Under Design

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

with 4 comments

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 (usually 5-6 per millimeter) 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.

Therefore, we can guess that the record needle moves a maximum of a few hundred microinches 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.

Can I compare the maximum depth/minimum depth of a groove on a record? Sorry, no. But, I can’t imagine that the sample depth can be compared to 65,536 different values available on a 16-bit CD recording.

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!

Written by underdesign

2012/02/10 at 4:20pm

4 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

    2012/03/01 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

      2012/03/04 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

        2012/03/05 at 12:32am

  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

    2012/03/01 at 1:10am


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