
Explanation of 44.1 kHz CD sampling rate - jcr
http://www1.cs.columbia.edu/~hgs/audio/44.1.html
======
bartekko
This has already been posted to HN before, but its the best explanation of
digital audio I have seen:
[http://xiph.org/video/vid2.shtml](http://xiph.org/video/vid2.shtml)

~~~
masklinn
[http://xiph.org/video/](http://xiph.org/video/) is probably a better link,
the first episode has plenty of interesting and important stuff.

~~~
smackfu
Also on Youtube:
[https://www.youtube.com/watch?v=Ny7krNFAD1s&feature=kp](https://www.youtube.com/watch?v=Ny7krNFAD1s&feature=kp)

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jhallenworld
This confuses me because the vertical rate is not 60 Hz, it's 3579545 Hz /
(525/2 * 455/2) = 59.94 Hz. In other words it's odd that they would have
chosen to be compatible with black and white instead of color.. instead of
44.1 KHz, it would be 44.056 KHz.

Edit:

Well it turns out that 44.056 KHz was used for the "EIAJ digital-audio-on-
videotape standard"

[http://recordingtheworld.infopop.cc/eve/forums/a/tpc/f/22260...](http://recordingtheworld.infopop.cc/eve/forums/a/tpc/f/222604446/m/3656003463)

~~~
paulgerhardt
Keen.

Sony _was_ originally proposing 44.056 kHz (NTSC - popular in Japan) with 16
bits while Philips was pushing for 44.1 kHz (PAL - popular in Europe) with 14
bits. The two reconciled their differences at the 4th Red Book meeting in
1980[1]. Sony was further ahead in developing the CD players but Philips
supposedly was in the lead when it came to making the CD's[2]. Sony insisted
on 16 bit vs while Philips was pushing for 14 bit. As a compromise they may
have gone with the 44.1 kHz Philips was proposing and the 16 bit Sony was
proposing because it would be easier to remember. Posts [1] and [2] are in
direct conflict with each other on this point. There was further tension over
what size disc to use [2].

The CD was one meeting away from launching another format war in the spirit of
VHS vs Betamax or Blu-ray vs HD-DVD

Of course 44.056 kHz products did make it into the field for professional
audio engineers. Anecdotally this made for some trouble: [http://www.realhd-
audio.com/?p=2197](http://www.realhd-audio.com/?p=2197)

[1] [http://www.exp-math.uni-
essen.de/~immink/pdf/beethoven.htm](http://www.exp-math.uni-
essen.de/~immink/pdf/beethoven.htm) [2] [http://www.whathifi.com/blog/the-cd-
is-30-years-old-today](http://www.whathifi.com/blog/the-cd-is-30-years-old-
today)

~~~
cnvogel
Quoting your first link [[http://www.realhd-
audio.com/?p=2197](http://www.realhd-audio.com/?p=2197)]...

❝Of course, lots of CDs were released with the original 44.056 kHz rate simple
reclocked at 44.1 kHz. This resulted in a very slight speed increase AND a
pitch shift of less than a quartertone.❞

While technically true (less than a quartertone), it's much, much, much less
than a quartertone. It's 1.7cent (1.7 percent of a half-tone, or 1/30th of a
quartertone). If you accidentally mix up 48kHz and 44.1, it's a much more
noticable 1.5 half-tones. I doubt that this slight detuning is so blatantly
obvious that it "feaks out" even a very well trained and very hot tempered
classical violinist.

If you want to check the math: There are 12 semitones in an octave. One octave
doubles the frequency, so the frequency difference between two adjacent
semitones (e.g. from any key on your piano to the adjacent white _or_ black
key) is the twelfth root of two: ~1.0595. When tuning your guitar, your tuner
might display the deviation from the true tone in cents, that's 1% of the
interval between two halftones, or (python) math.pow(2,1.0/12.0e2) ->
1.0005777895065548.

Frequency ration between 44.1 and 44.056 kHz is 1.0009987.

~~~
grapeshot
Here's what happens when you do mix up 44.1 khz and 48 khz. Van Halen - Jump
(Greensboro): [http://youtu.be/Mjx_GjyXCs4](http://youtu.be/Mjx_GjyXCs4)

------
ar7hur
Also, the fact that 44,100 can be factored as 2^2 * 3^2 * 5^2 * 7^2 makes it
very efficient to do Fast Fourrier Transforms on moving windows. Which we do a
lot in Speech Recognition and DSP in general.

~~~
nullc
Actually 44.1kHz is unhelpful for that... a lot of infrastructure exists that
expects things to work on 10 and 20ms intervals (and multiples there-of), e.g.
the normal windows audio apis work in 10ms chunks.

10ms of 44.1kHz is 441 samples, which is odd and thus a not really fantastic
size for easily implemented factorizations.

Of course, if you can pick your own analysis interval you can pick some nice
power of two or other very smooth number. But thats true regardless of the
sampling rate.

~~~
ar7hur
Almost all ASR engines use 25ms windows, not 10ms (they typically overlap and
are processed every 10ms).

~~~
dbecker
25ms of 44.1kHz isn't even an integer. So the original argument is even less
compelling with 25ms windows than it was with 10ms windows.

------
abbeyj
[https://www.youtube.com/watch?v=GAE-c7aksxI](https://www.youtube.com/watch?v=GAE-c7aksxI)
shows what audio recorded this way looks like when you play it back as video.

I'm only guessing but it looks like 3 stereo samples per line plus some extra
data (ECC?) on the right. Its quite interesting to see how the pattern changes
when the music fades out (around 3:50, 9:20, and 13:25).

I wonder what kind of sound you could extract given only the low-quality
YouTube video as a source.

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csense
It seems strange to me that they would be re-purposing video tape for digital
audio, given that digital tape technology was used in computers since UNIVAC
in the 1950's [1].

[1]
[http://en.wikipedia.org/wiki/Tape_storage](http://en.wikipedia.org/wiki/Tape_storage)

~~~
Theodores
The key innovation is 'helical scan':

[http://en.wikipedia.org/wiki/Helical_scan](http://en.wikipedia.org/wiki/Helical_scan)

This came along for video applications. Up until then the idea of tapes for
audio or data was to put as many linear tracks on them as possible. With video
some new thinking was needed, hence the helical scan. As it turned out helical
scan was the future for data and audio storage too.

~~~
cjensen
Quad recording [1] preceded helical. In Quad, the mag stripes are across the
tape almost perpendicular to the tape's movement. The head spun at an _insane_
speed -- 14,400 RPM in open air. Helical was originally invented as a lower-
cost recorder. Once helical gained the ability to do slow-mo and still-frame,
Quad died.

[https://en.wikipedia.org/wiki/Quadruplex_videotape](https://en.wikipedia.org/wiki/Quadruplex_videotape)

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cardiffspaceman
In the Wikipedia it states that the CD's capacity target was to hold
Beethoven's Ninth Symphony on one CD. There was a tale that this and the
desire to fit a CD in a standard Japanese car stereo form factor determined
the sampling rate. Submitted for your amusement.

------
__david__
Related: Digital Cinema uses a 48Khz sample rate which gives exactly 2000
samples per frame, per channel. That makes it _very_ easy to sync the audio to
the film.

~~~
lcrs
At 25fps and 48Khz you rather neatly have 1920 samples per frame, which is
coincidentally the width of an HD picture. At least I think it's a kind of a
coincidence... I believe the number 1920 was derived from the 720 horizontal
pixels of Rec. 709, which doubled give a 1440 pixel 4:3 picture and hence a
1920 pixel 16:9 picture.

The 48Khz rate used by everything apart from CDs also came from video
standards according to [http://www.tvtechnology.com/opinions/0087/digital-
audio-samp...](http://www.tvtechnology.com/opinions/0087/digital-audio-sample-
rates-the--khz-question-/184354)

Here's some more about the number-theory used in digital video, from 1990
during the standardisation of HD:
[http://www.poynton.com/papers/SMPTE_90_Magic_Numbers.html](http://www.poynton.com/papers/SMPTE_90_Magic_Numbers.html)

------
linuxhansl
It's also convenient that highest frequencies a human ear can detect is about
20khz, so the sampling rate needs to be at least 40khz (see "Nyquist Rate")

------
asimpletune
How does this make it to the top page?

~~~
noonespecial
I can't say for anyone else, but for me, I was an AV nut in the old days. I
remember pulling apart an early Sony CD player in '89 or '90 and screwing each
part down on a piece of wood so I could reach everything and looking at every
single trace with my "new" old Phillips oscilloscope trying to understand the
magic.

These stories are like finally getting to see the cards from a game long over.
Pure gold to me. Upvoted.

