What is behind a "warm" or "vinyl"sound?


I found an interesting article in The Saturday Toronto Star's entertainment section on the resurgence of vinyl.

What I found most interesting in this article was a description of why people describe vinyl as "warm". Peter J Moore, the famous producer/mastering engineer of the legendary one microphone recording of the Cowboy Junkies' Trinity Sessions recording says it all comes down to the fact that humans do not like square waves - ie. when you go from super quiet to super loud at no time at all. He gives the example that if someone was to slap two pieces of wood together right beside your ear would be about the only time one would feel a square wave - and that would make you jump right out of your skin! He says digital, particularly MP3s reproduce square waves like crazy, which triggers fear which also produces fatigue. He says if those same two pieces of wood were slapped together across the room, the square wave would be rounded off by the time the sound reached our ears. Turntables cannot reproduce square waves due to through time it takes for sound to get though the length of wire and the magnet that the wire is wrapped around in the cartridge. By the time the signal gets through that the sharpness, he ugliness, has been rounded and that, he says, is what people are talking about when they describe vinyl as "warm" sounding. Interesting!

I find there are a bunch of digital manufacturers, like Lumin, that are striving for a vinyl sound. I wonder if they are somehow rounding off the square waves in the digital signal to do so? If this is the case, "perfect" reproduction may NOT actually be beneficial to the sound...at least for someone who really wants a vinyl sound experience. Better may not actually be better when it comes to digital sound reproduction!
camb
Yes, that is a pretty good analogy!
Interesting take on 'warm'. But, that does not explain why digital into tube amps produce 'warm'. Any thoughts on this?
"Interesting take on 'warm'. But, that does not explain why digital into tube amps produce 'warm'. Any thoughts on this?"

TUbe amps, with their soft clipping nature and unique impedance characteristics among other things also tend to have a "rounding" effect compared to SS, much like vinyl versus digital.

THat makes tubes an attractive ingredient to add into many audio soups to help take an edge off to various degrees when needed.

The physics (heavily mass and inertia related) involved with a cart stylus and tonearm tracking a record is a big reason why vinyl sounds the way it does (rounded/smoother) compared to digital, where playback occurs exclusively in teh electronic domain with no physics of mass, inertia, etc. involved to inherently damp things from the start.
Sanity, cognitivity and normal desire to learn should definitely dominate "Someone said..." information to avoid this endless clownade and heresy.
MP3s reproduce square waves like crazy
Interesting perspective but there's one problem. There are digital sources that sound pleasingly naturally round and conversely there are some analog sources that can sound edgy, hard and sharpe (cartridge choice? ). There's definitely overlap involved with both approaches.
Charles,
I'm guessing digital done well in theory is better able to "pass a square wave" than vinyl, again due to the absence of natural physical damping factors like inertia, FWIW, similar to how wave bending (as opposed to pistonic motion solely as per most dynamic driver operations) in a pure Walsh driver has historically shown itself to lend itself well to the task, but just a guess.

Maybe AL or some of our other trusted EEs out there can shed some light on that one?
Waiting for Almarg to jump in and clarify all this. But I will add that it would be that humans tend to prefer even ordered distortion or low levels of odd harmonics as that would translate most closely to the natural, live acoustics we experience. Analog and tubes and well engineered solid state equipment can achieve these characteristics even if the measured results may indicate higher levels of measured distortion. Very intriguing to see how square waves could bring out the fear reaction in humans. I know that I easily prefer the natural sound of my turntable set up, especially vocals and stringed instruments, and bass. More three dimensionality and more density of image and specificity of the performers within the soundstage. And more relaxing and less fear.
Interesting indeed!
However, DSD is the closest I've ever heard to Vinyl.
DSD sounds warm, inviting, natural, easy flowing, you name it, just like a high-end Vinyl rig does.
Interestingly enough DSD is perfectly capable of square wave reproduction.

Go figure. :-)

Best,
Alex
"that does not explain why digital into tube amps produce 'warm'. Any thoughts on this?"

Most tube amps sound warm because their response rolls-off lower in frequency than SS amps. Most tube amps also have rather primitive power supplies for the plate voltages, not including fast-acting regulators or fast decoupling caps. These slower reacting power systems do not provide the power needed for high-frequency transients, so it softens the sound.

There are exceptions however. I have modded some tube equipment to fix these deficiencies and the top end softness disappears. They sound a lot more like SS, but with better midrange. The best of both worlds. Bass is always a problem with tube amps however. Its virtually impossible to get the really low impedance output required to control the bass of most speakers.

The mass of the needle assembly on a tonearm will also ultimately limit the reaction time and therefore the high-frequency dynamics. Even if the cartridge measures well beyond 20kHz using a steady-state waveform, it will fail to reproduce accurately a HF dynamic waveform, thus sounding softer.

Solid-state digital can also produce the dimensionality and smoothness of vinyl, but is requires several things:

1) very low jitter in the digital signal
2) lack of digital filtering in the DAC or minimize the effect
3) very linear I/V conversion in the DAC
4) excellent fast-reacting low-noise power supplies in the DAC

With 1-4, digital can actually beat vinyl. Makes sense because the physical limits of the cartridge are eliminated.

Steve N.
Empirical Audio
if anyone thinks that they're listening to these "square waves", it's absolutely wrong.
square waves are generated to divide ("slice") recorded continuous analogue signal onto samples that represented with bits as an amplitude and samples or "square waves" per second as sampling frequency.

the digital playback has dac that decodes these "square waves" back to the analogue signal and as Steve N mentioned, most of successful digital playback depends on it. it also depends on sample frequency and number of bits per amplitude. the larger sampling frequency and resolution, the lower losses of information during an analogue conversion. 1 5min song 36bits/192kHz format may occupy the whole CD that can fit over 1hr of 16/41kHz of digital music.

in neither of cases we do not listen to any square waves and more over we do not "round" them too. all we do we convert the recorded digital information into continuous analogue signal.
Here is what a square wave is and what used for:

Square Wave

Rise and fall time relate to attack and decay times, transient response, ringing and other aspects of accurate sound reproduction as well I am sure.
I think your brain just gets tired of converting endless 1's into sine waves and screams for mercy, aka listener fatigue.
Steve,
I agree with your list of the four requirements for excellent digital sound. Get these parameters right and you'll have very natural sound, if these aren't addressed properly the sound suffers. I/V conversion and power supply execution aren't fully appreciated for their major influence. Also less filtering is the right pathway toward a more natural presentation.
First, an ideal square wave does not exist in the real world, as it would have an infinitely fast transition time between its two voltage states. However, if those transition times (i.e., the risetime and falltime of the signal) are very small in comparison to the period of the square wave ("period" being the inverse of its "fundamental frequency," meaning the frequency of its lowest frequency component), then when a cycle (a single period) of that signal is graphically depicted (as on an oscilloscope) it will tend to pretty much *look* square.

Second, re:
Turntables cannot reproduce square waves due to through time it takes for sound to get though the length of wire and the magnet that the wire is wrapped around in the cartridge.
This is simply nonsense. So much so that I don't even know how to clarify it.

To the extent that accurate reproduction of what is on the recording is the goal, as opposed to compensation for the poor qualities that are present in many recordings, accurate reproduction of "square waves" whose "fundamental" (lowest) frequency component lies within the audible spectrum is desirable, at least as a goal. Accomplishing that requires bandwidth to be considerably greater than 20 kHz, to avoid phase shift issues and assure adequately fast risetimes and falltimes (bandwidth, i.e., the range of frequency response, is inversely related to risetime and falltime). And also to avoid causing overall system bandwidth to be too low when the bandwidth limitations of the various components in the system are combined. It also requires that overshoot and ringing be minimal. Many phono cartridges, especially Low Output Moving Coils, are easily capable of accomplishing all of that, certainly as well as it can be accomplished by redbook CD. In fact an issue that not uncommonly arises with LOMCs is a resonant peak (i.e., an over-emphasis) in frequency response in the ultrasonic region or even the lower RF region. Redbook CD, on the other hand, is theoretically limited to a bandwidth of 22.05 kHz (1/2 of the sample rate).

In other words, reproduction of "square waves" in digital can often be more "rounded" than in analog!

To the extent that vinyl might be inherently warmer and less fatiguing than digital (and I personally don't agree that that is necessarily the case, assuming the recordings being compared are similarly well engineered), the reasons have pretty much already been cited: Absence of jitter effects; how harmonic distortion may be distributed among its various frequency components, as Swanny alluded to; absence of overshoot, ringing, and phase shift anomalies that may result in part from filtering that occurs in digital playback equipment and digital recording equipment (although cartridges and phono stages can also certainly ring and overshoot to some extent); and design deficiencies and compromises that exist in a lot of digital equipment, such as in some of the ways Steve cited. Also, both record surface noise and low level noise generated in phono stages are perhaps euphonic in many cases, adding a sense of ambience and perhaps masking undesirable artifacts, and their absence in digital may sometimes be a negative in subjective terms.

Finally, if what the person quoted in the OP said were true, all it would take to make digital sound like analog would be implementation of a "rounding" (i.e., bandwidth limiting) function in the analog circuitry that follows D/A conversion, having some desired bandwidth characteristic. Implementing that electronically is trivial. It seems safe to assume, however, that making digital consistently sound like analog is not quite that simple.

Regards,
-- Al
Hi Al,
How ironic given the article author's premise, that in fact digital can round the square wave more than a cartridge in some cases. This is opposite of his explanation. Thanks for your input.
Charles,
In the digital domain, as long as one starts with high quality source material, almost anything can be made to sound like almost anything else relatively easily, if done well.

Christy Brinkley is a beautiful woman still, but does she really look like that magazine cover photo in person? Inquiring minds want to know....

Analog is more limited in this regard, though anything is still usually possible. Where there is a will (and a budget), there is usually a way. Just look at what Ray Harryhousen was able to achieve! Still beats a lot of SOTA CGI effects in effectiveness, if not technical execution.

This is an interesting question and I don't think there is a simple answer to it because nobody really knows how and why the ear hears what it does in reproduced music. I agree that, in general, vinyl and tubes do have a "warmer" sound compared to digital and solid state.

I listen mostly to classical music and to my ears, tubes do a better job of recreating the sound of a live performance in a concert hall, at least as I hear it. I don't necessarily agree that tubes sound warm because the high frequencies are rolled off. I have laboratory test equipment at home and I have measured the frequency response of my tube amp (ARC VS115) into my actual loudspeakers (SF Cremona M). The rolloff at 20 kHz is only -0.5 dB. My high frequency hearing (at age 62) cuts off sharply around 11-12 kHz, so it's really doubtful that rolloff is audible to my ears. My solid state amps, by comparison, are down about -0.2 dB at 20 kHz, yet they sound much brighter.

Digital does something to the sound of massed violins, a real acid test for sound reproduction, that can make them sound harsher and grittier than vinyl does. This is not an original observation, but on the other hand, vinyl captures the sound of the actual instrument more accurately as I hear it. However, in truth I do most of my listening to digital because of the convenience and the fact that LP surface noise becomes bothersome when you are used to the silent background of digital.
"in fact digital can round the square wave more than a cartridge in some cases"

This has to be some piss-poor digital design....

Steve N.
Empirical Audio
02-04-14: Audioengr
"in fact digital can round the square wave more than a cartridge in some cases"

This has to be some piss-poor digital design....
Steve, my comment which Charles referred to had to do with the fact that redbook CD cannot capture or reproduce frequency components in a signal that are greater than 22.05 kHz (half of the 44.1 kHz sampling rate), while many cartridges certainly can. The quality of the digital design has nothing to do with it.

As I'm sure you realize, elimination of high frequency components from a square wave signal corresponds to a slowing of its risetimes and falltimes.

Regards,
-- Al
A quick Google search shows some well documented cases and images of square wave tests with CD and the limitations there due to bandwidth, especially at higher frequencies.

Can't find much at all for a similar phono test. Stereophile apparently had a test record with a square wave test signal once. How does that measure.

Digital can do it better with greater bandwidth than redbook no doubt. How much does it matter practically though I wonder.

Show me the perfect square wave audio reproduction system and I am there, dude. At least as fast as material becomes available and I can afford it.

RTR tape maybe?

I know the best RTR puts CD and vinyl to shame. No doubt there!
"Digital does something to the sound of massed violins, a real acid test for sound reproduction, that can make them sound harsher and grittier than vinyl does. "

YEs, has a lot to do with jitter though I suspect.

The best massed violin CD reproduction I have heard came off DCS source equipment, which I consider to be pretty much SOTA.
the higher the frequency, the higher the error will be in digital playback.
in 44kHz sampling frequency 10kHz signal also have not too many samples for sufficient signal resolution when decoded from the DAC. It's only roughly 2 samples per half-wave and this is perfectly audible frequency alais from 22kHz that is not audible at all.
The massed strings off DCS source I heard on a standard issue Duetsche Gramophone CD was the closest to vinyl I have heard, I do not think I could have known it was CD in a blind test, whereas often not the case for me.

Massed violins=digital acid test, no doubt.

I've heard it done top notch though from CD, so I know it is possible.
Audioengr,

Can your reclocking device deliver massed strings as cleanly and grain-free as the best CD players out there? Or good vinyl?

If so, I might have to try one.
"10kHz signal also have not too many samples for sufficient signal resolution when decoded from the DAC. It's only roughly 2 samples per half-wave and this is perfectly audible frequency"

I'm having trouble getting my arms around this one?

Doesn't sound right, perhaps way off, based on Nyquist principle as I recall it but not sure. Better go break out my old digital audio book and study up....
Mapman --

Audioengr,

Can your reclocking device deliver massed strings as cleanly and grain-free as the best CD players out there? Or good vinyl?

If so, I might have to try one.

(I'm obviously not Audioengr, but here goes..)
A lot a digital aficionados may not know the true potential of LP-playback (myself included), but I'd wager the opposit - that analog freaks doesn't know the potential of digital playback either - is prevalent as well.
Why even begin to suddenly base sonic findings - or a principle belief, even - to the advantage of vinyl on a theoretical standing of a more ideally produced square wave due to better HF-extension? And CD-players being better a reproducing "massed strings" than PC-based playback? I mean, could it be the (nostalgic) love of a physical storage object spinning..? I left CD-players years ago (my last one being the Linn Mimik) to welcome PC-based playback for one reason only, even with an infectious PC-environment to deal with: better sound quality, which entailed - guess what? Analog virtues, to be exact; a more organic, resolved, fluid, and coherent presentation. Bye bye CD-players, and PC-based playback achieved the better sound at a much reduced price, which we were many individuals to conclude unequivocally and independently (I don't know why PC-based playback sounds better to our ears, but it does).
Since the introduction in my setup of the Audiophilleo2 + PurePower USB to S/PDIF converter, better DAC w/better power supply et al., many PC tweaks (many more to come) and better software playback (now JRiver MC19 + JPLAY 5.2), what was good has become indeed much better. It's truly amazing how much potential even 16-bit 44kHz source material holds, and that there is still more to have had in regards to sonic bliss with future tweaking.

When reading the above I get the slight sensation of people jumping , or even clinging to a theoretical standpoint that might partially (or not) explain why analog sounds better in some respects compared to digital, as if to tip the doubt into firm belief when supported theoretically. I guess the same could be said for the digital camp in other discussions, but I try to advocate listening without getting carried away too much by theory.
Where digital is as is I believe "warmer" could tilt towards too euphonic a character, but the lowering of jitter seems to bring with it an obvious lack of glare, better texture and clarity, a more organic feel, and sharper yet more pleasing delineations (contrary to edge enhancement), which does lead me to think of the sound, in a sense, as "warmer" and certainly more authentic.
"Digital does something to the sound of massed violins, a real acid test for sound reproduction, that can make them sound harsher and grittier than vinyl does."

This is true for the vast majority of digital equipment, but not all. With very low jitter and noise, it can sound smooth and silky, just like analog.

Steve N.
Empirical Audio
"Can your reclocking device deliver massed strings as cleanly and grain-free as the best CD players out there? Or good vinyl?"

The Synchro-Mesh can depending on the DAC, particularly if you add the Dynamo power supply and my own BNC-BNC coax cable with RCA adapters. This trifecta is world-class. SM resamples to 24/96.

dCS is good stuff for sure. I heard Vivaldi stacks in rooms on either side of me at RMAF last year. I prefer my Overdrive to it however.

Steve N.
Empirical Audio
Phus.

I haven't spun a CD in a couple years on my system. Music server + Squeezebox + DACs have replaced that.

But I use CD players as a reference in that they are typically associated with the format as well. Its more about the format and the technology options than CD players categorically.
"This is true for the vast majority of digital equipment, but not all. With very low jitter and noise, it can sound smooth and silky, just like analog."

Can you recommend a stand-alone CD player with these capabilities? I have over 1000 CD's in my music library and switching over to a different digital format won't help me get better sound from my CD's.
Mapman,
Digital audio is very similar to the radio transmission where you have to have a frequency generator of waves that propagate through the air.
Same thing you do with digital audio. You divide your signal using a sample generator, the generator of so long discussed "square waves" that also someone clames to listening to them too much to the point of fatigue. So called "square waves" can be analogued to the carying frequency that will be decoded with appropriate device and brought as an analogue audio signal.

These square waves divide an input analogue signal and cary digital information about our original analogue signal that had been transfered from microphones and instrument sound pickups.

The red book CD sampling frequency is 44.1kHz and it does not change. It's almost like carying frequency in radio transmission only it's carried internally through the digital processors to be decoded at the end just like in radio receiver.

It clearly means that 1kHz frequency will have roughly 22 samples in positive half-wave and 22 samples in negative half-wave of the sin function totalling roughly 44 samples. In analogy, if the radio carying frequency 2mHz, than 200Hz signal will have 20,000 waves of the carying frequency...

2 kHz will have only roughly with 11 in positive and negative half-waves respective totally roughly 22 samples. etc...etc...etc...

The above two paragraphs give the horizontal axis picture.
With vertical axis not everything is perfect either. For red book CD we have 16-bits resolution. It tells you that maximum amplitude is 16 bits and the whole dynamic range is divided by 16 portions of the vertical axis.

When the signal is loud, we get maximum resolution and when the signal is quiet we may only use 1...2 bits, so mastering of the digital CDs does involve great deal of compression in order to be able to hear quiet pieces with minimal distortion.

On the 'receiving' end we have DAC that reads either each bit or reads whole digital word which is in case of red book CD 16bit. Each bit will cary a very simple information in terms of either 1's or 0's. DAC determines the absolute value of each bit and reads it either as 1 or zero and so generates an analogue bit-portion of the signal of certain fixed magnitude.
Czar,

CD is based on principles of Nyquist sampling theory.

I have a lot of experience applying that in digital image processing and resampling. It works quite well in digital imaging. I ran a lot of test cases over the years on various forms of digital imagery that convinces me of that.

Granted, it leaves little room for error, but it works pretty well when done right, even if not 100% perfectly in all cases.

That jives with what my ears tell me these days. It's a fine line between good digital and poor, but luckily the technology used with the format has improved immensely over the years and most of the problems resolved. CDs still being as relevant as they are 30 years later and the lack of traction on any scale for high res audio formats these days despite the technology to enable it existing testifies to that.

It is true that CD redbook spec has a fixed limit for dynamic range and more there is clearly possible with more bits, but the dynamic range possible already well exceeds what most consider safe levels for listening, and I have heard good CD format playback sound indistinguishable from good vinyl to me even with massed orchestral violins(though not as often as I'd like), so there you go.
"It's almost like carrying frequency in radio transmission only it's carried internally through the digital processors to be decoded at the end just like in radio receiver. "

Not a good analogy. RF is always a modulated carrier frequency. Digital is encoded, not a modulated carrier. Most RF is really analog. Digital is discrete states and levels, not handled like analog.

Steve N. EE since 1976
Empirical Audio
Most of the SQ issues associated with digital have to do with poor digital filtering in the DAC, (whether in the CD player or other separate DAC), jitter and the sample-rate. For accurate dynamic playback at high-frequency 44.1kHz is insufficient. 88.2kHz and 96 kHz are sufficient. Poor digital filtering abounds unfortunately.

Even 44.1 can sound wonderful however, depending on how much HF information is in the track.

Steve N
Empirical Audio
I agree with the comments by Steve (Audioengr) and Mapman just above. One further point:
02-05-14: Czarivey
With vertical axis not everything is perfect either. For red book CD we have 16-bits resolution. It tells you that maximum amplitude is 16 bits and the whole dynamic range is divided by 16 portions of the vertical axis.
As you may realize, the vertical (amplitude) axis is divided into 65,535 portions (increments), not 16. For 16 bit data, there are 65,536 possible amplitude values (corresponding to 2 raised to the 16th power), which means that there are 65,536 - 1 = 65,535 increments.

To put things in perspective, it's perhaps worth noting that each of those increments is small enough to represent 0.0015 percent of the maximum possible ("full scale") amplitude.

Regards,
-- Al
Steve,

It's not only modulated carrier frequency, but also could be modulated phase or amplitude (AM signal is Amplitude Modulated)
Most RF is really analog
Why most? Square waves cannot propagate through the air unless there's again carrying frequency and in case of digital encoding phase modulation is used to define 1 or 0 in the air.
In all of the cases mentioned above and even more than above of this post we deal and deal and deal with carying frequency
Digital is discrete states and levels
It's not what Al said or even books. It will never be discrete or sudden. Before it forms "square wave" there's a process and certainly components that build it step by step so nothing is discrete for sure.

Mapman,

My objective was not to critisize digital playback vs. an analogue, but to express points where digital playback is inferior to analogue. There are bunch of points where analogue playback is inferior to digital as well...
Technology grows and there are far better formats than red book CD as well and post Y2K CDs in vast cases sound substantially better, but taken that and consumed, still I can spin records whole day while even after 2...3 perfectly mastered and recorded CDs I have to dial 'Analogue' function on my recently purchased DAC-preamp(hoped to boost my poor digital collection, but it's huh still poor). I'm also glad that my record shop visit more and more of teens and students who may or maynot have the idea why analogue is so cool, but they certainly hit on great past music of our analogue 60's, 70's and 80's :-).
If I were to think of the single most important thing standing in the way of getting better sound it's vibration, seismic type low frequency vibration, acoustic vibration and the vibration produced by the transformer and CD transport mechanism in the player that gets transmitted directly to the printed circuit boards.
Czarivey wrote,

"Technology grows and there are far better formats than red book CD as well and post Y2K CDs in vast cases sound substantially better, but taken that and consumed, still I can spin records whole day while even after 2...3 perfectly mastered and recorded CDs I have to dial 'Analogue' function on my recently purchased DAC-preamp(hoped to boost my poor digital collection, but it's huh still poor)."

The funny thing is that analog CDs, I.e. AAD, sound much more organic, open and correct than later ADD and DDD CDs. For all it's obvious potential for much higher dynamic range and signal to noise ratio than vinyl digital audio just doesn't sound like it's achieving it's potential.
"To put things in perspective, it's perhaps worth noting that each of those increments is small enough to represent 0.0015 percent of the maximum possible ("full scale") amplitude. "

Al, thanks for clarifying that! 2^16 is the correct number.

Back to the massed violin acid test, I am sure jitter (and digital filtering effects) are factors there to deliver smooth rather than coarser tones often heard, but I do wonder how much a few more than 16 bits of resolution per sample might help.

Still, I have heard it done as good as I have heard most anywhere with only 16 bits, so that tells me that it can be done if done right.

The guys who created Redbook CD format did a smashup job I would say by any fair measure. Not to say that better is always possible when it comes to things digital.
"Most RF is really analog
Why most?"

Because things like Bluetooth, which are RF are simply digital, not modulated

"Digital is discrete states and levels
It's not what Al said or even books."

Of course not, but discrete levels is how it is detected and treated. All electrical phenomena are analog.

"Before it forms "square wave" there's a process and certainly components that build it step by step so nothing is discrete for sure."

The serial signals are discrete and detected as such and the parallel digital words that are saved in registers are discrete. These discrete words are presented to the D/A circuit at discrete time intervals. Only then can the D/A output an analog waveform, which still needs filtering to resemble the original analog waveform.

The square-wave that we are talking about here is an analog waveform and treated as such by the analog circuits that follow. There is no switching and no discrete states as there is prior to the D/A conversion.

Steve N.
Empirical Audio
Its the discrete electronic equivalent of building with blocks that are all the same size and shape. Each block is conceptually a bit. Electronic signals, which are analog in nature, are "modulated" to form the electronic digital equivalent of blocks. To build the musical signal castle accurately, you need enough blocks and the ability to put them in place very accurately over a period of time.

CD Redbook defines how many blocks you need and have to work with based on the Nyquist principle.

Clearly, if the blocks you have are not assembled with great precision and accuracy, your castle may show defects.

If you follow the instructions, and do it right, you are in good shape!

Using more, smaller blocks alone may not get you any farther otherwise, and in fact will make things even harder to do right. Like doing a 5000 piece jigsaw puzzle compared to 1000 piece.
Steve,

It's not only modulated carrier frequency, but also could be modulated phase or amplitude (AM signal is Amplitude Modulated)
Most RF is really analog
Why most? Square waves cannot propagate through the air unless there's again carrying frequency and in case of digital encoding phase modulation is used to define 1 or 0 in the air.
In all of the cases mentioned above and even more than above of this post we deal and deal and deal with carying frequency
Digital is discrete states and levels
It's not what Al said or even books. It will never be discrete or sudden. Before it forms "square wave" there's a process and certainly components that build it step by step so nothing is discrete for sure.

Mapman,

My objective was not to critisize digital playback vs. an analogue, but to express points where digital playback is inferior to analogue. There are bunch of points where analogue playback is inferior to digital as well...
Technology grows and there are far better formats than red book CD as well and post Y2K CDs in vast cases sound substantially better, but taken that and consumed, still I can spin records whole day while even after 2...3 perfectly mastered and recorded CDs I have to dial 'Analogue' function on my recently purchased DAC-preamp(hoped to boost my poor digital collection, but it's huh still poor). I'm also glad that my record shop visit more and more of teens and students who may or maynot have the idea why analogue is so cool, but they certainly hit on great past music of our analogue 60's, 70's and 80's :-).
"The funny thing is that analog CDs, I.e. AAD, sound much more organic, open and correct than later ADD and DDD CDs."

This is primarily due to the mediocre DSP software that abounds. There is some good software out there though, such as Sonic Studio. Unfortunately not every recording studio uses it.

Steve N.
Empirical Audio
"This is primarily due to the mediocre DSP software that abounds."

Really? I thought it was due to the lack of tube electronics in the recording chain. ;-)