clearly see all the harmonics laid out from lowest frequency (the fundamental) to the highest across the audio band, left to right. So we can pick-out visually the 2nd, 3rd and so on. Luckily for us, the fundamental tone injected into this amp has been scaled to use the full vertical height of the graph, and peaks at exactly 0dB. That's perfect because we can now easily read-off the individual harmonics and their contribution will be correctly scaled relative to the stimulus. So, looking along the horizontal line, we can see that the 2nd harmonic of the test signal (100Hz) is a little smaller than the 3rd harmonic, which I read as being at about '-70dB relative to the fundamental'. Make sense?

Very important point! The test stimulus was a high precision, technically perfect, absolutely pure, computer generated 50Hz sine wave. It contained no harmonics at all*. So all those harmonics you see spread from left to right at multiples of the 50Hz were generated inside the amplifier alone. They should not be there at all. They will add some character to the music.

*The AP test set used is absolutely state-of-the-art. It's purity of tone generation would produce (a few, tiny, irrelevant) harmonics that are below the bottom of the vertical graph scale. We can safely say that what we see here is the amp alone, not the amp + test set together.

>

[STHLS5]

.... For example, ignoring the single, precision fundamental test tone, if there was some second harmonic distortion generated in the amp + some third + some fourth + some fifth ...... the final amount would be lumped together into one nice convenient number. Say, "1.5% THD @ 10W into 4 ohms, 50Hz - 10kHz" or something like that. What that didn't tell us at all was how much of each harmonic was present in the 1.5%. And that really matters because odd harmonics like 3rd, 5th, 7th ... sound horrible when excessive to the ear, whereas even order harmonics can actually sound very pleasant. Yes, true: they can warm-up the sound as musical instrument designers have known for centuries.....

Mmmm....very interesting. So if I have an Amp with THD of 1% but with predominately odd number harmonics and the other one with the same percentage of distortion but with predominately even number harmonics, then the latter would sound better than the former?

Could this mean, even if specs wise both Amps may be identical but sound wise they could be different? It cannot be, I have compared several amplifiers, and the difference only heard when the Amps driven to its limit.

ST

[A.S.]

...Could this mean, even if specs wise both Amps may be identical but sound wise they could be different? It cannot be, I have compared several amplifiers, and the difference only heard when the Amps driven to its limit. ST

That's a bold statement, and now you rather than me are going to have to do some thinking to justify it! I'm sure that you didn't expect my last post of a mere few hundred words would define the entire process of how amplifiers may/can/will/should sound different to the human ear. This is a multi-faceted issue as all things are relating to human perception.

Certainly, the specifications are only a snapshot of the amplifiers capability - they cannot (yet) define enough of the performance envelope to be comprehensively descriptive. But they are a useful starting point. The point you have driven amplifiers to when you've noticed more characteristic distortion is shown on the attached graph: at and beyond the 'knee' in the power/distortion curve where the distortion can shoot up to infinity (total) over a very small increase in output power. In short, the amp has just run out of steam but you are pushing it onwards. Like whipping a horse that is already galloping. The heart can only pump so much blood around. It would be interesting to compare this very well defined knee with a graph of a tube amp.

To recap: I've shown how an amplifier (although it could have been a pickup cartridge, a microphone, a speaker .....) has amplified a pure incoming signal and then, for whatever reason, generated, unasked for, a whole series of harmonics that are mathematically related in frequency to the incoming stimuli but are definitely not present at the input. We call these harmonic distortion(s). Even good loudspeakers produce plenty of these distortions. But you say that you are audibly unaware of these harmonics superimposed onto the music until the amplifier is driven to the upper limit of its power potential, when we would expect all the distortions to increase, perhaps dramatically. I assume that you could also comment that you are not audibly troubled by the harmonics generated in the loudspeaker until it is pushed hard, or from the pickup cartridge until it is tracing a really loud groove or from the microphone unless someone is screaming into it at close range.

How would you weave these observations into a cohesive working hypothesis?

>

[kittykat]

I am sorry, I do not understand what you mean by this. Could you (re)paraphrase?

Imo, Probably pretty difficult to find an obnoxious “sounding” amplifier, one you really couldn’t live with, even if it measures poorer as indicated by the graphs. In fact, some perverse measuring amps find followers. For a speaker however, an audition should reveal the slightest blemishes relatively quickly, which will magnify, the longer you sit/ stand in front of them.

@ST. Regarding harmonics. in my experience, amps. don't necessarily need to reach the limit for harmonics to be discernable.

[A.S.]

From my scanned archives, July 1977 just as the Harbeth company was producing its first speakers, an article covering the very subject of audibility of harmonics. In 1977 the fancy computer graph plotting system was many years away so engineers photographed the screen of their oscilloscope to show the fundamental and harmonics. Having become familiar with the new system (previous posts) it should be possible to interpret these photographs.

In those days, six years before CD was released, there was a real expectation that measurement and science would drive-up audio quality. But then the plot was well and truly lost.

>

[STHLS5]

That's a bold statement, and now you rather than me are going to have to do some thinking to justify it! .......

......But you say that you are audibly unaware of these harmonics superimposed onto the music until the amplifier is driven to the upper limit of its power potential, when we would expect all the distortions to increase, perhaps dramatically. I assume that you could also comment that you are not audibly troubled by the harmonics generated in the loudspeaker until it is pushed hard, or from the pickup cartridge until it is tracing a really loud groove or from the microphone unless someone is screaminginto it at close range.
How would you weave these observations into a cohesive working hypothesis?
>

Do I hear the harmonics generated by loudspeakers or amplifiers?Let us get past loudspeakers distortion first. I would very cautiously say I don’t even hear them in my 16 year old SHARP mini-compo,which serves me as my bedroom musical companion for late listening of oldies in FM Mono (through the centre speaker only). Coloration – Yes but to say they produce some sort of harmonics to the point it distorts the sound…..well….I have not been consciously aware of them. I usually listen at a very low level, i.e about 20 of60 of the digital volume unit. Probably, about 40 to 50dB. Of course, I hear all sorts of distortions from crackling sound to radio waves hiss at higher volumes but that’s usually in the early morning rush listening to the news where the message takes precedent over quality and it never bothered me but probably will do so for next few days since I am reminded of it in this post.

In the case of my car audio system, resolution aside, it performs alright up to a certain level and starts to sound cacophonous above that. Not sure if that is related to THD. And yes, due to old age of the speaker, I hear speaker distortion at a very low volume level, but it gets masked the moment, I increase the volume to my usual listening level. In this case, there’s a very audible distortion but still below and gets masked when the music is louder than the distortion noise. I am sure this distortion is thousand times higher than amplifiers distortion.
ST

[A.S.]

I hear the harmonics generated by loudspeakers or amplifiers?Let us get past loudspeakers distortion first. I would very cautiously say ....

Ummm. That looks like more observations not a worked-up theory of audibility to me. You're sending us two messages in one post:

You are saying ...

A) That you are not audibly aware of loudspeaker distortion even in a cheap mini-system and
B) That loudspeaker distortion "is a thousand times higher than amplifier distortion".

We seem to have reached a dead end here. Please, as you've cut across my train of thought, I offer you to take-over the subject from me. I obviously had a full, incremental explanation in mind. Walk us through to a reasonable understanding of distortion in your own, words. For starters what do you mean by the word "masking" which you have introduced without explanation.

The essence of explaining science to non-scientists is to avoid distractions, even well intentioned ones. I'm extremely busy and if you can take on this 'education' role to the same or better effect please do so. Please keep sharply in focus. Over to you ....

[EricW]

To recap: I've shown how an amplifier (although it could have been a pickup cartridge, a microphone, a speaker .....) has amplified a pure incoming signal and then, for whatever reason, generated, unasked for, a whole series of harmonics that are mathematically related in frequency to the incoming stimuli but are definitely not present at the input. We call these harmonic distortion(s). Even good loudspeakers produce plenty of these distortions. But you say that you are audibly unaware of these harmonics superimposed onto the music until the amplifier is driven to the upper limit of its power potential, when we would expect all the distortions to increase, perhaps dramatically. I assume that you could also comment that you are not audibly troubled by the harmonics generated in the loudspeaker until it is pushed hard, or from the pickup cartridge until it is tracing a really loud groove or from the microphone unless someone is screaming into it at close range.

How would you weave these observations into a cohesive working hypothesis?

>

Well, here is a limited hypothesis I think I can extract from the information presented thus far:

1. The audibility of harmonic distortion is dependent on a combination of:

a. overall signal level;

b. amplitude of the distortion relative to the amplitude of the musical signal.

The corollary I suppose would be that, at a sufficient low level in either absolute or relative terms, distortion would be inaudible.

If that's correct, I can think of two reasons that it might be so (and I recognize there may well be others):

1. When speaking of distortion relative to amplitude of a musical signal, I would conjecture that the "masking" principle that's been discussed in other posts would operate here as well; that is, a low level of distortion would be masked, i.e. rendered inaudible, by a higher-level non-distorted signal occurring at the same time.

2. There may also be a threshold of audibility depending on environmental factors, e.g. background noise.

Sorry if I'm off base; that's my best stab at it.

[kittykat]

1. The audibility of harmonic distortion ...

Will it be helpful to first ascertain if we have an idea what introduced harmonics sound like? The electric guitarists (and synthesizer musicians) amongst us, I suspect, might be most familiar with this phenomenon.

This practical test I believe might answer most, if not all the questions here…If its possible to find an electric guitar and a harmonics stomp box/ effects machine to play with, slowly dial this phenomenon in without altering the volume and making sure its not distorting in the traditional sense. Switch off harmonics and what do we hear?

[HUG-1]

Will it be helpful to first ascertain if we have an idea what introduced harmonics sound like? The electric guitarists (and synthesizer musicians) amongst us, I suspect, might be most familiar with this phenomenon.

This practical test I believe might answer most, if not all the questions here…If its possible to find an electric guitar and a harmonics stomp box/ effects machine to play with, slowly dial this phenomenon in without altering the volume and making sure its not distorting in the traditional sense. Switch off harmonics and what do we hear?

We planned to do that from the outset. (Make demo of deliberately increasing harmonic distortion).

[garmtz]

Dear Alan,

Maybe it's a good idea to open topics which remain closed for comments from other members. As a sort of a 'blog'? You might then open another topic to give people the opportunity to react to the 'blog' topics. This way, thoughts and discussions can better be separated.

[STHLS5]

... What message are you trying to convey? It just sound like a tone to me. If you use a prop to explain a point it's essential that you educate the listener, step by step, with what he is going to hear, how to listen for it and how to interpret it.

In {previous deleted example} DistortionVH.mp3, a 1% 2kHz wave was introduced to the test tone just after two seconds. In DistortionH, the whole recording consists of 5% of 2kHz along with the test tone. Attached again the same recording but in one 15 seconds file. After the 5th second, a 1% 2Khz added over the original test tone and after the 10 seconds a 5% two kHz added, and you can now hear how the tone changes its sound.

Attachment 1602

I will stop here and refrain from continuing so that we can continue to talk about the original topic. ST

[A.S.]

I'd like to take back this discussion now. First, thank you for making the distortion example, but I'm sorry I really can't hear what I think you want me to hear on these cheap PC speakers. Let's step back and do some foundation building as I planned to do.

First, what are the importance of harmonics to music?

Musical instruments create a sound by causing vibration of the air pressure around the instrument, and that pressure wave radiates away from the instrument to our ears. We covered that here. For example, the violin has several strings and when these strings are plucked or bowed they are set into vibration. Actually, the close proximity of non excited strings to the excited ones causes them to sing too, but at a low amplitude. The frequency of all notes is precisely defined by maths and we can play all music on a bank of finely tuned laboratory audio oscillators, one per note - this being the concept behind the Moog synthesiser. We can look up the exact frequency of all musical notes here.

If we set-up the synthesiser and play some classical music just according to the musical note frequencies we will hear something like this Bach tune. The tune is 100% accurate in tempo and notation to Bach's score but it sounds robotic and unnatural. Why? Because the harmonics are unlike what we would expect to hear from real instruments. But if an alien arrived from another planet who had never heard a real acoustic instrument, was given the musical note-to-frequency table above, he could generate the tune with sine wave oscillators and he'd think it quite normal. But we know that what Bach intended was rich in harmonics like here. Or with even more harmonics and hence a brighter tone here.

Modern musical instruments are tuned to a common base frequency of 440Hz (called musical A). That means, ignoring the harmonics which give each type of instrument their own unique voice, 440Hz will be perfectly in tune with all other instruments playing the same note in their range. But there would be no mistaking A or C on the piano compared with A or C on the flute. Here is what a single sine wave oscillator would generate as a 440Hz pure, harmonic-free tone. And that same note with its rich harmonics being tuned on a concert piano.

And here, taken to the other extreme is what you hear when there is little or no fundamental tone (because of the tiny, cheap speaker) and all you hear is the harmonics. So this 'rasping' bright high sound is what harmonics alone sound like which is why when there are no harmonics, the sound is so boring like the Bach tune here.

So can we say that harmonics are necessarily a bad thing? Definitely not; they freshen the sound of music and make it engaging. Can we say that there is an optimum balance between the quantity and loudness of harmonics and the fundamental note? Yes, this is why the same note on the piano and guitar have the same frequency but different richness and brightness. Can we say that amplifiers and other audio equipment should not generate harmonics of the music being played through them? Well, ideally they shouldn't but in the real world they do. Is that necessarily a problem as far as listening to music is concerned? No.

Here is a video of the rich harmonic make-up of the piano. Look at the lower trace on the 'scope which shows vertical spikes at the harmonic frequencies. Compare that with the picture of the distortion generated in an amplifier and you see the same idea of a fundamental (test) tone, plus a series of harmonics of varying level.

[Typing and researching this post took me 80 mins. on Sunday morning].

[garmtz]

MUCH appreciated Alan...

[A.S.]

In the last section of post No. 34 I drew attention to this video, here. The video shows the result of connecting a microphone to a dual channel oscilloscope and displays both the attack and decay of the piano note (top trace) and on the lower trace, the strength and frequency spread of the upper harmonics of the note. The lower 'spectral' trace is really interesting. It is giving us three very useful visual representations of what's happening inside the piano when the note is pressed.

First, the primary peak, the left most one must be that of the fundamental note, the one we could look up on the note-to-frequency chart; the one all instruments would generate if in-tune. Then the lower trace gives us a spread across the frequency spectrum upwards above the fundamental and we see distinct spikes at evenly spaced intervals along the frequency (left to right) horizontal axis. As the gaps between the spikes are regular, that tells us that the spikes are indeed harmonics of the fundamental tone. And there is a long series of them reaching out to many multiples of the fundamental note's frequency - I can see up to the 8th harmonic on this scale. So if the note played was a C, we know the fundamental frequency is 261.626Hz, what hifi listeners would call the lower midrange, and the 8th harmonic still in evidence on the 'scope screen would suggest some output from the piano at 261.626 x 8 = 2093.008Hz, right at the top end of the midrange driver, just as the tweeter flares-in.

Finally, the lower graph tells us about the relative loudness of the harmonics both relative to each other and relative to the fundamental. And if you were an expert at interpreting photographs of this oscilloscope screen without actually hearing the sound, you could say with certainty 'ah yes, that is a note being played on a piano' or, 'that's a different harmonic to fundamental balance so that's an organ' or whatever. That fact that wood, brass and string instruments can play in tune yet do sound so unmistakeably different is much to do with the make-up of the fundamental-harmonic structure of their notes. Companies like Yamaha who make excellent electronic pianos that reproduce the sound of a real piano over a built-in loudspeaker have spent years analysing the harmonics of real instruments and electronically synthesise all the vital harmonics in just the right quantity to satisfy the player that he's (almost) playing a real stringed piano.

We're able now to start drawing some comparisons between the nature of (wanted, desirable) harmonics our piano generates and the graphs we previously looked at of the amplifiers self-generated harmonics. Take a look at the attached picture which presents on the top, Graph A, a screen snap from the video and underneath (Graph B) I've pasted the Stereophile measurement of an amplifier's self-generated distortion. None of those spurious harmonics should be present at all in the amplifier's output. But they are. And that's inevitable because there is no such thing as a perfect amplifier. What the amplifier designer can manipulate during the design is how far up they go in frequency (to the 8th, 9th, 10th harmonic or beyond?) and how loud they are relative to the fundamental and to each other harmonic.

Is this logical? Can we see the general relationship between (wanted) instrument harmonics and the (unwanted) harmonics generated in an amplifier?

I'd like to look more closely at the loudness of the harmonic next time - that's really the key to understanding this, but first we needed these basic concepts to be solid.

>

[Supersnake]

Before Alan posts his next interesting contribution to this thread perhaps you may find these educational videos to be of interest.....

Music teacher Scott Laird from the North Carolina School of Science and Math:

Where Music Meet Science Part 1: Pitch and Frequency
http://www.youtube.com/watch?v=npGMh...eature=related

Where Music Meet Science Part 2: Timbre and Complex Waves
http://www.youtube.com/watch?v=nlv5bylQDsE&NR=1

Where Music Meet Science Part 3: Frequency and Harmonics
http://www.youtube.com/watch?v=sCi-3...eature=related

[EricW]

Alan:

So far, the information you've posted is extremely clear.

(I don't mean to get ahead of you, so please don't post this if I'm out of sequence.)

You've shown how the harmonics of an instrument, which occur at multiples of a specific fundamental frequency, determine an instrument's character. You've also shown how an amplifier self-generates harmonics (i.e. harmonic distortion) at specific multiples of a fundamental frequency, i.e. a signal injected from an audio test oscillator. From this I derive the following questions:

1. Since I assume the fundamental tone will exceed the harmonics in amplitude, and therefore presumably generate the most harmonic distortion, would not the harmonics of a musical instrument and the harmonic distortion of an amplifier tend to coincide?

2. If the answer to question 1 is "yes" (they'd occur at the same frequencies), is it not likely that harmonic distortion would have a subjectively benign character?

3. However, even if the harmonics of an instrument and the harmonic distortion of an amplifier coincide in frequency, the relative levels of the different harmonics are not likely to match. I therefore deduce that:

(a) above a certain level, harmonic distortion in the amp might begin to change the perceived tonality of an instrument, by preferentially reinforcing certain of its harmonics at the expense of others; and

(b) the effect referred to above might vary by instrument depending on how closely (or not) the harmonics of a specific instrument matched the harmonic distortion characteristics of a particular amplifier.

[A.S.]

...You've shown how the harmonics of an instrument, which occur at multiples of a specific fundamental frequency, determine an instrument's character. You've also shown how an amplifier self-generates harmonics (i.e. harmonic distortion) at specific multiples of a fundamental frequency, i.e. a signal injected from an audio test oscillator. From this I derive the following questions:

1. Since I assume the fundamental tone will exceed the harmonics in amplitude, and therefore presumably generate the most harmonic distortion, would not the harmonics of a musical instrument and the harmonic distortion of an amplifier tend to coincide?

2. If the answer to question 1 is "yes" (they'd occur at the same frequencies), is it not likely that harmonic distortion would have a subjectively benign character?

3. However, even if the harmonics of an instrument and the harmonic distortion of an amplifier coincide in frequency, the relative levels of the different harmonics are not likely to match. I therefore deduce that:

(a) above a certain level, harmonic distortion in the amp might begin to change the perceived tonality of an instrument, by preferentially reinforcing certain of its harmonics at the expense of others; and

(b) the effect referred to above might vary by instrument depending on how closely (or not) the harmonics of a specific instrument matched the harmonic distortion characteristics of a particular amplifier.

That is precisely and absolutely the point. Your analysis couldn't be better - or at least, it coincides with my own opinions.

That leads us a little further into this. You postulate that if, by some happy design fluke, the amplifier generated harmonic distortion with the same characteristic frequency spread (2nd, 3rd, 4th harmonics etc. etc.) as a musical instrument that providing the loudness of those harmonics was sufficiently below that of the instruments harmonics we might not be able to detect the addition of the amp's harmonic distortion. And if we did audibly detect the amps contribution, we might even like what we hear. We might find the extra 'sparkle' in the upper frequencies gives us the impression of 'greater clarity', 'more openness' and the like. The problem is, as we'll see, the characteristic nature of the harmonics is by quantity and frequency extremely unique to the class of instrument. All violins have generally similar violin-like sound so, logically, they must have a generally similar harmonic make-up. Outstandingly beautiful violins have a special blend of harmonics not found in the average violin - but they are still, unmistakably all violin family members. SO if the amp just so happened to generate the right harmonics to spice up the violin, it might be the wrong quantity/frequency of harmonics to give the human voice some sparkle. Or the piano. Or organ. And surely no one would by an amp that's only good on a certain type of solo instrument would they?

It's rather difficult to add harmonics to a pre-existing recording. I don't have the technology to do that, although I assume that it can be done. But what I can do is to let you hear the inverse - stripping harmonics from an existing recording so that you can get an idea of just how vital these harmonics are to truly high fidelity sound. Then perhaps you can imagine how should an amplifier (or any other component in the chain, including the speakers) tinker with the harmonics we can expect the overall sound to change a lot.

What I'm going to do, to kill the harmonics (this should work, but I need time to play with it) is to take a great recording - for example tonight's Radio 3 concert of Stravinsky delivered to me at 320kb AAC, saved as WAV at 48k, and then passed through an MP3 encoder at a moderate bit rate once, then passed through the encoder again, and again and again, recoding each time. We know that MP3 achieves file size reduction because it uses some psychoacoustic maths to decide what is really important to the human ear, and what can be dumped. And since the tune must remain recognisable, and the melody is all in the lower registers, MP3 achieves dramatic data reduction by discarding the fine detail - and those are our precious harmonics. My guess is that the harmonics will be severely diminished with progressive decode/re-encode, and by the 10th pass through, much detail will have been lost. After twenty cycles the tune is unchanged and perfectly recognisable, but the detail locked in the harmonics has been severely attenuated. Let's see ...

OK so here are the clips. Perhaps this isn't the best way to illustrate this sonic effect of good, clean harmonics in just the right quantity but I hope it will suffice.

1. First, the original source file (3.69MB):

Loading the player ...

2. Then after ten MP3 encode-decode cycles (175kB)

Loading the player ...

3. After twenty encode-decode cycles (137kB)

Loading the player ...

The file size tells its own story ... something has definitely been junked from the audio. The first generation as a WAV file was 3.69MB, and after twenty encode cycles down to 0.13MB. I calculate that, compared with the original WAV file, by the time we have reached example 3, the twentieth pass, 97% of the audio data has been erased.

Note: I picked this excerpt because of the dominance of the trumpet. We know that the shock wave, explosive nature of the brass generates strong harmonics, and whilst the MP3 coder would normally surreptitiously ignore harmonics if it can, the brass section is so loud that it can't be conveniently ignored - hence the coder's struggle and the smeared 'wooshing' quality after it reduces the fine harmonic detail. We are losing fidelity and that's very obvious. In fact, if you listen to the brass on 3 compared with 1, I think it sounds 'brighter'. And that is odd. I suspect that the codec has either deleted than tried to guess what the harmonic structure was, and then unconvincingly fake-it, or that the harmonics closer to the brass' fundamental have been processed differently (suppressed) and hence subjectively those further away from the fundamental sound disembodied. Hence the old term 'disembodied top'. Or it could be that the encode-decode process has generated additional spurious harmonics which we don't recognise as being part of the natural brass sound. Or all three hypothesis.

[A.S.]

OK, next step. What would it sound like if we deliberately add some harmonics to subjectively brighten the tone of an instrument? To give it more 'air', or 'sheen', more 'resolution' or 'detail'? We could add them in at the recording, the amplifier or speaker ... at any (or every) stage of the audio chain.

Let's imagine that this clip is our norm, our reference, exactly what the piano sound like in real life:

7. Our 'reference' piano here ....

Loading the player ...

8. And now we spice-up the hifi system, by adding some harmonics to bring out the detail ...

Loading the player ...

Which do you prefer? The reference recording (7) or the 'more detailed' recording (8)? Maybe (although this is really a side issue) Example 7 could perhaps be considered a 'valve' sound and Example 8 a 'transistor' sound? Not that they are, but I wonder if they have some characteristics associated with those two amplifiers?