What's in a CD?
A CD contains a long list of 16bit signed integers encoded as tiny pits in the (usually aluminium) silvering layer. Spinning the disk and bouncing a laser off it allows these numbers to be read into the player, ideally exactly the same numbers that went on at the factory. In practice - barring the odd faulty player - the data usually comes off the CD OK, especially when ripped by computer drive.
These numbers provide a linear grid of level vs time that forms a series of 2D points (like drawing on graph paper when you are only allowed to put a dot on an intersection), how well we join those dots to re-construct the original waveform will influence the quality of the reproduction.
The data on the CD is designed to be played back at 44.1kHz and each 16bit value has linear magnitude, which allows an excellent full level 1kHz sinewave to be reproduced with very little distortion.
The origins of the CD - 1979
The CD's influence on downloaded music
Downloads and MP3s, FLAC etc are all echos of this CD data because despite the lack of the shiny disk, record companies continue to stick to the format of 44.1kHz and 16bit except in very limited cases. This format was set over 37 years ago before computers had anywhere near the speed or capacity of today.
While a well mastered 44.1/16 track can still sound pretty good the limited sample rate and bits used present challenges every time you listen, and is an unnecessary and archaic compromise. The 24bit 96kHz format would be a far better format to use (and would easily fit onto DVD disks) but the music industry has dug its heels in are steadfastly refuses to move forward.
There is a view that for HiFi purposes the coarseness of both timing and resolution causes some immediate problems that lead to more subtle long term issues, issues that have arguably caused a decline of both the Hifi and recording industry by a very subtle mechanism described below in the 16bit section.
CD sampling rate: 44.1kHz
This rate minimises storage while still giving a 20kHz audio bandwidth. The bandwidth is given just over a 10% guard band for filtering, ending up with 22.05kHz, which is then sampled according to the Nyquist theorem at 44.1kHz.
If you sample a signal above 22.05kHz you exceed the Nyquist limit and get aliasing or foldover and the frequency becomes stored as a lower (incorrect) one. So you must absolutely never hit 22.05kHz, and given the 96dB dynamic range of a 16bit CD you need to 'scrub off' 96dB between 20kHz and 22.05kHz - a 2.05kHz band. This is a very sharp filter and always a compromise, meaning that you always either get low levels of aliasing or a distortion of the 20kHz band, i.e. not HiFi. For recording however a higher frequency is generally used.
In practice the 44.1kHz sound is sweeter when upsampled (by a decent pro-audio DSP) to 88.2kHz, before being fed into a DAC. Possibly because it allows for simple, easy filtering and the sound has a far more analog ambience/feel to it. I can recommend doing that.
Despite being able to get around the filter issue there is still however an absolute data limit of around 22.05kHz, while most people can't hear anywhere near that some studies suggest that going higher does sound better to some people, so a 96kHz sampling rate would appear to be a far safer target for HiFi.
References:
CD 16bit linear and Inverse level distortion
In nature distortion rises with level, as with analog recording methods, but the opposite occurs with CDs - distortion rises as levels fall.
The digital integer scale is linear whereas the ear hears logarithmically, so the ideal format is floating point.
Using small integers (i.e. 16bit) to store audio levels causes distortion/quantisation issues at low levels. I.e. quiet stuff distorts more than louder signals because as the levels come down you start running out of bits, and therefore resolution.
Incidentally the issue of rising distortion with lower levels is also an issue with Class B audio amps due to their crossover distortion, which has led to discussion about the 'First Watt' - i.e. how well the amplifier deals with quiet and everyday levels. This also implies that playing a quiet CD into a class B amp is not a route to good sound.
In a perfect world we'd all be using 32bit float, but 24 bit audio has so many points (> 16 million) that even at low levels there are still enough to do the job. Unfortunately mastering to 16bits means that low level information is truncated and replaced with a dither noise dignal (see below). Even 8 bit audio (a CD at -48dB) can sound reasonable, but again the question for us here is - is it HiFi?
Just before a track is ready to be released the quality is truely HiFi, but we never get access to that - we'll get the processed form squeezed onto the 1979 standard instead. Ironically an average 1979 LP is still far better quality than an average modern pop CD.
CDs sound grainy as you run out of bits
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| Amplitude | Bits | Levels available
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| 0dB | 16 | 65536
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| -6dB | 15 | 32768
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| -12dB | 14 | 16384
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| -18dB | 13 | 8192
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| -24dB | 12 | 4096
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| -30dB | 11 | 2048
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| -36dB | 10 | 1024
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| -42dB | 9 | 512
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| -48dB | 8 | 256
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| -54dB | 7 | 128
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| -60dB | 6 | 64
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| -66dB | 5 | 32
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| -72dB | 4 | 16
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| -78dB | 3 | 8
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| -84dB | 2 | 4
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| -90dB | 1 | 2
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If you have a reasonably recorded track at -20dB RMS and a quiet part is -40dB down from that (e.g. parts of Floyd's The Wall), you are at a total of -60dB or a 64 level signal = 6 bits.
But is 6bit digital still HiFi?
To compute dB amplitude levels the simple formula: 20 x log(ratio) is used, so to see how loud a digital level of A is compared to B, you simply compute 20 x log(A÷B) as the dB change in audible level.
At the limit of a signal -90dB you have only got 1 bit of music, the effect is merely digital noise. Analog would probably have a much worse noise floor of -70dB at best, but the analog signal is gently superimposed upon the noise. Digital quantisation noise has a different and more onjectionable character however.
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16bits and the Loudness War
A nasty side effect of the linear 16bit format is therefore that it works best when recorded as loud as possible.
The most obvious subtle long term consequence of not having enough bits - and therefore having to record loud - is a subtle push toward the Loudness War. It's easy to blame CD clipping, mastering damage and the abandonment of HiFi on ignorance in the mastering engineers but there is a view that the limited 16bits of the CD is the subtle, chronic driver behind this trend, a driver that the undisciplined record industry has succumbed to as they're too dumb to simply cure the issue with 24 or 32bit releases.
Especially dumb as extra storage today is essentially free and they could resell much of their back catalogue as Hi-Res DVD.
The additional input of the Loudness War means that the final master isn't a simple 24bit → 16bit conversion either, but involves compression, limiting and clipping to mash down to the type of amateur hour efforts we're all now accustomed to suffer, which become the low grade core product of these multi million dollar businesses.
For many the enthusiasm in which they damage their own product is a total mystery, especially as the type of damage means that MP3s tend to sound exactly the same as the CDs, essentially rendering them a pointless purchase.
The resultant lack of dynamics tends toward an industry obsession with voice at the expense of the rest of the drama that used to add so much to a song, but are now thoroughly processed out before you get to listen.
Dither
Another 15dB or so of detail can be 'preserved' by using 'dither'.
Dither is a mastering operation, and is a form of (usually single bit) noise that improves the sound on continuous waveforms. However the effectiveness of dither over very short numbers of samples (A quiet rim shot for instance) is debatable. Note that all explanations will involve continuous tones rather than short dynamic images of waveforms, so it's really good it your music constists mainly of continuous tones.
Additionally dither is of course a source of low level noise.
With 24bit dither isn't really needed because there are 8 extra bits, so instead of having to hop from one value to another there are now extra 256 levels in between to choose from, so each and every sample has a far more accurate level.
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