Artisanal Audio

Just enjoying reading an article about Artisanal Audiophilia – a phrase that makes you look twice, I think – by Richard Varey (who was kind enough to link to one of my posts on his web site). I am looking forward to reading many more of his articles.

…artisan audio is handbuilt, usually by the designer, and is not mass-produced but made in small batches, made-to-order as a customised one-off, or is customisable and upgradable. They carry the name of the creator as the brand. They combine boutique audio engineering with design creativity driven by functionality and craftsmanship. They are made for audiophiles, promising authenticity, so not for the hipster or fashion conscious, nor the casual listener.

I was going to leave a comment, but it turned out a bit too long!

I take a sceptical view about boutique audio in general. I think that the crucial factors are:
1. It’s very hard to make audio equipment that doesn’t work to some extent.
2. Music is an exquisite, possibly expensive art form created by very talented, skilled people, and at the same time something that we hear spontaneously when birds sing or someone drums their fingers.
3. While other ‘artisan’ products (pens, watches, etc.) have to create their own ‘art’, audio equipment merely passes through someone else’s art.

Put these things together, and it becomes easy to equate a beautiful hand made passive volume control (or whatever) with art, craftsmanship, skill, etc. But my view (please challenge me on this) is that the reality is that its sound is all in the user’s mind. Of course, this is not in itself a bad thing – the perceived sound is real at the only level that really matters. However, it may be cheaper for the listener to train themselves to go into that state of mind when listening to a standard volume control!

What many people may not understand is that it would be very difficult to make a piece of wire or some other electrical conductor do anything at all to the signal except pass it unchanged. Creating an audiophile passive volume control or connecting cable is not like creating a fountain pen or a watch – even if the creator of it borrows the same aesthetic. All audio equipment, particularly the passive variety, *will* ‘work’ – you cannot stop it from doing so even if you try quite hard!

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The Logic of Listening Tests

Casual readers may not believe this, but in the world of audiophilia there are people who enjoy organising scientific listening tests – or more aptly ‘trials’. These involve assembling panels of human ‘subjects’ to listen to snippets of music played through different setups in double blind tests, pressing buttons or filling in forms to indicate audible differences and preferences. The motivation is often to use science to debunk the ideas of a rival group, who may be known as ‘subjectivists’ or ‘objectivists’, or to confirm the ideas of one’s own group.

There are many, many inherent reasons why such listening tests may not be valid e.g.

  • no one can demonstrate that the knowledge you are taking part in an experiment doesn’t impede your ability to hear differences
  • a participant who has his own agenda may choose to ‘lie’ in order to pretend he is not hearing differences when he, in fact, is.
  • etc. etc.

The tests are difficult and tedious for the participants, and no one who holds the opposing viewpoint will be convinced by the results. At a logical level, they are dubious. So why bother to do the tests? I think it is an ‘appeal to a higher authority’ to arbitrate an argument that cannot be solved any other way. ‘Science’ is that higher authority.

But let’s look at just the logic.

We are told that there are two basic types of listening test:

  1. Determining or identifying audible difference
  2. Determining ‘preference’

Presumably the idea is that (1) suggests whether two or more devices or processes are equivalent, or whether their insertion into the audio chain is audibly transparent. If a difference is identified, then (2) can make the information useful and tell us which permutation sounds best to a human. Perhaps there is a notion that in the best case scenario a £100 DAC is found to sound identical to a £100,000 DAC, or that if they do sound different, the £100 DAC is preferred by listeners. Or vice versa.

But would anything actually have been gained by a listening test over simple measurements? A DAC has a very specific, well-defined job to do – we are not talking about observing the natural world and trying to work out what is going on. With today’s technology, it is trivial to make a DAC that is accurate to very close objective tolerances for £100 – it is not necessary to listen to it to know whether it works.

For two DACs to actually sound different, they must be measurably quite far apart. At least one of them is not even close to being a DAC: it is, in fact, an effects box of some kind. And such are the fundamental uncertainties in all experiments involving the asking of humans how they feel, it is entirely possible that in a preference-based listening test, the listeners are found to prefer the sound of the effects box.

Or not. It depends on myriad unstable factors. An effects box that adds some harmonic distortion may make certain recordings sound ‘louder’ or ‘more exciting’ thus eliciting a preference for it today – with those specific recordings. But the experiment cannot show that the listeners wouldn’t be bored with the effect three hours, days or months down the line. Or that they wouldn’t hate it if it happened to be raining. Or if the walls were painted yellow, not blue. You get the idea: it is nothing but aesthetic judgement, the classic condition where science becomes pseudoscience no matter how ‘scientific’ the methodology.

The results may be fed into statistical formulae and the handle cranked, allowing the experimenter to declare “statistical significance”, but this is just the usual misunderstanding of statistics, which are only valid under very specific mathematical conditions. If your experiment is built on invalid assumptions, the statistics mean nothing.

If we think it is acceptable for a ‘DAC’ to impose its own “effects” on the sound, where do we stop? Home theatre amps often have buttons labelled ‘Super Stereo’ or ‘Concert Hall’. Before we go declaring that the £100,000 DAC’s ‘effect’ is worth the money, shouldn’t we also verify that our experiment doesn’t show that ‘Super Stereo’ is even better? Or that a £10 DAC off Amazon isn’t even better than that? This is the open-ended illogicality of preference-based listening tests.

If the device is supposed to be a “DAC”, it can do no more than meet the objective definition of a DAC to a tolerably close degree. How do we know what “tolerably close” is? Well, if we were to simulate the known, objective, measured error, and amplify it by a factor of a hundred, and still fail to be able to hear it at normal listening levels in a quiet room, I think we would have our answer. This is the one listening test that I think would be useful.

The Trouble with Hobbies

Have you ever suddenly been inspired to embark on a brand new hobby?

Maybe you’ve never owned a boat before, but having seen one chug by on the river you have thought “I’d love to do that!”. A quick browse in the classified ads shows lots of boats that look fine, and they don’t cost all that much. Basically any boat would be great, and you could gradually do it up, even if it is a bit shabby now. In your mind’s eye, your family will love you when you are able to take them on spur-of-the-moment, cheap weekends messing about on the water, starting in a few weeks’ time.

From this high point where the world is your oyster, you begin to take the advice of the magazines and other experienced hobbyists. Before you have even owned a boat, you become aware of the hierarchy of boat owners, and the boats that would render you a laughing stock if you owned them. You become aware of the general consensus on different types of bilge pump – not something you ever wanted to know. You begin to form an idea of the boat you should really go for – and it is not one of the bargain basement jobs you first saw. You might just about be able to stretch to a boat that would put you in the lower echelons of boat ownership but, importantly, not on the very lowest rung. You could always, perhaps, move up from there over time.

It now turns into an all-consuming hobby with the goal of having a boat on the river at the end of the year. In the end it costs thousands, and your children have grown up and left home before your boat finally takes to the water. You hit a bridge and rip the top off your boat the first time you take it out. You feel sick and abandon the whole hobby (a true story).

That’s the nature of male hobbies. They start out as wonderful, spontaneous ideas, but can turn into nightmares – mainly due to the existence of other hobbyists! Audio is one of those hobbies, I think. Ridiculously, the prices paid for bits of audio knickknackery rival the costs of boats.

A person could be seized one day by the idea of hi-fi as a way to improve their life, buy an amp and some secondhand speakers off Gumtree for £100, and plug their tablet or laptop headphone socket into the amp using a £2 cable. Hey presto, a hi-fi system that will sound much better than what they had before, and which has tinker-ability via the buying and selling of speakers and the audio streaming/library software options; there is no urgency in changing the amp and tablet hardware as they are pretty much perfect in what they do. The speakers are almost like pieces of furniture, so the person can indulge their tastes in how they look as well as how they sound, and they can be restored using standard DIY skills – a nice mini-hobby.

But what if the person does the natural male thing, and starts to read the magazines and forums? Immediately they will realise that their tablet’s headphone output is a joke in the audio world. They need to spend at least a few hundred pounds on a half-decent ‘DAC’, plus a couple of hundred on a budget cable. And of course, this is only for convenience: real audio quality can only be had if they own a decent turntable and a special vibration-free shelf to put it on. Where do they go from there? They need to make a decision on which turntable and which cartridge to go for. They need to take a view on cables, power conditioners, valve or solid state amps, accessories like cable lifters and record cleaning machines. Each decision, they are assured by their fellow hobbyists, will result in “night and day” differences in the sound.

After some months agonising over it, they assemble a beginner’s system for about £3,000 – they will upgrade as budget allows. It sounds OK, but they know that even though the brand is a highly recommended one, the particular model of valve amplifier they could afford has “hints of a slightly reticent mid range” – one of the magazines said so – and if they listen carefully, perhaps they can hear that… But the more powerful 18 Watt model cost £800 more and they decided against it. Perhaps they made the wrong decision. The nightmare unfolds…

Thoughts on creating stuff

IMG_0206

The mysterious driver at the bottom is the original tweeter left in place to avoid having to plug the hole

I just spent an enjoyable evening tuning my converted KEF Concord III speakers. Faced with three drivers in a box, I was able to do the following:

  • Make impulse response measurements of the drivers – near and far field as appropriate to the size and frequency ranges of the drivers (although it’s not a great room for making the far field measurements in)
  • Apply linear phase crossovers at 500Hz/3100Hz with a 4th order slope. Much scope for changing these later.
  • Correct the drivers’ phase based on the measurements.
  • Apply baffle step compensation using a formula based on baffle width.
  • Trim the gain of each driver.
  • Adjust delays by ear to get the ‘fullest’ pink noise sound over several positions around the listening position.
  • ‘Overwrite’ the woofer’s natural response to obtain a new corner frequency at 40 Hz with 12dB per octave roll off.

The KEFs are now sounding beautiful although I didn’t do any room measurements as such – maybe later. Instead, I have been using more of a ‘feedforward’ technique i.e. trust the polypropylene drivers to behave over the narrow frequency ranges we’re using, and don’t mess about with them too much.

The benefits of good imaging

There is lovely deep bass, and the imaging is spectacular – even better than my bigger system. There really is no way to tell that a voice from the middle of the ‘soundstage’ is coming from anywhere but straight ahead and not from the two speakers at the sides. As a result, not only are the individual acoustic sources well separated, but the acoustic surroundings are also reproduced better. These aspects, I think, may be responsible for more than just the enjoyment of hearing voices and instruments coming from different places: I think that imaging, when done well, may trump other aspects of the system. Poorly implemented stereo is probably more confusing to the ear/brain than mono, leaving the listener in no doubt that they are listening to an artificial system. With good stereo, it becomes possible to simply listen to music without thinking about anything else.

Build a four way?

In conjunction with the standard expectation bias warning, I would say the overall sound of the KEFs (so far) is subtly different from my big system and I suspect the baffle widths will have something to do with this – as well as the obvious fact that the 8 inch woofers have got half the area of 12 inch drivers, and the enclosures are one third the volume.

A truly terrible thought is taking shape, however: what would it sound like if I combined these speakers with the 12 inch woofers and enclosures from my large system, to make a huge four way system..? No, I must put the thought out of my head…

The passive alternative

How could all this be done with passive crossovers? How many iterations of the settings did it take me to get to here? Fifty maybe? Surely it would be impossible to do anything like this with soldering irons and bits of wire and passive components. I suppose some people would say that with a comprehensive set of measurements, it would be possible to push a button on a computer and get it to calculate the optimum configuration of resistors, capacitors and inductors to match the target response. Possibly, but (a) it can never work as well as an active system (literally, it can’t – no point in pretending that the two systems are equivalent), and (b) you have to know what your target response is in the first place. It must surely always be a bit of an art, with multiple iterations needed to home in on a really good ‘envelope’ of settings – I am not saying that there is some unique golden combination that is best in every way.

In developing a passive system, every iteration would take between minutes and hours to complete and I don’t think you would get anywhere near the accuracy of matching of responses between adjacent drivers and so on. I wouldn’t even attempt such a thing without first building a computerised box of relays and passive components that could automatically implement the crossover from a SPICE model or whatever output my software produced – it would be quite big box, I think. (A new product idea?)

Something real

With these KEFs, I feel that I have achieved something real which, I think, contrasts strongly with the preoccupations of many technically-oriented audio enthusiasts. In forums I see threads lasting tens or even hundreds of pages concerning the efficacy of USB “re-clockers” or similar. Theory says they don’t do anything; measurements show they don’t do anything (or even make things worse with added ground noise); enthusiasts claim they make a night and day improvement to the sound -> let’s have a listening test; it shows there is no improvement; there must have been something wrong with the test -> let’s do it again.

Or investigations of which lossless file format sounds best. Or which type of ethernet cable is the most musical.

Then there’s MQA and the idea that we must use higher sample rates and ‘de-blurring’ because timing is critical. Then the result is played through passive speakers with massive timing errors between the drivers.

All of these people have far more expertise than me in everything to do with audio, yet they spend their precious time on stuff that produces, literally, nothing.

The Subjectivist/Objectivist Synthesis (Audiostream’s latest article)

Audiostream has posted a new article on the Objectivist/”Subjectivist” debate.

(I have to be careful to put inverted commas around the word “subjectivist” because, as an earlier commenter pointed out quite rightly, “subjectivists” rarely justify their name; in reality they are usually claiming that their subjective experiences are a superior form of objective measurement).

In summary, the new article says “Hey, everyone’s views are valid. Let’s not too get dogmatic, and just have a beer”. I think this misses the point (or several points). For me, the biggest ones are these:

  • Measurements are always incomplete, and are just part of the picture; this seems to be misunderstood by many people, who think that there is a supernatural mystery as to why supposedly good measurements don’t always correlate with good sound. I don’t think there is a mystery.
  • Subjective experiences are always affected by spurious factors; if the measurements of what comes out of the speakers show substantial deviation from the signal (i.e. are ‘bad’), this, for me, trumps the subjective opinion. But as mentioned above, if the measurements are ‘good’ they may still be incomplete.
  • Let’s only start worrying about the above when we’ve designed the system to avoid the obvious errors as best we can. This is neither objectivism, nor “subjectivism”, but rationalism. For reasons of tradition and ‘folk intuition’, this may be rare in the world of hi-fi.
  • I would be only too keen to hear people’s subjective experiences if they are referring to something measurably out of the ordinary and arguably good; less so if they are describing differences between digital cables that, rationally, cannot be affecting the sound. Some people do it all within the same article!

More digital cable fun

Audiostream has another digital cable promotional article.

Within it is a little aside of a type that I often see:

<some company> is choosing to keep mum on the specifics relating to how these cable’s differing materials and construction impart different sonic flavors.

In fact no one has ever revealed the secret of how an ethernet cable (or any cable for that matter) imparts different sonic flavours – for the simple reason that it is impossible. We know it is impossible because this is a man-made, engineered system, one of whose primary purposes is to make it impossible. If, in fact, an ethernet cable physically changes the sound (as opposed to placebo effects), then this is not a digital audio system at all. It would probably be best to repair it, re-design it, or throw it away sell it to the nearest person who believes that manufacturers of audio cables “keep mum” only because they have valuable secrets to safeguard.

Digital cables: a lack of understanding

eyediabinary cropped

There’s a new article about digital cables which is directly relevant to my post a couple of weeks back – it even features the “eye diagram” I referred to.

It purports to ‘debunk’ the idea that “bits are bits”, but in reality it does nothing of the sort. It starts off with a question that it fails to answer and doesn’t come back to again:

Asynchronous USB audio to the rescue?

The remainder of the article is about isochronous USB and seeks to suggest that it is not just about getting all the data through intact, but that there are issues with timing, jitter and noise. Judging by the comments that follow, the readership is entirely unaware that it is a non sequitur they have been reading.

There is a strange little “Note” placed halfway down in tiny lettering that says

Do not confuse ‘asynchronous USB’ with ‘Isochronous,’ an asynchronous USB system still uses Isochronous mode to transfer audio.

I am not quite sure what that is supposed to mean, but again it seems to be an appeal to the false idea that it is beyond the wit of man to deliver digital audio data without it being corrupted, or affected by timing. As I have said before, if this were true, then systems such as TIDAL could not work: the data has come through thousands of miles of cheap cable not even made of silver or raised from the floor on little ceramic pots, through hundreds of utilitarian digital switches, and eventually into your home via the cheapest connector that your telecoms company could provide. And yet it works perfectly; all the electrical noise of the world’s internet, and all the jitter that comes from being re-routed dynamically hundreds of times every second, is completely absent.

As I said in my earlier post, we need to understand the system at a higher level. Asynchronous USB and other on-demand packet-based systems are immune to cable quality once it is beyond some minimum standard, and electrical isolation removes the possibility of noise being injected into your audio system – even enabling you to listen to music off the WWW without all the electrical noise of the global internet spoiling your listening pleasure. Really, getting data from a file/CD/stream into your DAC and reading it out at a precise rate is a simple engineering problem, rendered trivial and cheap for the consumer by some very clever people who actually understand the problem, and have solved it.

Understanding vs. Knowledge vs. Expertise

Reading Archimago’s latest article, I am struck by two things:

(a) he’s probably a much nicer person than me

(b) the high end audio business may not be so much a scam as a <word that begins with “cluster”>.

What I’m thinking is that millions of words (not Archimago’s I hasten to add) and thousands of product developments can all stem from an incomplete understanding of something, plus the obscuring of central ideas with mere facts and ‘expertise’. Case in point is the subject of digital cables, discussed in the article. Archimago has endless patience and ‘plays along’ with the manufacturers and their disciples, giving them the benefit of the doubt by testing their products, even though he knows that they will always give more-or-less identical results. I am more inclined towards the idea that we should just ignore them. Unfortunately, neither approach can rid us of the cloud of confusion that surrounds the subject, and which must ultimately divert attention away from real progress (and with the Kii Three and Beolab 90, for example, we at last have some real progress to evaluate, and hopefully to make cheaper).

Which of the the following propositions are false?

1. Digital audio is degraded by jitter.

2. Cables carrying digital audio signals impart jitter onto those signals.

3. High quality cables can be designed to reduce jitter compared to others.

4. Digital audio can be improved by high quality cables.

I would say that none of them is completely false in all circumstances, and herein lies the problem. An entire industry is sustained on these propositions; manufacturers talk knowledgeably (and who knows, maybe honestly) about them. But while the propositions may all be true individually and with qualifications, they are an incomplete representation of the role of cables in digital audio. An understanding of digital audio at a system level would show that many implementations are certain to be immune to cable quality (and the remainder of implementations are highly insensitive to it). Those bi-directional implementations that deliver the audio data in packets on demand, slaved to the DAC’s sample rate, are immune to cable-induced jitter by design. Case closed. We could simply move on.

But if you have the misfortune to enter into a discussion about the subject on a forum, you will quickly encounter many vociferous people with detailed factual knowledge and expertise regarding cables, and that that is all they want to talk about; it won’t be long before someone brings up “eye patterns”, transmission line theory, the “skin effect”, “six nines” copper, monocrystalline metal and so on. Or they want to talk about listening tests and statistical ‘p-values’. This lower level knowledge, even if correct within its own little sub-fields, is not really relevant, but unfortunately forms a smokescreen that obscures all understanding.

Light entertainment

Here’s a little controversy from the archives of Stereophile magazine.

Stereophile has an interesting policy whereby an equipment reviewer writes up his subjective experience of testing a device, and only then is it measured for distortion, frequency response and so on. It seems that the magazine has the integrity to publish the two reports whatever the outcome.

Have you ever seen a more polarised review than this one from 2005?

The reviewer says:

The CyberLights represent one of the greatest technological breakthroughs in high-performance audio that I have experienced in my audiophile lifetime….

…for the first time in your life you’ll hear no cables whatsoever. When you switch back to any brand of metal conductors, you’ll know you’re hearing cables—because what’s transmitted via CyberLight will be the most gloriously open, coherent, delicate, extended, transparent, pristine sound you’ve ever heard from your system…

The measurements person says:

If this review were of a conventional product, I would dismiss it as being broken. …I really don’t see how the CyberLight P2A and Wave cables can be recommended. I am puzzled that Harmonic Technology, which makes good-sounding, reasonably priced conventional cables, would risk their reputation with something as technically flawed as the CyberLight.

You’ll have to read the full review for yourself, because the contrast between the two opinions is almost comical. The measurements are quite something to behold.

You see, I sometimes worry that perhaps I just don’t ‘get’ this hi-fi business. £80,000 analogue systems don’t sound anything special to me. Vinyl doesn’t sound as good as digital to my ears but everyone else says it is much better. Designing and building my own system was really quite straightforward, yet the internet is full of intense discussion about how difficult it is; people spend their entire lives building their own speakers and are never happy with them yet it’s almost three years in and counting, and I haven’t felt motivated to modify mine yet. Are the experts hearing something I am not? Perhaps this review sheds some light on the answer.

Analogue enthusiasts often claim that the signal-modifying effects of whatever product they are listening to actually improve the sound. The usual line is that the indefinable magic of valves and vinyl is down to what those devices add: they are serendipitously restoring something that is supposedly missing from the recording. ‘Poor’ measurements are simply an indication of an harmonious combination of factors that enable the leap from clinical, neutral signal to real music. There is no argument possible against this assertion.

However, in the above review, the writer cannot make that claim. Clearly he has confused high levels of distortion and noise plus extreme frequency response variations as an absence of colouration. For him, replacing metal cables with “light” was all about removing “grunge” and other “well-known problems”. Because of his extreme analogo-philia, I don’t think he actually knew what ‘neutral’ sounded like. When he heard something that was different from anything he had heard before, he automatically assumed that it must be because cables really are the sonic quagmire he thought they were and that the product was doing what he assumed it was designed to do. For once, it actually was a “night and day” difference but his understanding of what he was hearing was 180 degrees wrong. In the scheme of things, it doesn’t really matter, but it reassures me that 99% of the ‘expert’ opinion based on listening is very dubious indeed – I do think there are people out there who would find much to like in a pair of yoghurt pots linked with string as long as they cost enough.

Stereophile, it appears, doesn’t normally measure cables when they are reviewed. I think we can guess why: there is nothing to measure. Each and every review would feature the same distortion and noise measurements at the very lowest depths of the test equipment’s range, plus a ruler-flat frequency response when using the cable in normal circumstances. It wouldn’t matter if the cable cost £1 or £10,000 – which, absurdly, they sometimes do. To arrange anything different would actually be quite difficult. It is this complete, boring neutrality that Michael Fremer and other cable mythologisers are convinced is plagued with “grunge” and other problems. The justification for the Cyberlight product, so appealing to Fremer, is that it replaces a short section of metal with light and fibre optics, and is analogue – you still connect to the input and output with those awful grungy wires. It is no different from becoming excited about the audio quality of headphones that use an analogue wireless link rather than a cable. Just as with those headphones, there is a little “background hiss” but this is a small price to pay, apparently. And just like those headphones, the signal goes through a link of dubious quality. Very dubious. At least there is a valid justification for wireless headphones, though.

If you gave me about £20 to buy a few parts, I could build you this device in an afternoon, probably. But if I did, I would try to make it work properly. I would certainly try to convince you that the whole product was unnecessary and was corrupting the signal, and that if we really had to use fibre optics we should digitise the signal and send it as pulses. I might also point out that the commercial product is a mess: various “wall warts”, $400 battery packs and “pigtails” that could, depending on what equipment you’re using, destroy your speakers.

And don’t ever unplug or plug in the power to the cables with the amplifier turned on or you’ll send a horrendous THUMP through your system.

For people who might dismiss active speakers and DSP as too complex, there are no limits to the Heath Robinson-esqueness that they can tolerate in the name of ‘analogue’.

The amazing interior world of cables

colfairy

Looking at one of thousands of ‘reviews’ of audio cables that are out there, I was struck by the vivid language that described what the reviewer had heard. I looked at a handful of other reviews and compiled a far from comprehensive list of the words and language on offer. Here is a small fraction of it:

…happier; melody; emotion; sunlight; fast; tired; cold; “mood of the musician”; languid; darker; zest; tempo; warmth; iciness; sweet; confidence; insinuation; gesture; informative; provocative; calm; assuredness; forthright; frantic; “trying too hard”; somnambulant; fire; tantalising; insightful; relaxed; refined; composed; uplifting; gravitas; nonchalant; sympathetic; magical; “unearthing the feeling and meaning”…

Audiophiles like to say that “the best cable is no cable at all” suggesting that a cable can only degrade a signal. In this light, the findings of the cable reviewers are remarkable. In order to get the signal into the cable, vibrations in the air have been converted into a different ‘domain’ – electricity – where, presumably, things could happen to the signal that cannot happen in the acoustic world. Yet the reviewers of cables don’t hear electrical, signal-degrading effects and nor do they hear ‘no effect’. What they perceive is an amazing, coherent, functioning interior world of laughter, tears, sunlight, butterflies, palaces and fairies. All this is going on inside that functional polyester braided jacket and those often-lumpy applications of heatshrink sleeving that cover a multitude of sins.

And it gets even more amazing. In audio we can change the audio signal into yet another domain: that of discrete numbers. A handy way of transmitting those numbers is electrically via cables, but what is being carried is only the numbers. Amazingly, the same magical interior worlds exist there too!

When I was very young, my dad told me that inside our Hacker valve radio there were tiny people singing and dancing. He never told me that inside the wires themselves there was a far more exciting and exotic world waiting to be discovered.