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Direct Link To This Post Posted: October 24 2012 at 09:27
Originally posted by Dean Dean wrote:


Do you give up now?
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Direct Link To This Post Posted: October 24 2012 at 09:28
Originally posted by Dean Dean wrote:


 
 
 
 
 
Let's talk about efficiency of valve amplifiers. Geek
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Direct Link To This Post Posted: October 24 2012 at 09:30
Originally posted by Snow Dog Snow Dog wrote:

Originally posted by Dean Dean wrote:


Do you give up now?
I do.
 
For the first time in over fifteen years online I actually do give up.
 
 
I'm speechless.
 
 


Edited by Dean - October 24 2012 at 10:00
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Direct Link To This Post Posted: October 24 2012 at 09:31
Originally posted by Snow Dog Snow Dog wrote:

Originally posted by Dean Dean wrote:


 
 
 
 
 
Let's talk about efficiency of valve amplifiers. Geek
Oh for fCensoredksakes no... he couldn't possibly have anything to say I need to hear.
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Direct Link To This Post Posted: October 24 2012 at 09:33
Originally posted by Dean Dean wrote:

Originally posted by Snow Dog Snow Dog wrote:

Originally posted by Dean Dean wrote:


 
 
 
 
 
Let's talk about efficiency of valve amplifiers. Geek
Oh for fCensoredksakes no... he couldn't possibly have anything to say I need to hear.

You are absolutely right!Tongue
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Direct Link To This Post Posted: October 24 2012 at 12:14
   Good afternoon to all. Listen guys I found a really good article that I feel best explains both the importance of digital and analogue sound. This article does give great presidence to what we've been discussing about for the last few days.
Mainly, near the end of the article by B&W they talk about the emergence of FLAC by how the FLAC format can take 16bit recordings and upgrade it to 24bit. Personally, I find this a bit hard to digest but read on my friends and fellow proggers. Like to know what you think. That goes for all of you!


http://blog.bowers-wilkins.com/speakers/definitive-guides/the-definitive-guide-to-24-bit-flac/?hq_e=el&hq_m=2060885&hq_l=8&hq_v=6022c80984


🎃
Gimmie my headphones now!!! 🎧🤣
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Direct Link To This Post Posted: October 24 2012 at 12:41
Originally posted by progbethyname progbethyname wrote:

...by how the FLAC format can take 16bit recordings and upgrade it to 24bit. 
I don't think it makes sense. 
Who are you and who am I to say we know the reason why... (D. Gilmour)
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Direct Link To This Post Posted: October 24 2012 at 12:47
Dean,

You are giving up because you finally admitted that both the inward and outward conversions to and from the digital domain are inherently flawed.  This is something analog listeners have known because we hear it.  If 1's and 0's are so perfect, which I can accept to some degree as long as things stay in the inaudible digital domain, there is no problem and the science all works great... but once you bring in the necessity of having ot convert in and out.. you run into the same problems analog had before.  It's inescapable, and each machine has subjective characteristics that sound different and these differences cannot be accurate, because if they were simply accurate, there would be no deviation from one machine to the other.
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Direct Link To This Post Posted: October 24 2012 at 13:05
"consider a perfectly clean mirror". break it into a million pieces then glue it back together. then look at it. it is accurate. in all the places you see the reflection it shows an accurate refection. but; there are all the areas of the mirror (where you see little cracks filled with glue) without any information; so in the whole it does not look real. then consider a mirror that is dirty, there are not areas which are missing, but the slight amount of dirt is there. it's dirty but it is also complete. the reflection looks real.
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Direct Link To This Post Posted: October 24 2012 at 13:13
Thoughts from a mathematician...

The real issue with digital is the Red Book Standard and the use of sine x/x.
I'm sure you are aware the use of sine x/x means that all the calculations are truncated.
If they had used tan x for example the calculations would have yielded whole numbers and there would be no truncation errors.
My view is that digital is fundamentally flawed, not because of the concept, but due to the maths being incorrect and the way it has been implemented..
One of the biggest issues in developing digital product is that most audio engineers are engineers not mathematicians.

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Direct Link To This Post Posted: October 24 2012 at 13:25
More scientific talk:

With modern tape, 1/2" format, this means that you have the possibility of a 110 db dynamic range, if you include the range above 0 VU, a range that digital does not have.

This simple fact explains why an analog system of rather modest noise specs can have more low level detail than the best digital systems -*even though it appears to be noisier*. Add to that the fact that digital systems use less bits to resolve lower level signals (IOW, they have loose resolution as signal level decreases, which is why the normalization process is so important in the production of a CD) and you have a great part of why digital systems **as they are** can't keep up with analog.

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Direct Link To This Post Posted: October 24 2012 at 16:19
*sigh*
 
I am my own worse enemy Ouch
 
Originally posted by Surrealist Surrealist wrote:

Dean,

You are giving up because you finally admitted that both the inward and outward conversions to and from the digital domain are inherently flawed. This is something analog listeners have known because we hear it.  If 1's and 0's are so perfect, which I can accept to some degree as long as things stay in the inaudible digital domain, there is no problem and the science all works great... but once you bring in the necessity of having ot convert in and out.. you run into the same problems analog had before.  It's inescapable, and each machine has subjective characteristics that sound different and these differences cannot be accurate, because if they were simply accurate, there would be no deviation from one machine to the other.
Your explanation for what causes the differences between one system and another is fundamentally incorrect, therefore I cannot possibly agree with any conclusion you draw from it. Everything I have written in this thread corrects all the mistakes and fundamental errors you have made, the conclusions I arrived at are not the same as yours even though they appear to say the same thing. You will not understand the difference, and that's why I "give up" - I am not admitting anything, I have reached the point where "discussing" this with you is pointless because you never listen, never show any sign of understanding and you never answer direct questions.
 
 
 
 
I really don't like un-cited quotes, if you use someone elses words then cite them or give links, for example I now know that the person who wrote the following quote owns a $17,500 Playback Designs Music Playback System 5 CD/SACD player. Geek
Originally posted by Surrealist Surrealist wrote:

"consider a perfectly clean mirror". break it into a million pieces then glue it back together. then look at it. it is accurate. in all the places you see the reflection it shows an accurate refection. but; there are all the areas of the mirror (where you see little cracks filled with glue) without any information; so in the whole it does not look real. then consider a mirror that is dirty, there are not areas which are missing, but the slight amount of dirt is there. it's dirty but it is also complete. the reflection looks real.
This is a poor analogy and an unecessary one. The reason for making an analogy is to simplify the explanation of a hard to understand point - here there is no direct analogy to digitising - there are no "cracks filled with glue" in digital sampling, also there is no explanation of what this "dirty" is - if there is dirt then that has to be analogous to something in the real world, and since this is supposed to show the difference between analogue and digital, wouldn't that dirty mirror be dirty even if the mirror hadn't been broken - ie the analogue would be "dirty" too?
 
A mirror of 1 million pieces would be pretty good and give an acceptably accurate reflection for 99% of the uses a mirror has - my laptop screen has a resolution of one million twenty-four thousand pieces.
 
 
 
 
Originally posted by Surrealist Surrealist wrote:

Thoughts from a mathematician...
The real issue with digital is the Red Book Standard and the use of sine x/x.
I'm sure you are aware the use of sine x/x means that all the calculations are truncated.
If they had used tan x for example the calculations would have yielded whole numbers and there would be no truncation errors.
My view is that digital is fundamentally flawed, not because of the concept, but due to the maths being incorrect and the way it has been implemented..
One of the biggest issues in developing digital product is that most audio engineers are engineers not mathematicians.

I could ask you what this all means to you, but I don't believe that you would ever answer that question even if you knew the answer. Engineers have known about sin x over x roll-off on DAC converters for a very long time, long before the Red Book was produced, it causes problems as the sampled frequency approaches the Nyquist point, which by now everyone knows that for Red Book standard that is 22.05KHz. The solution is simple and trivial, and is called pre-equalisation or post-equalisation in DACs depending on where it is applied:
 
Figure 4. A pre-equalization digital filter is used to cancel the effect of sinc rolloff in a DAC (a). As an alternative, you can use a post-equalization analog filter for the same purpose (b).
 
and that results in a flat response from the ADC and the DAC upto the Nyquist point. The author of the uncited quote also states: "The oversampling reduces the sine x/x errors" - in another quote he also states "proprietary algorithms reverse out the sine x/x truncations errors as well as any other measureable system errors upstream".
 
The biggest problem with mathematicians is they are not engineers. But since neither of us are mathematicians perhaps you could help me out and tell me what the tan of 90° is? Do you think that could be a problem when putting theory into practice? Wink
 
 
 
Originally posted by Surrealist Surrealist wrote:

More scientific talk:

With modern tape, 1/2" format, this means that you have the possibility of a 110 db dynamic range, if you include the range above 0 VU, a range that digital does not have.

This simple fact explains why an analog system of rather modest noise specs can have more low level detail than the best digital systems -*even though it appears to be noisier*. Add to that the fact that digital systems use less bits to resolve lower level signals (IOW, they have loose resolution as signal level decreases, which is why the normalization process is so important in the production of a CD) and you have a great part of why digital systems **as they are** can't keep up with analog.

I have said before - "let's compare items made for the same purpose" No one outside a studio can use ½" tape format - you cannot buy pre-recorded albums in ½" tape anywhere. Even if you could record onto tape with a dynamic range of 110dB you cannot then transfer that to vinyl without compressing the whole album so it fits into the 60dB dynamic range of the best quality vinyl in the whole world ever.
 
The only place you can uses ½" tape format is in a studio and in a digital studio they uses 24-bit digitisers with a theoretical dynamic range of 144dB. The difference between 110dB and 144dB is 34dB and that's a voltage ratio of 50:1. Sure the digitiser will produce a low-resolution signals at very low signal levels, but these are signals so small that the tape cannot record them at all.
 
 


Edited by Dean - October 24 2012 at 18:23
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Direct Link To This Post Posted: October 24 2012 at 17:21
If it is true that there are inherent flaws in all mediums then digital and analog are no exception.And if history proves correct we must take into account that new technology and innovations are almost always beset on all sides by an initial and incessant resistance from the masses(remember,going to the moon was sci-fi before we actually went and did it).
My only critique at this point is not against digital per se but the digital download which I feel has done a great deal of harm to the quality of music.My hope is that someone will remedy this situation before any more harm is done.Musician Neil Young is actually working on such a technology:
Young is also personally spearheading the development of Pono, a revolutionary new audio music system presenting the highest digital resolution possible, the studio quality sound that artists and producers heard when they created their original recordings. Young wants consumers to be able to take full advantage of Pono's cloud-based libraries of recordings by their favorite artists and, with Pono, enjoy a convenient music listening experience that is superior in sound quality to anything ever presented.

We can vote against it or be advocates for it whatever the case the most important thing to remember is that music is a gift and blessing to be enjoyed by all...whatever formatWink

Read the full article on the new download technology:
http://www.audiostream.com/content/neil-youngs-pono-what-it


Edited by Lifeofprog - October 24 2012 at 17:55
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Direct Link To This Post Posted: October 24 2012 at 18:28
Give it up Dean. This guy will never listen. He is totally entrenched in his view. Whenever you stop posting he will consider it a victory. 
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Direct Link To This Post Posted: October 24 2012 at 23:19
Originally posted by Dean Dean wrote:

The biggest problem with mathematicians is they are not engineers. But since neither of us are mathematicians perhaps you could help me out and tell me what the tan of 90° is? Do you think that could be a problem when putting theory into practice? Wink
 


Speaking as a mathematician (though not an engineer), this made me chuckle internally.
When it comes to music, very little is objective.
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Direct Link To This Post Posted: October 25 2012 at 11:18
Dean,

To 99.9% of the people who will ever read this thread, no one is going to understand the science formulas.  What people do know is their ears.  Most people don't have a good enough system to tell the difference between hi fidelity sound and poor sound.  These days, the majority of people are listening to music on ipods which is a shame.  This thread is about the importance of analog sound in prog.  Being somewhat opened ended, I would include the recording process in that also. 

There really is no digital music.  One can argue CD, Redbook etc.. but we can't hear digits.  The fantasy land of digital only exists inside the computer represented by 1's and 0's.. but it is not that way coming in or leaving the conversions.

The digital concept is inherently flawed by this conversion process.  You have stated it in your own words that the analog circuitry needed for the conversion in and out of the digital domain has limits, it has "characteristics" which will always be subjective and as any logical person knows.. a digital representation cannot exceed the quality of the input source.

The reason things went digital in the first place is for convenience.  The rouge consumer doesn't want to clean and take care of their vinyl collection.  They didn't like 1/8th inch magnetic tape getting eaten up in their car stereo.  They can't play vinyl at the beach very easily.  Solid state amps the same thing.  They don't sound as good, but the user doesn't have to worry about changing tubes or dealing with selenium rectifiers.   But again, while convenient, it is not better.

Prog arrived in the analog age. The music was created and performed and recorded to be heard on tape and vinyl.  All the greatest pro offerings came from the golden age when musicians had to play better than they do now. 

The digital world of editing is nothing more than a black hole of dishonesty.  Anything can and is done.  One can alter the pitch, the metering, the tightness, and the end users now get homogenized sounding releases that are not representative of the artists abilities.   It's become more about the engineering post recording than playing in a natural human groove with all the flaws and characteristics of human musicians. 

Digital playback is hampered by the sound card conversion... both in and out.  Then the user has to deal with another their conversion from digits to sound waves often on very poor equipment such as ipods or car stereo CD players.

While this was good enough for Steve Jobs, it sure is not good enough for the true audiophile.  The dumbing down of humanity is a far greater concern that just digital music. 
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Direct Link To This Post Posted: October 25 2012 at 14:21
Originally posted by Lifeofprog Lifeofprog wrote:

If it is true that there are inherent flaws in all mediums then digital and analog are no exception.And if history proves correct we must take into account that new technology and innovations are almost always beset on all sides by an initial and incessant resistance from the masses(remember,going to the moon was sci-fi before we actually went and did it).
My only critique at this point is not against digital per se but the digital download which I feel has done a great deal of harm to the quality of music.My hope is that someone will remedy this situation before any more harm is done.Musician Neil Young is actually working on such a technology:
Young is also personally spearheading the development of Pono, a revolutionary new audio music system presenting the highest digital resolution possible, the studio quality sound that artists and producers heard when they created their original recordings. Young wants consumers to be able to take full advantage of Pono's cloud-based libraries of recordings by their favorite artists and, with Pono, enjoy a convenient music listening experience that is superior in sound quality to anything ever presented.

We can vote against it or be advocates for it whatever the case the most important thing to remember is that music is a gift and blessing to be enjoyed by all...whatever formatWink

Read the full article on the new download technology:
http://www.audiostream.com/content/neil-youngs-pono-what-it
 
I don't know much about this, other than articles like what you posted. What I understand is that Pono may be a proprietary program for specific files? So they will only play on a Pono.....That is fine.
 
To me the issue is the music file itself needs to be a high-resolution file that Neil Young is talking about using, to take advantage of this Pono high quality playback system.
To me it seems like a glorified SACD system...maybe better, but we are not sure yet. Will it be better than DVD-A/PCM audio at 24/96 or 24/192? Again we do not know (I assume) and that media already exists as downloads from HDTracks.com. But of course to take advantage of the higher resolution you need a player with a DAC that can play them at 24/96 or 24/192.
New DACs are coming out that will do even higher. NAD has a new DAC that will process 35bit info at a sampling rate up to 844kHz. I have not heard it yet, but of course the reviews are raving for the sound reproduction.
 
I still wonder about this Pono...is just a high end iPod to process expensive hi-rez files that still not many pop, rock music fans are buying?
A very large proportion of downloads are still of the lowend lossy quality MP3 at 192-320kbps.....From a portable perspective that is fine......In my house I want much better.
 
I am glad he is trying to do something, not sure it will catch on to anything significant thou
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Direct Link To This Post Posted: October 25 2012 at 16:24
Originally posted by Surrealist Surrealist wrote:

Dean,
I've no idea who you are so I'll call you Normon
Originally posted by Surrealist Surrealist wrote:

Dean,
Normon,
Originally posted by Surrealist Surrealist wrote:


To 99.9% of the people who will ever read this thread, no one is going to understand the science formulas.
I've only ever gave two formulae in this entire thread and both were high-school mathematics, not science. Also, this is technology and electronics engineering, it is not science. I have also avoided going into any depth in the explanations I've given that would require any specialist knowledge to understand. If you do not understand these simplified explanations I have given then you should not make dumb unqualified statements that require technical explanations to correct them, and you should not cut and paste pseudo-technical comments from other websites that contain erroneous and unqualified statements that also need correcting. I would much rather not post technical explanations at all, but when someone makes an unqualified statement about technology then I need to use technological explanations to answer them.
 
Your maths is wrong - if only one person (me) understands this then that does not equate to 99.9% because (unfortunately) 1000 people have not read this or ever will. BUT I would not underestimate the ability of people to understand technology if explained well - I may not be skilled enough to explain it well but I may have piqued enough curiosity in some people for them to find a better explanation (or even just look this stuff up on Wikipedia). My only intent is to prevent a few people swallowing the bad explanations offered by people who do not understand how any of this works.
Originally posted by Surrealist Surrealist wrote:

  What people do know is their ears. 
This is true - which is why a lot of people who care about music don't pick sides. If a format sounds good to them then what is the problem? You have decided that unless people discard all digital media and adopt your philosophy then their ears are not good enough to tell the difference. Some people here have said they prefer digital and I have committed the cardinal sin of not saying what I prefer, you have been overly critical and rude about people who do not see things your way even if they do have ears and know how to use them, as the following statement from you shows:
Originally posted by Surrealist Surrealist wrote:

Most people don't have a good enough system to tell the difference between hi fidelity sound and poor sound. 
Then what's the problem? If you have to have a good enough system to tell the difference then by that broken-logic it's better not to have a good enough system.
Originally posted by Surrealist Surrealist wrote:

These days, the majority of people are listening to music on ipods which is a shame. 
This is a Prog site, we are not in a majority of anything. Generalisations don't work here - I think you'll find that more people here own vinyl than on many other music-based websites. What you won't find here is an abundance of audiophilists - we have people who like their hi-fi, but they like listening to music much much more.
Originally posted by Surrealist Surrealist wrote:

This thread is about the importance of analog sound in prog.  Being somewhat opened ended, I would include the recording process in that also. 
It wasn't open ended if you read the OP, but as the person who started this thread is long gone. I have no issue with including the recording process if we compare like with like - you'd be more than a little upset if I kept comparing 24-bit studio gear with Edison's wax cylinder phonograph wouldn't you?
Originally posted by Surrealist Surrealist wrote:


There really is no digital music.  One can argue CD, Redbook etc.. but we can't hear digits.  The fantasy land of digital only exists inside the computer represented by 1's and 0's.. but it is not that way coming in or leaving the conversions.
That was a really specious argument:
- we cannot hear scratches cut into a plastic surface; the fantasy land of grooves on plastic only exist on an LP.. but it is not that way coming in or leaving the conversions.
- we cannot hear changes in magentic flux on a strip of plastic covered in a thin layer of rust; the fantasy land of magentic flux on plastic strip only exist on a magentic tape.. but it is not that way coming in or leaving the conversions.
 
If you can hear either of these analogue "fantasy lands" without a converter then throw out your precision turntables, ¼" reel-to-reel tape decks, antique amplifiers, expensive loudspeakers and all the paraphernalia that goes with it because you evidently don't need them.
Originally posted by Surrealist Surrealist wrote:


The digital concept is inherently flawed by this conversion process. 
Every conversion process is inherently flawed
- converting sound-waves into electrical signals in a microphone is inherently flawed.
- cutting grooves in plastic is inherently flawed, using a diamond stylus and an electromagnet to convert those to electrical signals is inherently flawed.
- changing the polarity of rust particles on a tape is inherently flawed, converting that pattern of magnetic polarity variations back into electrical signals is inherently flawed.
- converting electrical signals into sound waves in a loudspeaker is inherently flawed.
 
 
Originally posted by Surrealist Surrealist wrote:


You have stated it in your own words that the analog circuitry needed for the conversion in and out of the digital domain has limits, it has "characteristics" which will always be subjective and as any logical person knows.. a digital representation cannot exceed the quality of the input source.
In the example I gave the point I was making is that this analogue circuitry is the same kind of analogue circuitry that is used in a tape deck or a phono preamplifier. The effect of those analogue circuits is similar in all cases - it is minimal and subtle.
 
The difference, and it is a humongous difference, is that the digital domain does not have a transfer characteristic whereas the tape and the vinyl processes do have  transfer characteristics, so when those transfer characteristics are added to the characteristics of those electronic analogue circuits it gives:
 
MX80:
 
Starmax ADC (oh, look it's not perfectly flat - there's the analogue circuitry characteristic in all its horrible glory):
 
And if you cannot see that the tape deck has a bigger variation in the characteristic than the ADC then you should have gone to SpecSavers.
 
And if your ears tell you that the top curve sounds better to your ears then it's not because the graph is lying, or because the "science" cannot explain it, it is simple because you like the sound that shape makes better than the sound a flat response makes. And whether you like it or not, that top curve repressents distortion -  not harsh and nasty distortion, but nice and smooth distortion. This isn't rocket science. Mate.
Originally posted by Surrealist Surrealist wrote:


The reason things went digital in the first place is for convenience. 
No it wasn't. We went cassette for convenience, we went to CD for better quality than cassette. Like it or not, things went digital because the quality was better.
Originally posted by Surrealist Surrealist wrote:

The rouge consumer doesn't want to clean and take care of their vinyl collection.  They didn't like 1/8th inch magnetic tape getting eaten up in their car stereo.  They can't play vinyl at the beach very easily.  Solid state amps the same thing.  They don't sound as good, but the user doesn't have to worry about changing tubes or dealing with selenium rectifiers.   But again, while convenient, it is not better.
Back in the day people only changed their valves when the things died - the valve-swapping game is a recent pasttime to amuse audiophiles. In the early 70s I was buying old valve amps from thrift shops and church bazaars for a few pennies each - a quick valve change or simple power-supply fix and they were back working again. Most people, with their modest hi-fi setups and Wharfedale Denton speakers, prefered solid-state not because it was convenient, (and far more reliable), but because they liked how it sounded. If it was purely a sound thing then the use and sale of valve amplifiers would not have gone into such a huge decline as it did - they would have held-on in the mid-range market for people who like hi-fi but cannot be bothered by all the audiophilist kerfuffle.
 
There is another obvious reason why solid-state was attractive to the average consumer - stereo. Back in the 60s most albums sold were mono and most valve-based "gramophones" were mono - solid-state provided a cost-effective solution, all packaged in a sleek brushed aluminium case that looked modern and sounded great.
Originally posted by Surrealist Surrealist wrote:


Prog arrived in the analog age. The music was created and performed and recorded to be heard on tape and vinyl.  All the greatest pro offerings came from the golden age when musicians had to play better than they do now. 
That's a terrible argument that has nothing to do with the technology used or playing ability of the musicians.
Originally posted by Surrealist Surrealist wrote:


The digital world of editing is nothing more than a black hole of dishonesty.  Anything can and is done.  One can alter the pitch, the metering, the tightness, and the end users now get homogenized sounding releases that are not representative of the artists abilities.   It's become more about the engineering post recording than playing in a natural human groove with all the flaws and characteristics of human musicians. 
That is a terrible argument, an insulting one and a dishonest one. Just because something is possible it does not mean that it must be used and just because it can be done does not mean it is being done. And things were not perfect back then, in the old days, as the production on the early Genesis albums shows, musicians were no more capable than they are now, they made mistakes.
As Steve Hackett said on UK national television yesterday (talking about re-recording old Genesis tunes) - "it's a chance to get my guitar parts in tune and in time simultaneously .... [back then] they were rushed between tours and gigs, um, just a brush with the studio."
Originally posted by Surrealist Surrealist wrote:


Digital playback is hampered by the sound card conversion... both in and out.  Then the user has to deal with another their conversion from digits to sound waves often on very poor equipment such as ipods or car stereo CD players.
Tape is hampered by the conversion to and from magnetic patterns on a thin tape, vinyl is hampered by the conversion from wiggly scratches on a plastic platter into electrical signals. 
 
iPods and car CD players, so much worse than Edison's wax-cylinder, those horrible little plastic things don't even have clockwork motors or brass ear trumpets - how do those poor fools bear to listen to them?
Originally posted by Surrealist Surrealist wrote:


While this was good enough for Steve Jobs, it sure is not good enough for the true audiophile.  The dumbing down of humanity is a far greater concern that just digital music. 
What the hell does Steve Jobs have to do with this?


Edited by Dean - October 25 2012 at 16:53
What?
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Direct Link To This Post Posted: October 25 2012 at 16:40
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Direct Link To This Post Posted: October 25 2012 at 20:37
The simple answer is, that, for music recorded before 1980, you are missing a lot if you only have C..D.
16 bit 44.1 digital is capable of 65,000 variations of level ( the human ear is capable of much more & can detect differences as small as 6ns). 

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