Under Design

…hates to admit he might have a blog.

The Math behind why Compact Disc’s sound better than Vinyl Records!

I’ve heard the vinyl purists who claim that vinyl records have better audio reproduction than Compact Discs. They rant and rave about bit’s and show choppy wave forms with smooth ‘analog’ overlays depicting the sheer obviousness of the ‘better’ audio signal. Bullshit! The top Calvin and Hobbes cartoon is your first hint at the real dilemma with vinyl records.

Vinyl has a Steadily Decreasing Sample Rate

Since the record plays at a steady speed, the audio fidelity (sample rate) starts to decrease from the very beginning! This is why albums tend to pack the ‘hit’ songs into the first 2 tracks of a side, in order to get the best clarity.

This is equivalent to the Sample Rate on a Compact Disc. A Compact Disc’s Sample Rate never changes, mostly due to the red book audio standard, and all audio files encoded onto a CD are expected to have 44100 samples per second (44.1kHz). Therefore, there is no compression, and a CD will hold a maximum of 79.8 minutes; the audio can be silence or punk music, and the CD spec doesn’t care.

Example of a 16-bit 44kHz Stereo Audio File as seen in an Audio Editor - each Dot on the line is a Sample Point.

Doing the Sample Rate Math…

I used basic high-school geometry. I measured a typical 12″ vinyl record’s grooves from the center of the record. The ‘start’ groove, on the outside of the record measured 5.75″ from the center. The ‘end’ groove measured at around 2.25″ from center. Calculating for circumference, then rotation speed, I came up with the final inches per second the needle covers at the beginning and end of the record, assuming a steady 33 revolutions per minute (rpm), or 45 rpm.

As you can see in the lower right hand corner of the above graphic, a 33rpm record spins at 19.8 inches per second at the outside of the record, then gradually slows to a meager 7.7 inches per second. Less than half the sample rate.

Even at 45 rpm, the starting speed is the best resolution available, at a speedy 27.09 inches per second, slowing to 10.59 inches per second in the center. Note that a 45rpm record would actually be producing a higher fidelity signal compared to a 33rpm, since it’s moving 136% faster at the outermost point. This also demonstrates the wider audio response available to vinyl spinning at 45rpm: much more bass.

Assuming that a vinyl record has the equivalent sample rate of a CD at it’s outermost point (ignoring rotational speed), we can extrapolate it’s sample rate at it’s innermost point as well. 33rpm records sample rate decreases to 17150 samples per second (17.1kHz), whereas 45rpm records sample rates decrease to 17240 samples per second (17.2kHz). Maybe (not) surprisingly, both speeds end with a nearly equivalent sample rate.

Below, a picture of the two sample rates side by side (in a single microsecond) to demonstrate the loss of detail:

Vinyl has a Tiny Sample Depth, too!

There is but a single spiral groove on each side of the record. Each groove cannot touch or get too close to it’s neighboring groove, otherwise the record will be unplayable. If you imagine a wobbly line as the groove, let this simple page of animated files show how the stereo signal is embedded into the groove of a record! This shows that the groove, in essence, stays steady in the middle of the needle, which has a maximum tip radius of .001 inches. Since the record groove is packed to achieve a 24-minute maximum playtime per side, the sample size (read: groove width) is also lowered, offering less volume of the audio stream.

Luckily, I ran across this fantastic Electron Microscope photo of the cross-cut detail of a vinyl record, taken just earlier this year in February 2012 (source unknown).

830x Close Up of 3 Grooves in a Typical Vinyl Record

Thankfully, in the full version of the photo, they included a helpful legend for scale. Now we can take some accurate measurements, and extrapolate the physical distance a needle moves on a vinyl record.

I’ve superimposed the legend on top of the art to deduce that the grooves in this record are between 120-160 Micrometres apart (a micrometre is a millionth of a meter, a thousandth of a millimeter). This is .12 millimeters, so we can expect to get 4-6 or so grooves per millimeter on a record. The grooves are also around 80 micrometers wide. This gives them a decent amount of headroom (i.e. distance between each groove so they can play lounder), but it’s not much.

I can also deduce the approximate separation (and maximum output) of stereo signals using this same method, and the depth of the groove in this particular image. We can also see the depth of the groove is between 35-40 Micrometres, and the difference in loudest and silence in around 25 Micrometres.

Therefore, we can guess that the record needle moves a maximum of a few dozen micrometres up and down in either 45 degree axis in order to create an audio wave. This slight tremor is amplified by the needle pickup, the turntable, and sometimes again by a RIAA pre-amplifier in order to deliver you this audio stream. Each amplification also reduces perceptual bit depth, although since this is an analog wave, it’s decay is measurable.

25-40 Micrometres vs. 65,536 digital values

Which has more nuance and detail? A wiggling groove moving a mere 25-40 thousands of a millimeter, or 65,536 different values available on a 16-bit CD recording?

Vinyl Needle SCU

Laundry List of other Vinyl Shortcomings

  • Records are large and heavy, making transporting them logistically difficult.
  • Mold can grow on vinyl and may permamently damage it and its sleeve, and can spread from record to record.
  • Surface noise, while often inaudible, will always be present and measurable, even on a brand new LP.
  • Certain parameters of vinyl recording and playback were never formally standardized, and vary considerably between records. Distortion from these effects is generally considered extremely audible and very difficult (if not impossible) to correct.
  • Any play of a record, even one, has the risk of permanently damaging the record. Repeated playback with an excessively worn or misaligned cartridge will cause permanent damage.
  • Cartridge stylii wear out over time (typically 200-1000 hours) and require periodic replacement.

Further Reading and Resources:

I always like to start at the ever-comprehensive Wikipedia article on the LP Record, but also check out this Audio Engineers advice in Mastering for Vinyl and the typical shortcomings of Vinyl playback.

Convert your Records to Compact Discs

Use my Vinyl to CD Conversion service – You’ll love the professional results, and only $12 for the basic transfer! Returned in a more convenient Compact Disc format, along with free MP3 versions for your media player! No record player needed!

Comments are closed

There’s far too much discussion going on in the comments of this article by analog purists, so I’m blocking future comments on this article. If you have something to say, or your own well-versed rebuttal, I’d suggest you get your own free WordPress Blog, and link back to this article with your detailed analysis of the many ways why I’m wrong. Otherwise, my soap box is too crowded for more naysayers.

Written by Under

February 10, 2012 at 4:20pm

20 Responses

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  1. Interesting article. Your basis is flawed on many points though (as I’m sure you’re well aware)

    Firstly, the initial sample rate on a record is likely to significantly higher than 44.1k, so whilst your point remains, the comparison is meaningless (especially in the context of implying that CD audio is outright better)

    Secondly, you poke a ‘guess’ at the bit rate, this is I’m afraid not admissible as “I’ve worked out the research, and I’ve done the math.”

    visinaut

    March 1, 2012 at 1:05am

    • Significantly higher? I doubt it. Even so, in order to give Vinyl a significant playtime, it’s expected to have half the fidelity on the inside. Not so with a CD, whether it’s track 1 or 89.

      I’ve deleted that boastful line, as you’re correct. It’s apple’s and oranges to say the least. How would you convert micrometers in needle travel to quantifiable sound spectrum? It boggles the mind.

      I’d love your expect advice if you know more. No one talks about breakthroughs in vinyl record production anymore… Thanks for taking time to comment!

      underdesign

      March 4, 2012 at 8:30pm

      • Hi again – having re-read my above comment let me first apologise for my carelessly off-hand phrasing; no rudeness was intended, I sometimes forget my facial expressions and tone of voice aren’t visible whilst typing :)

        On the “significantly higher” thing – this was definitely a guess on my part based solely on my (amateur, but extensive) experience with DSP. My other comment probably clarifies the intent a little more, but I’ll recap:

        I guess this is another apples and oranges situation, but the main point for me was that the /shape/ of higher frequency tones would be better preserved in vinyl (since they’re not all approaching square waves as as the frequency increases) which is the improvement you would get by upping the sample rate in a digital recording. So that translates (for me) as vinyl having a higher -equivalent- sample rate.

        This is – to me – a logical argument, but I’m in no way trying to sit on one side of the vinyl vs. digital argument as I think they’ve both got their benefits (a lot of which you’ve already mentioned) — however I am splashing in the wading pool of speculative science..

        The main thing here being that we tend to think of sample rate as “which frequencies *can* be represented” rather than “which frequencies *should* be represented”. Which makes it a poor metric for comparison with analog systems since they may (and often *do*) have a narrower frequency range, but what they represent in that range is far smoother in character (despite additional flaws).

        Hmm.. perhaps a metric to measure audio quality which is a per-frequency histogram of how well a sine wave can be reproduced at different frequencies?

        visinaut

        March 5, 2012 at 12:32am

    • wow…an actual civil discussion with opposing viewpoints that didn’t erupt into a total flame war. i’ll be taking a screen shot of this as proof that there is still hope for the prosperity of mankind…thank you both. PS. when’s the last time you took your record player with you in your pocket or jogging? quality is irrelevant if you can’t hear it past your front door….BOOM digital media FTW!!!

      Tim

      October 2, 2012 at 3:33pm

  2. Oh – and I forgot to mention:

    whilst it’s interesting that the sample rate of a record decreases with time, you forgot to mention that the bit-depth of digital audio decreases with frequency.

    At 44.1khz, the Nyquist frequency (highest frequency that can be represented) is 22050. This is generally dismissed as high enough above average hearing to be a logical cap. However, at the nyquist you can _only_represent_a_square_wave_.

    This means that as your signal increases in frequency you get more and more supersonic harmonics, which in turn may result in aliasing and phasing issues.

    Digital is great for bass, analog is great for treble.

    visinaut

    March 1, 2012 at 1:10am

    • Thank you for defending the record. I didn’t have the knowledge to do so, and I was hoping someone would step up and defend the LP.

      Tony

      January 6, 2013 at 6:18am

  3. According to Tim De Paravicini vinyl molecules are so tiny that you get impulses on the needle in the region of 500 mHz. This is a much much much higher sample frequency that your assumed 44.1kHz.

    Tim Burr

    January 9, 2013 at 2:28am

    • 500mHz is inaudible to every human being. 20hz – 20kHz is audible. You’re selling headroom that we don’t need or can’t use. Why would you need to capture (and replay) this inaudible information?

      Half the sample rate of 44.1kHz is 22 kHz, which is still 20kHz over the audible range of all humans. Making a 44.1 sample rate a smart decision based on Human standards. The shortcoming of being unable to reproduce super-high (inaudible) frequencies is actually a benefit.

      Under

      January 9, 2013 at 1:02pm

      • Really sounds like you’re confusing frequency with sample rate here.

        G-Reg

        July 23, 2013 at 1:58pm

      • Not at all – they are intrinsically linked on purpose. Higher frequencies cannot be represented by slower sample rates. 44.1Khz CD standard is twice the 22K audible human range for a reason.

        Under

        July 24, 2013 at 1:50pm

      • You are confusing sample rate and audio frequency… they are not the same. They are related in that the sample rate of a digital representation MUST be twice as much as the highest frequency you want to represent but they are not the same.

        Damien

        December 9, 2013 at 9:22am

  4. [...] We record a ton of vinyl for our value priced Vinyl to CD Conversion services, and in our years of flipping wax, we’ve noted some of the small subtle deficiencies of the vinyl medium as an audio playback format. Today, we’re going to highlight one of the negative side effects of Vinyl audio: Vinyl has a Steadily Decreasing Sample Rate. From our older article: The Math behind why Compact Disc’s sound better than Vinyl Records!: [...]

  5. Good information. Lucky me I came across your blog by accident (stumbleupon).

    I have bookmarked it for later!

    nyc hobbies

    April 7, 2013 at 11:41pm

  6. There is no argument here. Vinyl doesn’t have a sample rate. Digital audio is the only medium that has a sample rate. The rate of speed change within the grooves (between the outer and inner parts of modulation) are more accurately relatable to varying speeds on a tape machine (inches per second). There is no argument that a vinyl record is a better reproduction of audio than a normal CD. In fact, the CD redbook standard is of such low quality that most studios (even shitty home studios) will record at higher sample & bit depths, and only reduce it to 16/44.1 when it has to be on the CD.

    Carlos

    June 17, 2013 at 11:19am

    • We used the term ‘audio fidelity’ to make it clear we’re comparing apples to oranges. And I crossed out your boastful line, as this blog post is one.

      Under

      June 17, 2013 at 4:43pm

    • Just to be clear, studios record at a higher level of quality than CD audio because they’re going to be doing manipulation on that audio. Any time you manipulate a signal, quality suffers, so you make sure to start at something higher than what you want your final copy to be. This has nothing to do with CD audio being of insufficient quality.

      Raymond

      August 25, 2013 at 2:29pm

      • Fully agree. CD audio is an output format produced during the last stage of production, like masters for vinyl production.
        This has nothing to do with digital studio recording standards which starts with 176.4 kHz @ 24 bits as a minimum.

        Jan

        September 20, 2013 at 9:31am

  7. Just ran across this, very interesting, but one thing no one has mentioned, or pointed out. A record doesn’t have “grooves” in only has one groove, singular, per side, sure there are two grooves total so you could say grooves in that regard. But, my point is that you are talking about a single groove, start to end, in a spiral. So, even though your eye sees and your brain may think it’s grooves it’s only one single groove in a spiral per side. Sorry I have a pet peeve about people describing the groove on one side of a record as “grooves”.

    Groove not grooves

    November 15, 2013 at 11:20am

  8. Thanks, really Interesting article, great pictures and a great attempt at a comparison between two very different mediums. With two such differing technologies, I agree its difficult to create meaningful comparisons, with analogies that are applicable. I must say the “maths” behind your arguments is OK at times, but irrational at others and not a basis for proof of your argument. Some of your assumptions are lacking basis too. Just wanted to add some more empirical maths/logic to the original statements. No offence intended at all.

    Whilst your claims of quality comparisons may be true, I think the arguments could be better presented. OK that’s the positive and some negatives out of the way, let me see if I can provide some related but alternative explanations/views to the topics discussed and open up for some more feedback perhaps.

    Firstly the sample rate argument. Lets be clear, analog by its nature does not have a sampling rate. It has frequency response, and frequency response is the nearest equivalent in Analog to the concept of sample rate in digital. This should be the basis of the comparison. As others have stated, Audio CD’s frequency response is clearly limited by the Nyquist theory around sampling rate, yep max frequency available is 22Khz, half the sampling rate. As stated this is constant for all tracks on a CD which is a great thing. And unlike analog, it stays constant after multiple duplication phases, whereas analog typically degrades at the higher frequencies. .

    How high a frequency can vinyl recording and playback support? That would depend on so many factors. Firstly on the production end, there is the original recording equipment, mixing, mastering, the cutting lathe characteristics (note these typically have high block filters above around 50 kHz to aid in stability, so perhaps can perform well above 20 khz?), master duplicates, moulding of the vinyl, and the vinyl itself. Then on playback, there’s the stylus, cartridge, alignment, and finally the pre-amp. From there on, its that same path for a CD playback.

    ASSUMPTION #1: “Assuming that a vinyl record has the equivalent sample rate of a CD at it’s outermost point” – what on earth is the basis of this wild assumption? Yes I agree the slowing down of effective stylus speed on the innermost track may affect the frequency response available at the inner part of the record vs the outer, but this assumption needs some more basis. Suggestion: Firstly what’s the available max frequency response on the outer track of a record? As per above mentioned variables, it could be anything!

    “a 33rpm record spins at 19.8 inches per second at the outside of the record, then gradually slows to a meager 7.7 inches per second. Less than half the sample rate”
    And whats the reduction in available frequency response towards the inner track of the record? Again, some more info is needed here. Just because the inner track speed has less than half the grove cutting speed of the outer track, does that mean that only half the frequency response is available? I doubt it, it may depend on the cutting lathe performance, and how well your stylus can track etc. But half speed = half the frequency response is NOT a valid assumption and would need further investigation. Its not digital so we are not reading a reduced sample rate. If a 20 Khz signal can still be cut into vinyl at 7.7 inches per second, and also at 19.8 inches per second, then perhaps there’s no reduction at all?

    Perhaps 20 khz is available all the way to the inner groove? If so, perhaps something above 20 kHz may be available towards the outer tracks, but if so, the limiting factor then becomes the stylus and cartridge. Noting that most cartridges only go to about 20 Khz, perhaps this is the limiting factor across all tracks? But maybe not, need more info. Also at what groove speed are the cartridge frequency response stats stated for? Dunno.

    Secondly the Sample Depth Analysis:
    Lets also be very clear, there is no such thing as sample depth on an analog medium. The only equivalent parameter to digital sample depth with analog is dynamic range, which is absolutely dependant upon Signal to Noise ratio (SNR) of the analog signal. This is how they are related:

    Digital Bit Depth Digital SNRDynamic Range
    Analog SNR Dynamic Range

    Note also that reducing digital bit depth with digital audio has no effect except to increase the noise floor level and resultant SNR and dynamic range (so long as dithering is employed). Yes no other impact on resolution. There are plenty of articles on-line covering this.

    “Sample size (read: groove width) is also lowered, offering less volume of the audio stream”. This is a little misleading. Yes as groove width reduces, the output from the cartridge will decrease due to the smaller oscillations in the groove, but you can still have as high a volume as you like – you simply need to amplify the signal more. The limiting factor as you get a smaller analog source signal that needs to be amplified higher is the unwanted background noise which also gets amplified. As the signal gets smaller, the relative background noise remains the same, and the resulting SNR reduces, and therefor the dynamic range drops. Low level wanted signals get buried in the noise. The real comparison needs to be around available dynamic range.

    “Which has more nuance and detail? A wiggling groove moving a mere 25-40 thousands of a millimeter, or 65,536 different values available on a 16-bit CD recording?”

    You are comparing no of bit values with a groove width – yes apples and oranges. This is a bit like saying which car engine is more powerful, the Electronically fuel injected one, or the carburettor engine, with no other backup information such as engine type, fuel used etc….Also a stylus wiggling in a smoothly cut 25 to 40 thousanths of a millimeter groove still has almost infinite smoothness within that range, ie many more position options than the 65,536 digital sample, simply because its analog.
    Therefore your “Sample Depth” comparison should have really been a Dynamic Range comparison.

    There’s nothing to say you could not potentially (theoretically) achieve equal dynamic range (ie equivalent “bit depth” performance) from vinyl than you can on CD. Its a matter of minimising the analog SNR. This requires dropping the noise floor to extremely low levels. If we had perfectly smooth cuts in the vinyl, a perfectly aligned stylus, almost perfectly smooth bearings and drive on the turntable, low noise amplifer (even cooled) etc this could theoretically be possible. However in practice its never achieved. The best you can get from vinyl is about 50-60 dB dynamic range, compared with 93dB from CD audio. So yes, the equivalent bit depth performance for CD is better than vinyl, but its not about groove width alone, its all related to available dynamic range.

    I am by no means claiming Vinyl is a better medium that CD. I love it, but more for its humanistic elements rather than its technical performance. Just wanted to add some more realistic logic to the comparisons.

    Tony

    December 9, 2013 at 4:09am


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