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As a practical matter, only SQ, QS and Dolby Surround have a lot of encoded content (SQ and QS in the form of Vinyl and some CD reissues, DS in the form of TV and movie soundtracks).

All the other matrix systems have very little content encoded in them and it may not be a good investment to develop (new) specific decoders for them.


Kirk Bayne
 
Midi you seem to be asking for a total redesign (with much added complexity) to the decoder. I don't think that would be practical. Adding a simple pre-synth circuit, even a passive one like you suggested would itself accomplish a lot.

I've long thought that the perfect way to decode asymmetrical encodes such as EV-4 could be done using two separate decoders one for the front the other for the rear. One unit would be tweaked for the front and the other for the rear. In reality QS or Involve decoding works well enough with EV-4 without going to that extreme. A double decoder decode might be an interesting experiment however.

I thought of that. Twice the cost. And it does not work for SQ back.

I was thinking of how the QS Variomatrix has two resistors that could be replaced by pots to vary the matrix parameters. And the original SQ chips use the same kinds of resistors. I didn't know there was a digimogrification needed to do that.

I have a decoder that uses a modified Metrotec decoder with the blends switched out and a Width pot (front blend) and a Depth pot (back blend). Works for all of the matrix systems on my big post (but no separation enhancement).

Another possibility: move the speakers. Hard to do with wall mounts.

Move the chair?
 
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Ye ha! Now i just need the gear to hook it up!
IMG_4718.jpeg
 
I find myself furiously in agreement with Barfle and AR Surround in that you must when listening if possible use stuff you are very familiar with (or at least include that in your selections) and if you can minimize any form of distortion well if its cost achievable then lets do it! This in fact has formed the basis of everything we have done in Involve. I can assure everyone that every chunk of software / hardware and new concepts have all been rigorously time synchronized A/B compared to see if we made things worse or better or neutral. Sometimes we did not hear any improvement but we left it in as we felt there was some theoretical advantage.

So when it comes down to the 16 bit/ 44kHz compared to 24 bit/ 96 kHz debate we naturally favored the higher resolution devices as it was cost effective, is better and it stops negative market connotations- hey I am honest.

I can honestly say I am obsessive in this area and from a young age. I have always ensured in the blind A/B 's that I or my test monkey had no idea which one it is , often I would rotate/ not label and confuse the A/B switch in doing these tests. In the test I did with the Philips CD 204 it was with music I was very familiar with. I listened to the top end, bottom end, in between, on quiet passage, transient stuff and all sorts of material and in the end I could not hear any difference to the high end $10K machine. I repeated this with 2 other victims with the same end result. Not saying that someone could not pick it and I confess I am not good at distortion perception (Bitch is great at it), however I am very perceptive to image matters.

I remember many years ago there was a hifi fad to mark the outside edge of CD's with a green ink marker, hifi nuts were convinced it made a considerable improvement, I tried it out on time sych A/ B and found exactly zero. I think in audio its a badge of honour to say you can hear the subtle difference and there is a feeling of failure if you do not and as such its easier to agree with the group view ........Hey I did a year of psychology before 2 engineering degrees as I was too young at 15 to enter the engineering course and I studied group personality, interesting subject! As for moron reviewers picking up subtle effect at bass frequencies on some CD player or magic cable- forget it they are wankers.

I remember years ago TDK did a challenge to pay a heap of money to anyone who could pick the difference between the original CD source and that recorded on a Nakamichi dragon cassette on Dolby C. Many people rolled up convinced they were taking the money home and the result was - no one got better than statistical chance!!!! Now remember the cassette on Dolby C would have had a SN ratio of 70 dB and distortion of say 1 %. I can confirm this myself as I became frustrated with clicks and pops on vinyl, plus the microphonics -yes the platter feedback is as much as - 15 dB down (I tested it). So I would upon getting a new record immediately enact electrical silence in the house turning off fridges etc, turn off speakers, use record clamp on a heavy platter Technics 120 turntable, SME ARM with an ADC ZLM cartridge and record it on my Nakamichi ZX7 with HIGHCOM noise reduction. I can assure you on A/ B testing I could not tell the difference to the Vinyl - with STAX headphones.

Similarly I remember the Australian skeptics society made a challenge to water diviners throughout Australia and the world to give $10,000 prize (back in the 80's I think) if anyone could detect which underground parallel water pipe out of 10 possibilities had water flowing in it. Lots of contestants rolled up most saying it would be easy and many had great reputations. The result was no one did better than random chance!! You must be so careful. I must confess I am a massive skeptic on many matters and I make myself unpopular on stuff like homeopathy, acupuncture, chiropractic and I just know many of the QQ members now hate me!

Vinyl sounds great and I would be the first to agree that it can be as good, if not better than CD in some instances but as mentioned previously it has lots of issues for example:

1 Tangential tracking error distortion (I remember doing the math and working out the theoretical best spot for my tone arm)
2 Self microphonics from stylus within the vinyl (say -20 db)
3 Microphonics from the speaker to platter - - 15dB
4 Cartridge distortion between 1 - 5% refer Cartridge tests

Yet 16 bit distortion at around 0.0015% dominates the above say 1-5% level???

How about speakers (They are by far the worst offender but not for the reasons you have been taught), they typically have distortion between 0.5 - 3%. One common factor I use a lot is psychoaccoustic masking where the quieter sound or noise is masked by the louder sound - for example on cassettes you hear the hiss on quiet passages but not on the loud bits. So human hearing must pick up this 0.0015% is a sea of other distortion of say up to 5% , that's interesting. Having said that I have heard subtle amplifier distortion- I suspect in a band or area different to where the speakers/ cartridge/ cassette were distorting.

Having said that I published elsewhere in QQ our ex Nakamichi dragon electrostatic actually achieve 0.06% distortion across the whole frequency range- but that's not the reason it sounded great.

While I am at it did you know that the whole - you cannot directionalise bass below 80- Hz is bullshit! We did comprehensive tests years ago and found that on band limited pink noise and music with ultra low distortion woofers subjects could directionise right down to 35 Hz. On pure sine wave tone it was different, people had no idea where the woofer was all the way up to 800 Hz. It turns out that we initially for say 15 seconds percieve where the woofer is but then the brain cuts in and fools you to believing the sound is integrated with the music!! So much for the Lucas/ Dolby lie.

Hey back to quad- did you know that when all 4 speakers are putting out sound sinchronised transient in similar (even different) frequency bands the listener cannot pick where the directions of sound is. It turns out the brain can only directionalise one sound at a time! Its one of the holes we crawl under and why discrete is overrated ....now I know you guys hate me.

Nigh Nigh time for me down under
Dear golden 4 ears

Well here ya go .....take the test Puny 8 bit vs 16 bit!!!!!!!!
Surely the crap 8 bit will stand out like dogs balls

The 16-bit v/s 8-bit Blind Listening Test push the ? on the test and it will play the tune and then you vote

Here is our results

The Bitch did well!!! He is 43 years old and is my distortion go to man
1665317247776.png


As for ol lead eared 64 year old me, a dismal failure:
1665317381839.png


oh dear.

Still think about 2^8 represents 1 part in 256 or a distortion of 0.39% or expressed as a signal to noise ratio of 20 log256=48db (similar to cassettes with no Dolby). If its playing loud music such as the test piece you will not hear the noise!

Lets take 12 bit represents 1 part in 4096 or a distortion of 0.024% or expressed as a signal to noise ratio of 20 log4096= 72 db (similar to the best vinyl records).

Lets take 16 bit represents 1 part in 65,563 or a distortion of 0.0015% or expressed as a signal to noise ratio of 20 log65,563= 96 db .

So 24 bit????????????????????????????????????????????????????
 
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Dear golden 4 ears

Well here ya go .....take the test Puny 8 bit vs 16 bit!!!!!!!!
Surely the crap 8 bit will stand out like dogs balls

The 16-bit v/s 8-bit Blind Listening Test push the ? on the test and it will play the tune and then you vote

Here is our results

The Bitch did well!!! He is 43 years old and is my distortion go to man
View attachment 84398

As for ol lead eared 64 year old me, a dismal failure:
View attachment 84399

oh dear.

Still think about 2^8 represents 1 part in 256 or a distortion of 0.39% or expressed as a signal to noise ratio of 20 log256=48db (similar to cassettes with no Dolby). If its playing loud music such as the test piece you will not hear the noise!

Lets take 12 bit represents 1 part in 4096 or a distortion of 0.024% or expressed as a signal to noise ratio of 20 log4096= 72 db (similar to the best vinyl records).

Lets take 16 bit represents 1 part in 65,563 or a distortion of 0.0015% or expressed as a signal to noise ratio of 20 log65,563= 96 db .

So 24 bit????????????????????????????????????????????????????

Bits be damned. $10 to the first one who can make me a version of New Miserable Experience that does not sound too compressed with an insanely hot high end. Recording and mastering is 99.9% of the battle.
 
Common you guys....... Take the test!!!!!! LV-B kicked my sad arse
Nah, why ya wanna torture me with reminders I'm old; besides it's using music with built-in instrument distortion yadda yadda and could be smashed mastered ta boot. Yes, like Johnny, you're rotten to the core @chucky3042, and I'm also a lazy bastard!!!
You sure LV-B didn't cheat, that just seems... WTF 🤯:unsure:
 
I suppose that the reason I have a been in my bonnet on this issue is that a I really hate audio bullshit and bollocks reviewers who have made a living out of false pretenses on their super hearing with crap like this idiot:

Best CD players 2022: CD players for every budget

lines like.....dynamic expressions, rhythmic ability, expressive punchy dynamics, powerful and articulate lows, clear elegant vocals, layered and articulate soundscape.....waffle waffle, lie.

We have a whole industry being reviewed by these frauds and an unquestioning public being sold on stuff with no additional gain. Recently on a facebook surround forum (I am not a facebook type really) someone asked me if the new SM 3 would sound any better that the old SM1.....I basically replied NUP. Having said that I really prefer the new ones with the metal box and KNOBS!!

Really spend your budget on where you will hear a difference......speakers, room and amplifiers (if you are running brutes like ribbons or electrostatics- soft clipping etc).

Here is an excellent article, please read! What you think you know about bit-depth is probably wrong

What you think you know about bit-depth is probably wrong​

In the modern age of audio, you can't move for mention of "Hi-Res" and 24 bit depth "Studio Quality" music, but does anyone understand what that actually means?
By


July 13, 2021


BIT-DEPTH-HERO.jpg


In the modern age of audio, you can’t move for mentions of “Hi-Res” and 24-bit “Studio Quality” music. If you haven’t spotted the trend in high-end smartphones—Sony’s LDAC Bluetooth codec—and streaming services like Qobuz, then you really need to start reading this site more.
The promise is simple—superior listening quality thanks to more data, aka bit depth. That’s 24 bits of digital ones and zeroes versus the puny 16-bit hangover from the CD era. Of course, you’ll have to pay extra for these higher quality products and services, but more bits are surely better right?
Bit-depth explained: difference between 16bit and 24bit waveform


“Low res” audio is often shown off as a staircase waveform. This is not how audio sampling works and isn’t what audio looks like coming out of a device.
Not necessarily. The need for higher and higher bit depths isn’t based on scientific reality, but rather on a twisting of the truth and exploiting a lack of consumer awareness about the science of sound. Ultimately, companies marketing 24-bit audio have far more to gain in profit than you do in superior playback quality.

Editor’s note: this article was updated on July 13, 2021, to update some technical wording and to add a contents menu.

Bit depth and sound quality: Stair-stepping isn’t a thing​

To suggest that 24-bit audio is a must-have, marketers (and many others who try to explain this topic) trot out the very familiar audio quality stairway to heaven. The 16-bit example always shows a bumpy, jagged reproduction of a sine-wave or other signal, while the 24-bit equivalent looks beautifully smooth and higher resolution. It’s a simple visual aid, but one that relies on the ignorance of the topic and the science to lead consumers to the wrong conclusions.
Before someone bites my head off, technically speaking these stair-step examples do somewhat accurately portray audio in the digital domain. However, a stem plot/lollipop chart is a more accurate graphic to visual audio sampling than these stair-steps. Think about it this way—a sample contains an amplitude at a very specific point in time, not an amplitude held for a specific length of time.
Quantization Stairs vs Stem Graphs


The use of stair graphs is deliberately misleading when stem charts provide a more accurate representation of digital audio. These two graphs plot the same data points but the stair plot appears much less accurate.
However, it’s correct that an analog to digital converter (ADC) has to fit an infinitely variable analog audio signal into a finite number of bits. A bit that falls between two levels has to be rounded to the closest approximation, which is known as quantization error or quantization noise. (Remember this, as we’ll come back to it.)

However, if you look at the audio output of any audio digital to analog converter (DAC) built this century, you won’t see any stair-steps. Not even if you output an 8-bit signal. So what gives?
10khz sine wave output capture with an oscilloscope


An 8-bit, 10kHz sine wave output captured from a low-cost Pixel 3a smartphone. We can see some noise but no noticeable stair-steps so often portrayed by audio companies.
First, what these stair-step diagrams describe, if we apply them to an audio output, is something called a zero-order-hold DAC. This is a very simple and cheap DAC technology where a signal is switched between various levels every new sample to give an output. This is not used in any professional or half-decent consumer audio products. You might find it in a $5 microcontroller, but certainly not anywhere else. Misrepresenting audio outputs in this way implies a distorted, inaccurate waveform, but this isn’t what you’re getting.
A chart depicts a DAC output signal.


In reality, a modern ∆Σ DAC output is an oversampled 1-bit PDM signal (right), rather than a zero-hold signal (left). The latter produces a lower noise analog output when filtered.
Audio-grade ADCs and DACs are predominantly based on delta-sigma (∆Σ) modulation. Components of this caliber include interpolation and oversampling, noise shaping, and filtering to smooth out and reduce noise. Delta-sigma DACs convert audio samples into a 1-bit stream (pulse-density modulation) with a very high sample rate. When filtered, this produces a smooth output signal with noise pushed well out of audible frequencies.

In a nutshell: modern DACs don’t output rough-looking jagged audio samples—they output a bit stream that is noise filtered into a very accurate, smooth output. This stair-stepping visualization is wrong because of something called “quantization noise.”


Understanding quantization noise​

In any finite system, rounding errors happen. It’s true that a 24 bit ADC or DAC will have a smaller rounding error than a 16-bit equivalent, but what does that actually mean? More importantly, what do we actually hear? Is it distortion or fuzz, are details lost forever?
It’s actually a little bit of both depending on whether you’re in the digital or analog realms. But the key concept to understanding both is getting to grips with noise floor, and how this improves as bit-depth increases. To demonstrate, let’s step back from 16 and 24 bits and look at very small bit-depth examples.
The difference between 16 and 24 bit depths is not the accuracy in the shape of a waveform, but the available limit before digital noise interferes with our signal.
There are quite a few things to check out in the example below, so first a quick explanation of what we’re looking at. We have our input (blue) and quantized (orange) waveforms in the top charts, with bit depths of 2, 4, and 8 bits. We’ve also added a small amount of noise to our signal to better simulate the real world. At the bottom, we have a graph of the quantization error or rounding noise, which is calculated by subtracting the quantized signal from the input signal.

Quantization noise example between 2 bits, 4 bits, and 8 bits.


Quantization noise increases the smaller the bit depth is, through rounding errors.
Increasing the bit depth clearly makes the quantized signal a better match for the input signal. However that’s not what’s important, observe the much larger error/noise signal for the lower bit depths. The quantized signal hasn’t removed data from our input, it’s actually added in that error signal. Additive Synthesis tells us that a signal can be reproduced by the sum of any other two signals, including out of phase signals that act as subtraction. That’s how noise cancellation works. So these rounding errors are introducing a new noise signal.
This isn’t just theoretical, you can actually hear more and more noise in lower bit-depth audio files. To understand why, examine what’s happening in the 2-bit example with very small signals, such as before 0.2 seconds. Click here for a zoomed-in graphic. Very small changes in the input signal produce big changes in the quantized version. This is the rounding error in action, which has the effect of amplifying small-signal noise. So once again, noise becomes louder as bit-depth decreases.
Quantization doesn't remove data from our input, it actually adds in a noisy error signal.
Think about this in reverse too: it’s not possible to capture a signal smaller than the size of the quantization step—ironically known as the least significant bit. Small signal changes have to jump up to the nearest quantization level. Larger bit depths have smaller quantization steps and thus smaller levels of noise amplification.

Most importantly though, note that the amplitude of quantization noise remains consistent, regardless of the amplitude of the input signals. This demonstrates that noise happens at all the different quantization levels, so there’s a consistent level of noise for any given bit-depth. Larger bit depths produce less noise. We should, therefore, think of the differences between 16 and 24 bit depths not as the accuracy in the shape of a waveform, but as the available limit before digital noise interferes with our signal.

Bit depth is all about noise​

A woman editing audio in a DAW monitors over headphones.

Kelly Sikkema We require a bit-depth with enough SNR to accommodate for our background noise to capture our audio as perfectly as it sounds in the real world.

Now that we are talking about bit depth in terms of noise, let’s go back to our above graphics one last time. Note how the 8-bit example looks like an almost perfect match for our noisy input signal. This is because its 8-bit resolution is actually sufficient to capture the level of the background noise. In other words: the quantization step size is smaller than the amplitude of the noise, or the signal-to-noise ratio (SNR) is better than the background noise level.
The equation 20log(2n), where n is the bit-depth, gives us the SNR. An 8-bit signal has an SNR of 48dB, 12 bits is 72dB, while 16-bit hits 96dB, and 24 bits a whopping 144dB. This is important because we now know that we only need a bit depth with enough SNR to accommodate the dynamic range between our background noise and the loudest signal we want to capture to reproduce audio as perfectly as it appears in the real world. It gets a little tricky moving from the relative scales of the digital realm to the sound pressure-based scales of the physical world, so we’ll try to keep it simple.

A photo of a stack of CDs on a wooden table - comparing cd quality bit-depth


CD-quality may be “only” 16 bit, but it’s overkill for quality.
Your ear has a sensitivity ranging from 0dB (silence) to about 120dB (painfully loud sound), and the theoretical ability (depending on a few factors) to discern volumes is just 1dB apart. So the dynamic range of your ear is about 120dB, or close to 20 bits.
However, you can’t hear all this at once, as the tympanic membrane, or eardrum, tightens to reduce the amount of volume actually reaching the inner ear in loud environments. You’re also not going to be listening to music anywhere near this loud, because you’ll go deaf. Furthermore, the environments you and I listen to music in are not as silent as healthy ears can hear. A well-treated recording studio may take us down to below 20dB for background noise, but listening in a bustling living room or on the bus will obviously worsen the conditions and reduce the usefulness of a high dynamic range.
The human ear has a huge dynamic range, but just not all at one time. Masking and our ear's own hearing protection reduces its effectiveness.
On top of all that: as loudness increases, higher frequency masking takes effect in your ear. At low volumes of 20 to 40dB, masking doesn’t occur except for sounds close in pitch. However, at 80dB sounds below 40dB will be masked, while at 100dB sound below 70dB are impossible to hear. The dynamic nature of the ear and listening material makes it hard to give a precise number, but the real dynamic range of your hearing is likely in the region of 70dB in an average environment, down to just 40dB in very loud environments. A bit depth of just 12 bits would probably have most people covered, so 16-bit CDs give us plenty of headroom.

Human Hearing Masking Patterns


hyperphysics High-frequency masking occurs at loud listening volumes, limiting our perception of quieter sounds.
Instruments and recording equipment introduce noise too (especially guitar amps), even in very quiet recording studios. There have also been a few studies into the dynamic range of different genres, including this one which shows a typical 60dB dynamic range. Unsurprisingly, genres with a greater affinity for quiet parts, such as choir, opera, and piano, showed maximum dynamic ranges around 70dB, while “louder” rock, pop, and rap genres tended towards 60dB and below. Ultimately, music is only produced and recorded with so much fidelity.
You might be familiar with the music industry “loudness wars“, which certainly defeats the purpose of today’s Hi-Res audio formats. Heavy use of compression (which boosts noise and attenuates peaks) reduces dynamic range. Modern music has considerably less dynamic range than albums from 30 years ago. Theoretically, modern music could be distributed at lower bit rates than old music. You can check out the dynamic range of many albums here.

16 bits is all you need​

This has been quite a journey, but hopefully, you’ve come away with a much more nuanced picture of bit depth, noise, and dynamic range, than those misleading stair-case examples you so often see.
Bit depth is all about noise, and the more bits of data you have to store audio, the less quantization noise will be introduced into your recording. By the same token, you’ll also be able to capture smaller signals more accurately, helping to drive the digital noise floor below the recording or listening environment. That’s all we need bit depth for. There’s no benefit in using huge bit depths for audio masters.

Close up of faders on a mixing console.

Alexey Ruban Due to the way noise gets summed during the mixing process, recording audio at 24 bits makes sense. It’s not necessary for the final stereo master.

Surprisingly, 12 bits is probably enough for a decent sounding music master and to cater to the dynamic range of most listening environments. However, digital audio transports more than just music, and examples like speech or environmental recordings for TV can make use of a wider dynamic range than most music does. Plus a little headroom for separation between loud and quiet never hurt anyone.
On balance, 16 bits (96dB of dynamic range or 120dB with dithering applied) accommodates a wide range of audio types, as well as the limits of human hearing and typical listening environments. The perceptual increases in 24-bit quality are highly debatable if not simply a placebo, as I hope I’ve demonstrated. Plus, the increase in file sizes and bandwidth makes them unnecessary. The type of compression used to shrink down the file size of your music library or stream has a much more noticeable impact on sound quality than whether it’s a 16 or 24-bit file.
 
I ran it out of my Android to RCA, right into my pre-amp. I bet the ability to hear 8 bit to 24 bit would be a much higher occurrence. 16 to 24....mmmmm....not so sure.

The difference I thought I could hear, was more of an overall...liveliness...noticed within the first seconds of play. Just more alive and full to my ears, when I could catch it.

I think it was probably all due to the Involve Master Amp, signature edition. 😆 Give it a whirl @J. PUPSTER!
 
I suppose that the reason I have a been in my bonnet on this issue is that a I really hate audio bullshit and bollocks reviewers who have made a living out of false pretenses on their super hearing with crap like this idiot:

Best CD players 2022: CD players for every budget

lines like.....dynamic expressions, rhythmic ability, expressive punchy dynamics, powerful and articulate lows, clear elegant vocals, layered and articulate soundscape.....waffle waffle, lie.

We have a whole industry being reviewed by these frauds and an unquestioning public being sold on stuff with no additional gain. Recently on a facebook surround forum (I am not a facebook type really) someone asked me if the new SM 3 would sound any better that the old SM1.....I basically replied NUP. Having said that I really prefer the new ones with the metal box and KNOBS!!

Really spend your budget on where you will hear a difference......speakers, room and amplifiers (if you are running brutes like ribbons or electrostatics- soft clipping etc).

Here is an excellent article, please read! What you think you know about bit-depth is probably wrong

What you think you know about bit-depth is probably wrong​

In the modern age of audio, you can't move for mention of "Hi-Res" and 24 bit depth "Studio Quality" music, but does anyone understand what that actually means?
By


July 13, 2021


BIT-DEPTH-HERO.jpg


In the modern age of audio, you can’t move for mentions of “Hi-Res” and 24-bit “Studio Quality” music. If you haven’t spotted the trend in high-end smartphones—Sony’s LDAC Bluetooth codec—and streaming services like Qobuz, then you really need to start reading this site more.
The promise is simple—superior listening quality thanks to more data, aka bit depth. That’s 24 bits of digital ones and zeroes versus the puny 16-bit hangover from the CD era. Of course, you’ll have to pay extra for these higher quality products and services, but more bits are surely better right?
Bit-depth explained: difference between 16bit and 24bit waveform


“Low res” audio is often shown off as a staircase waveform. This is not how audio sampling works and isn’t what audio looks like coming out of a device.
Not necessarily. The need for higher and higher bit depths isn’t based on scientific reality, but rather on a twisting of the truth and exploiting a lack of consumer awareness about the science of sound. Ultimately, companies marketing 24-bit audio have far more to gain in profit than you do in superior playback quality.

Editor’s note: this article was updated on July 13, 2021, to update some technical wording and to add a contents menu.

Bit depth and sound quality: Stair-stepping isn’t a thing​

To suggest that 24-bit audio is a must-have, marketers (and many others who try to explain this topic) trot out the very familiar audio quality stairway to heaven. The 16-bit example always shows a bumpy, jagged reproduction of a sine-wave or other signal, while the 24-bit equivalent looks beautifully smooth and higher resolution. It’s a simple visual aid, but one that relies on the ignorance of the topic and the science to lead consumers to the wrong conclusions.
Before someone bites my head off, technically speaking these stair-step examples do somewhat accurately portray audio in the digital domain. However, a stem plot/lollipop chart is a more accurate graphic to visual audio sampling than these stair-steps. Think about it this way—a sample contains an amplitude at a very specific point in time, not an amplitude held for a specific length of time.
Quantization Stairs vs Stem Graphs


The use of stair graphs is deliberately misleading when stem charts provide a more accurate representation of digital audio. These two graphs plot the same data points but the stair plot appears much less accurate.
However, it’s correct that an analog to digital converter (ADC) has to fit an infinitely variable analog audio signal into a finite number of bits. A bit that falls between two levels has to be rounded to the closest approximation, which is known as quantization error or quantization noise. (Remember this, as we’ll come back to it.)

However, if you look at the audio output of any audio digital to analog converter (DAC) built this century, you won’t see any stair-steps. Not even if you output an 8-bit signal. So what gives?
10khz sine wave output capture with an oscilloscope


An 8-bit, 10kHz sine wave output captured from a low-cost Pixel 3a smartphone. We can see some noise but no noticeable stair-steps so often portrayed by audio companies.
First, what these stair-step diagrams describe, if we apply them to an audio output, is something called a zero-order-hold DAC. This is a very simple and cheap DAC technology where a signal is switched between various levels every new sample to give an output. This is not used in any professional or half-decent consumer audio products. You might find it in a $5 microcontroller, but certainly not anywhere else. Misrepresenting audio outputs in this way implies a distorted, inaccurate waveform, but this isn’t what you’re getting.
A chart depicts a DAC output signal.


In reality, a modern ∆Σ DAC output is an oversampled 1-bit PDM signal (right), rather than a zero-hold signal (left). The latter produces a lower noise analog output when filtered.
Audio-grade ADCs and DACs are predominantly based on delta-sigma (∆Σ) modulation. Components of this caliber include interpolation and oversampling, noise shaping, and filtering to smooth out and reduce noise. Delta-sigma DACs convert audio samples into a 1-bit stream (pulse-density modulation) with a very high sample rate. When filtered, this produces a smooth output signal with noise pushed well out of audible frequencies.

In a nutshell: modern DACs don’t output rough-looking jagged audio samples—they output a bit stream that is noise filtered into a very accurate, smooth output. This stair-stepping visualization is wrong because of something called “quantization noise.”


Understanding quantization noise​

In any finite system, rounding errors happen. It’s true that a 24 bit ADC or DAC will have a smaller rounding error than a 16-bit equivalent, but what does that actually mean? More importantly, what do we actually hear? Is it distortion or fuzz, are details lost forever?
It’s actually a little bit of both depending on whether you’re in the digital or analog realms. But the key concept to understanding both is getting to grips with noise floor, and how this improves as bit-depth increases. To demonstrate, let’s step back from 16 and 24 bits and look at very small bit-depth examples.
The difference between 16 and 24 bit depths is not the accuracy in the shape of a waveform, but the available limit before digital noise interferes with our signal.
There are quite a few things to check out in the example below, so first a quick explanation of what we’re looking at. We have our input (blue) and quantized (orange) waveforms in the top charts, with bit depths of 2, 4, and 8 bits. We’ve also added a small amount of noise to our signal to better simulate the real world. At the bottom, we have a graph of the quantization error or rounding noise, which is calculated by subtracting the quantized signal from the input signal.

Quantization noise example between 2 bits, 4 bits, and 8 bits.


Quantization noise increases the smaller the bit depth is, through rounding errors.
Increasing the bit depth clearly makes the quantized signal a better match for the input signal. However that’s not what’s important, observe the much larger error/noise signal for the lower bit depths. The quantized signal hasn’t removed data from our input, it’s actually added in that error signal. Additive Synthesis tells us that a signal can be reproduced by the sum of any other two signals, including out of phase signals that act as subtraction. That’s how noise cancellation works. So these rounding errors are introducing a new noise signal.
This isn’t just theoretical, you can actually hear more and more noise in lower bit-depth audio files. To understand why, examine what’s happening in the 2-bit example with very small signals, such as before 0.2 seconds. Click here for a zoomed-in graphic. Very small changes in the input signal produce big changes in the quantized version. This is the rounding error in action, which has the effect of amplifying small-signal noise. So once again, noise becomes louder as bit-depth decreases.
Quantization doesn't remove data from our input, it actually adds in a noisy error signal.
Think about this in reverse too: it’s not possible to capture a signal smaller than the size of the quantization step—ironically known as the least significant bit. Small signal changes have to jump up to the nearest quantization level. Larger bit depths have smaller quantization steps and thus smaller levels of noise amplification.

Most importantly though, note that the amplitude of quantization noise remains consistent, regardless of the amplitude of the input signals. This demonstrates that noise happens at all the different quantization levels, so there’s a consistent level of noise for any given bit-depth. Larger bit depths produce less noise. We should, therefore, think of the differences between 16 and 24 bit depths not as the accuracy in the shape of a waveform, but as the available limit before digital noise interferes with our signal.

Bit depth is all about noise​

A woman editing audio in a DAW monitors over headphones.

Kelly Sikkema We require a bit-depth with enough SNR to accommodate for our background noise to capture our audio as perfectly as it sounds in the real world.

Now that we are talking about bit depth in terms of noise, let’s go back to our above graphics one last time. Note how the 8-bit example looks like an almost perfect match for our noisy input signal. This is because its 8-bit resolution is actually sufficient to capture the level of the background noise. In other words: the quantization step size is smaller than the amplitude of the noise, or the signal-to-noise ratio (SNR) is better than the background noise level.
The equation 20log(2n), where n is the bit-depth, gives us the SNR. An 8-bit signal has an SNR of 48dB, 12 bits is 72dB, while 16-bit hits 96dB, and 24 bits a whopping 144dB. This is important because we now know that we only need a bit depth with enough SNR to accommodate the dynamic range between our background noise and the loudest signal we want to capture to reproduce audio as perfectly as it appears in the real world. It gets a little tricky moving from the relative scales of the digital realm to the sound pressure-based scales of the physical world, so we’ll try to keep it simple.

A photo of a stack of CDs on a wooden table - comparing cd quality bit-depth


CD-quality may be “only” 16 bit, but it’s overkill for quality.
Your ear has a sensitivity ranging from 0dB (silence) to about 120dB (painfully loud sound), and the theoretical ability (depending on a few factors) to discern volumes is just 1dB apart. So the dynamic range of your ear is about 120dB, or close to 20 bits.
However, you can’t hear all this at once, as the tympanic membrane, or eardrum, tightens to reduce the amount of volume actually reaching the inner ear in loud environments. You’re also not going to be listening to music anywhere near this loud, because you’ll go deaf. Furthermore, the environments you and I listen to music in are not as silent as healthy ears can hear. A well-treated recording studio may take us down to below 20dB for background noise, but listening in a bustling living room or on the bus will obviously worsen the conditions and reduce the usefulness of a high dynamic range.
The human ear has a huge dynamic range, but just not all at one time. Masking and our ear's own hearing protection reduces its effectiveness.
On top of all that: as loudness increases, higher frequency masking takes effect in your ear. At low volumes of 20 to 40dB, masking doesn’t occur except for sounds close in pitch. However, at 80dB sounds below 40dB will be masked, while at 100dB sound below 70dB are impossible to hear. The dynamic nature of the ear and listening material makes it hard to give a precise number, but the real dynamic range of your hearing is likely in the region of 70dB in an average environment, down to just 40dB in very loud environments. A bit depth of just 12 bits would probably have most people covered, so 16-bit CDs give us plenty of headroom.

Human Hearing Masking Patterns


hyperphysics High-frequency masking occurs at loud listening volumes, limiting our perception of quieter sounds.
Instruments and recording equipment introduce noise too (especially guitar amps), even in very quiet recording studios. There have also been a few studies into the dynamic range of different genres, including this one which shows a typical 60dB dynamic range. Unsurprisingly, genres with a greater affinity for quiet parts, such as choir, opera, and piano, showed maximum dynamic ranges around 70dB, while “louder” rock, pop, and rap genres tended towards 60dB and below. Ultimately, music is only produced and recorded with so much fidelity.
You might be familiar with the music industry “loudness wars“, which certainly defeats the purpose of today’s Hi-Res audio formats. Heavy use of compression (which boosts noise and attenuates peaks) reduces dynamic range. Modern music has considerably less dynamic range than albums from 30 years ago. Theoretically, modern music could be distributed at lower bit rates than old music. You can check out the dynamic range of many albums here.

16 bits is all you need​

This has been quite a journey, but hopefully, you’ve come away with a much more nuanced picture of bit depth, noise, and dynamic range, than those misleading stair-case examples you so often see.
Bit depth is all about noise, and the more bits of data you have to store audio, the less quantization noise will be introduced into your recording. By the same token, you’ll also be able to capture smaller signals more accurately, helping to drive the digital noise floor below the recording or listening environment. That’s all we need bit depth for. There’s no benefit in using huge bit depths for audio masters.

Close up of faders on a mixing console.

Alexey Ruban Due to the way noise gets summed during the mixing process, recording audio at 24 bits makes sense. It’s not necessary for the final stereo master.

Surprisingly, 12 bits is probably enough for a decent sounding music master and to cater to the dynamic range of most listening environments. However, digital audio transports more than just music, and examples like speech or environmental recordings for TV can make use of a wider dynamic range than most music does. Plus a little headroom for separation between loud and quiet never hurt anyone.
On balance, 16 bits (96dB of dynamic range or 120dB with dithering applied) accommodates a wide range of audio types, as well as the limits of human hearing and typical listening environments. The perceptual increases in 24-bit quality are highly debatable if not simply a placebo, as I hope I’ve demonstrated. Plus, the increase in file sizes and bandwidth makes them unnecessary. The type of compression used to shrink down the file size of your music library or stream has a much more noticeable impact on sound quality than whether it’s a 16 or 24-bit file.

For what my perspective is worth, I find the whole 16 / 24 discussion very interesting from a technical standpoint, and the ability of a human's mechanical equipment (i.e. ears) and processor (i.e. brain) to identify differences between the two. And I find, what seems to be inborn for many of us QQ types, the drive for cleaner, higher quality music reproduction, quite extraordinary. But it seems to be for many of us, just knowing we have the highest quality is valued more than perhaps actually hearing the incremental improvements our investments, modifications, adjustments, etc. bring to our listening experience.

Over time, based on several accounts I've read over the years, our brains pretty much settle on the music quality it gets used to hearing. I interpret that as, after a certain quality level of music reproduction, the music creates the same emotional response, chemical and electrical, in our body and minds regardless of the quality (above a certain level).

Perhaps, despite the limits of our mechanical ability to discern the difference in sound quality (i.e. 16 vs. 24), our mind and body can in fact sense a difference, translating to a more intense emotional and physical response....which is what we are ultimately after.

Then again, maybe I smoked too much weed and rolled up too many bills back in the day. I spent a couple of decades actively searching the next level of an emotional high.
 
I do recall fooling with a Fairlight on many occasions in studios some (?) time back. Only later when tech devolved into bits discussion I was told that they couldn't really sound that good because they were only 8 bit and a low sampling rate. I thought then and now (mixed in recordings) that sounded great
 
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