Exactly.
For speaker wires, the resistance is what matters, not the resistivity of the conductor material. If you’re using a conductor material that has high resistivity (e.g. aluminum), simply use a larger gauge wire.
Couple of points.
You need to master a recording differently for LP versus CD. scabpicker described some of the elements above. In general the mastering takes into account he vagaries of the LP format, and corrects for those in the final balance of the mix. Early CDs were simply digital recordings, often taken off n’th generation cutting masters previously used for the creation of pressing masters. So they had welded into them these same compensations. When the CD format didn’t roll of the highs and the like, people noted that they sounded horrid.
Shannon’s theorem and Nyquist Shannon. People get this mixed up.
There are two things here, and very often the Nyquist sampling theorem is quoted without any understanding of Shannon and the underpinning mathematics. When this happens you get all the usual accusations the “Nyquist doesn’t apply” and so on. Shannon is one of the most important and really neat bits of theory. It describes the limits of information in a noisy channel. Nobody disputes this theory. Somehow describing it as “old hat” or outmoded is no different to saying that calculus is “old hat” and not relevant because it was worked out so long ago.
Historically Nyquist postulated the sampling theorem before Shannon had worked out his basic information capacity theory. They both worked at Bell Labs. Shannon, as a part of the work he did on information capacity proved the Nyquist theory mathematically. So nowadays it is common to call it the Nyquist-Shannon theory. However, that is not the same as Shannon’s theory. Shannon is the core component of information theory and has extraordinarily wide reach. Shannon is crucial here too.
Recording sound is inherently a process of communicating information in a bandwidth limited noisy channel. The entire universe is a bandwidth limited noisy channel. Before you do anything, you need to know what those limits are.
Now, without going into things too deeply, there is a perfect mathematical symmetry between the operation of a sampled quantising (ie “digital”) audio system and a continuous, unquantised one (ie “analog”). The presence of a bandwidth limit and a defined dynamic range are symmetric between the two, and result in identical performance.
Where people get confused, and you see these ridiculous stair step diagrams, is that they don’t understand what bandwidth limited means. The anti-alias filter and reconstruction filter present in a digital system are there to define the bandwidth. Their inherent nature ensures that there is no energy from outside the defined bandwidth present. On recording this prevents higher frequencies aliasing into the pass band, and on reconstruction they prevent any energy outside the pass band being present. This latter aspect exactly prevents the existence of the stair step. Better, it ensures, from a pure mathematical basis, that there is exactly the same waveform as the sampled bandwidth limited waveform. Analog audio has bandwidth limits (or for LP these are worse, both for bandwidth and dynamic range) and the final wash-up is that the performance of any pair of systems is identical when you compare like with like with bandwidth and dynamic range.
Where you get hand-waving arguments is things like transients. Somehow the idea is that a transient peak is magical, and has a steepness that an analog system can capture but a sampling system cannot. And you get silly stair step arguments. No. Both are bandwidth limited. The presence of this limit ensures that both capture exactly the same thing, and later reproduce exactly the same thing (If the channel specs are the same). You might argue that the bandwidth is insufficient, but that argument must apply equally to both media, analog recordings don’t get a leave pass because one doesn’t understand the mathematics.
Nice explanation, Francis Vaughan! I do have one question. I’ve read a lot of different stuff online about this topic so I don’t remember exactly where it was, but I remember one rather confident chap saying that he could tell the difference between a CD-level sampling rate and something significantly higher with 100% accuracy. At the same time, he recognized that the extremely high-sampling-rate formats being touted in some quarters are bullshit.
BTW, the whole digital thing finally clicked for me when I understood the relationship between sampling rate and frequency. Correct me if I’m wrong, but the sampling rate is analogous to frequency. We need to keep in mind that sound is a wave, not an infinitely divisible substance. If the sampling rate can cover the frequency, then that’s all the ears can handle anyway. Perhaps you could explain why sampling double the frequency is needed. Thanks!
In a very fundamental manner, there is a duality between the amplitude of a signal and its frequency. It is common to transform a signal from the amplitude domain to the frequency domain (with a Fourier transform). In frequency space you can reason about some aspects of a signal much more naturally than on amplitude space. (And others not.) Everything is noisy. That is what the dynamic range is about. Not only do you have a maximum amplitude, but there is a minimum one as well, the point where you hit the inherent noise in the system. In amplitude space is obvious that the noise places a limit on how well you can resolve the amplitude of the signal. For any sample there is a range of amplitudes that the signal has bounded by the level of noise. So your quantisation mechanism will bin its samples to an accuracy that is no better than the noise amplitude of the channel. What is less intuitive is that this same logic applies in the frequency domain. Noise is present here was well. You ability to resolve the frequency of a signal is limited by sampling of frequencies and the noise. In exactly the same way as you can resolve a signal’s amplitude to within one quantisation step (with noise) so to you can resolve a frequency to within one frequency sample. The minimum number of samples it takes to represent an oscillating waveform is two. So, within the bandwidth and with the noise, it takes two samples at twice the frequency to locate that frequency.
There is another critical nuance here. I keep mentioning noise. If you try to model sampling quantised systems without noise you won’t get the right answers. It seems initially counter-intuitive, but noise is a fundamental part of how all systems work. In the continuous on-sampled regime, noise is simply a limit on capability. In the digital domain it is part of how it works. But - and this is the superbly neat but, the end result in both cases is identical. The really important point is when it comes to dither. If you sample a signal and the quantisation levels are significantly greater than the noise floor, you will get poor results. If the quantisation level is the same as the noise floor (ie the distance between samples that vary by one bit is the same as the RMS noise amplitude) you get much better results. And the better is again counter intuitive. Most people think that the noise “floor” is the level beneath which you can’t get any signal. This isn’t so. Again, this is pure Shannon. There is signal beneath the noise, and it is easy to hear it, and to find it. Both digital and analog sound systems reproduce it. In digital systems however you must control the noise, and this is especially so when you are creating the final digital master. The name this comes under is dither. But in the recording process controlled noise is used to de-correlate sampling noise in the analog-to-digital converters. If you don’t, the system doesn’t work correctly.
This is the fundamental beauty of how the systems work, and the implications of Shannon. Communicating in a bandwidth limited noisy channel (which is all of them) is fully charaterised by that bandwidth and dynamic range. Whether you impose the limits via analog means (which may just be the inherent limitations in the media) on in the digital domain, the answers are identical. But they are only identical if you include all of the parameters. Noise is the one most people don’t appreciate the deep significance of.
CD sound is right on the limit of the range of human perception. That is so long as you are careful a CD can capture everything your ear can. But even small glitches in the encoding will drop it down to the point where the ear outperforms it.
The Nyquist criterion is simply that you need to sample at over double the rate of the frequency width of the band. (This is a nit-picking definition, for audio the highest frequency is also the bandwidth, but it needed be so.) But in order to capture the information in the band you must have bandwidth limited the signal. If you were to sample at 40kHz, in principle you can capture up to 20kHz. But you then need an infinity steep anti-alias filter (the name usually given to the bandwidth limiting filter). Infinity steep filters are neither easy or totally benign. So there is always going to be a bit of wiggle room added. CD uses 44.1kHz sampling. But if you sample higher you can use a whole range of nicer behaved filters. The same occurs on playback. The reconstruction filter is identical to the anti-alias filter (the process is symmetric).
In pro-audio it is usual to use sample rates much higher than 44.1kHz. And also to use higher bit-depths. 96kHz and 24 bits is probably the default. This allows the mixing, effects, and mastering processes all the latitude they need to do their work. There are all sorts of things that go wrong in the digital domain if you don’t take care. Many are the same as bad things in the analog domain, but with different names. (For instance - gain staging is a critical aspect of the recording and mixing process. In the digital domain you can get loss of precision or overflows in exactly the same manner. Having the deeper bit depth and a wider sample rate helps enormously here.) When a CD master is created the higher bit-depth data is dithered when it is re-sampled to 16 bits. You cannot just truncate the bits. But using shaped noise dither, it is possible to trade off amplitude resolution in the very high frequencies (where our ear is insensitive) to the critical mid-bands. 16 bits is 96dB. But with proper dither, the mid bands can get at least another 9db of resolution. This gets us to the point where our ears can no longer resolve better than the CD. The down side is that once done, you can’t re-sample. Dithering is, and must, be the last step.
Awesome explanation, Francis Vaughan! So was the guy I read full of bullpoo–or do you think he could really tell the difference of a higher sampling rate?
And do you think it would be better if CDs had a somewhat higher sampling rate? Thanks!
It is more likely that he could hear artefacts due to the particular implementation. This is much easier. It isn’t hard to learn to listen for the particular sonic signature of part of a system. Or just differences between systems.
This is similar in compressing schemes as well. It isn’t hard to pick an MP3. Listen to the fade out to silence at the end of a track. Or, listen to high frequency percussives (the triangle is brutal, cymbals are good too) or as noted above, a plucked steel string. There is a clear signature that is often termed “splashy”. There might be nothing wrong with the sound in general, but some people find that once they notice these artefacts they can’t stop noticing them.
For the purposes CD was designed for it is fine. Things like oversampling get past the problems reproducing the signal at 44.1kHz generate. We are lucky they did get it to the level they did. Initial suggestions for the standard did fall short. As it is, it is just OK.
(Big problem in the early days was that arbitrary rate sample converters had not yet been developed, and sample rate conversion was only possible between integer ratios. Pro audio tended to work at 48kHz, and broadcast radio would use 32kHz to reticulate signals to FM transmitters. 44.1kHz was thus a pest.)
Thanks again! If you were to design the optimum system, what would it be?
How about the system that makes you happiest?
I love vinyl, even though it’s objectively inferior to a good digital system. For me, it’s the ritual of watching the tubes warm up, the nostalgia of sliding the disk out of the sleeve… a sleeve that’s almost 150 square inches of Art, I might add… and placing the needle anywhere I want. Being able to see the quiet passage in the middle of a jam that I want to skip to is fun.
Oh, wait. Does “fun” count in this debate?
ETA: I’ll admit, even more fun is loading up a vintage iPod Nano with audiobooks (downloaded at shallow bit-depths, like 32 bits/channel) and taking off on my bike.
Eh, 24bit 96kHz would make life easy.
I’m interested in active speakers and active speaker correction systems, and these mean I am fiddling with the audio again after it has been mastered. Most systems run at 96kHz, and if the native distribution of audio was this, and with 24 bits of depth, there would be much less worry about how to avoid losing information. 24/96 has so much resolution in hand you really need to work to screw up.
SACD (or more correctly the DSD encoding) is btw simply ridiculous. It has nothing going for it. One wonders what the heck Sony and Philps were smoking.
Heck yes. I can perfectly relate to the whole LP thing. I have a stash of LPs, much like many people, and still have my Rega Planar 3 (bought with some of the first money I ever earned) fitted with a Mission 774 tonearm and Fidelity Research 201 moving coil cartridge. It sits on a shelf in my cellar. And it did sound gloriously nice. But life moves on.
I like my HiFi listening, but I also do many other things in life, so little rituals come in other forms. Once you have everything ripped into a lossless digital store, you get the best of all worlds.
About 300 of those millions of vinyl LP’s are sitting in my basement where they have been untouched in 25+ years.
And this is why I love the Dope. Thanks Francis. 
I don’t dispute that there are people who can hear higher frequencies than others. it is possible, assuming the music content has information there, he could pick out stuff above 22 kHz. I kind of doubt it, though, and tend to agree with Francis Vaughan (as I always do) in that he might be keying in on some artifact which isn’t there at a higher sampling frequency.
if you try to reproduce sounds with frequencies above half of the sampling frequency, you’ll get aliasing. meaning, you’ll hear sounds lower in frequency which aren’t supposed to be there because there are insufficient samples to properly characterize the sound you’re trying to sample.
that’s why one of the early stages of digitizing signals is to run it through an anti-aliasing low-pass filter; you have to define the bandwidth of the signal before you can accurately sample it.
As a bit of fun light reading, any engineer, mathematician, scientist, or anyone who aspires to be, who has not read this paper should. It is both a delight, and one of the most important papers of the 20th century.
http://math.harvard.edu/~ctm/home/text/others/shannon/entropy/entropy.pdf
And for completeness - Shannon’s paper on communicating in the presence of noise.
http://nms.csail.mit.edu/spinal/shannonpaper.pdf
The paper I linked to above - A Mathematical Theory of Communication, includes the first ever published use (and definition) of the word “bit” to describe a binary digit unit of information. (The term was coined by JW Tukey (of the Cooley-Tukey FFT algorithm fame).
**Francis Vaughn **- you da man; fascinating.
Two observations/questions:
- Bottom line: it sounds like there is nothing digital can’t do that analog can. But the real point is that analog does have limitations/artifacts that are pleasing to Human ears. It seems like digital has had to evolve to include some of those artifacts so it digitally replicates what analog does. So, for instance: ice-picky highs. Digital can get all of a sharp, high signal - which can sound harsh. Analog filters out some of the harshness.
Is that a fair summary? That digital needs to be set up to include some of the filtering that analog imparts naturally?
I come to this from the world of electric guitars. There are older parts like potentiometers what were made in ways previously that were more inefficient vs. today. But that inefficiency is more musical, i.e., they don’t cut off frequencies as brutally as you roll off the Tone knob, so it sounds warm and not antiseptic.
- other point: I would argue that part of the appeal of vinyl is the process of listening. If you can listen to anything, any time, are you really listening? If you have to set up an LP, play it through and flip it over, are you giving more to the listening you do? I have gotten a sense that this is a bit part of the vinyl experience. I took it for granted as a kid, so to hear young vinyl fans describe how cool and new a dedicated listening experience is, it makes me stop and smile.
Good point. After reading your post, my new plan is that I’ll have to save my “idyllic Saturday sitting on the floor surrounded by LPs and comic books and a bowl of Lucky Charms” for retirement…
I must admit, this and the nostalgia factor are a big reason why I have a fancy turntable and a bunch of vinyl in my house. I’ve got a decent ear, but I’m no audiophile. I attended a demo for top-of-the-line equipment; $200k in speakers, amps and power supplies. And they played .wav files on a laptop.
Yep. Vinyl/turntables have a ‘sound’, but that sound is not some hi-fi unicorn, where true ‘quality’ is only achieved via the right ritual. It’s a specific coloration that can be recorded (digitally) and played back with functionally perfect fidelity, or even added in production/mastering without actual vinyl ever coming into the process.
A person can have a subjectively different experience interacting with a turntable than with another medium, but that has nothing to do with some kind of inability of digital recording to get as ‘good’ a sound as an analog system (or even to replicate it, if that’s what the engineer/designer wanted).
Also, I’ll add my thanks to Francis Vaughan for providing some detailed actual expert explanation here.
Nicely stated. Music is almost ubiquitous now. It’s in my car, the iphone in my packet has 90GB of music on it. Sitting here in my home office, I have online access to play probably 90% of all the music recorded in the last 60 years.
It’s too easy. I have music streaming right now, and I had to pause for a second to actually listen and identify what song was playing. (Backyard Skulls by Frightened Rabbit) But when I go to the room I have my turntable set up in, pick out an album, and go through the motions of playing it, I will sit down in the one chair in the room (ideally positioned) and actually listen.
Sure, it’s part nostalgia. But it’s also a tactile thing. And it’s for sure a focus thing. I won’t try to get technical and say it SOUNDS better. But I know I for sure I LISTEN better. And it does seem (see, that’s a feeling thing right there) to sound better to me. Maybe it’s that some of the harshness/spiky bits are rounded off. Maybe it is that the seeming scientific fact that analog HAS TO BE a lesser technology than digital is a good match for my 52 year old ears.
My Marantz receiver is from 1980. My speakers are from the early 90s. Turntable is new. But at the end of all that, my ears are from 1964. 