ef37a wrote:The "wives tale" is that the size was insisted upon to get the playing time and the odd sampling rate for much the same reason (the disc HAD to fit a Euro car slot?) I mean, why are they not 48kHz?
Last question first, The reasons CDs (and the standard for other commercial music) use a 44.1kHz sample rate is entirely due to Mr Sony having a warehouse full of NTSC U-matic recorders. Prior to Sony's development of the CD format early digital audio experimenters were generally working with bespoke hardware recorders of various types and sample rates of 50 or 60kHz.
Of course, it was clear that the sample rate had to be sufficient to allow a 20kHz bandwidth, which meant a rate of greater than 40kHz, but higher sample rates were increasingly difficult to generate so Mr Sony wanted to keep it as close to 40kHz as he could. It was also clear that 14 bit wordlength was the minimum for an acceptable dynamic range in a consumer product, with 16 bit as the target for professional applications (at that time that was the absolute state of the art).
Mr Sony could build A-D and D-A converters well enough (for the time), but the question was what to store all this audio data on for the CD mastering houses and production plants? The answer was those Umatic video recorders, and consequently the Sony PCM1600 (and later the 1610 and 1630) digital audio boxes digitised audio and made it look like a black and white video signal to be recorded and replayed on/off Umatic machines. (They also did the same with the F1 and later PCM701/601/501 consumer digital encoders using betamax.)
Being in Japan, the Umatic video recorders worked with a 30 frame, 525 line (B&W) video format. Not all of the video lines are available in a rotary-head video recorder because of the head-switching, and they settled on using 490 lines for the digital audio. It was also essential that whole audio samples are stored per line (rather than splitting them over adjacent lines), and with 16-bits per sample the video resolution allowed three samples per line plus some basic error protection coding.
So, do the maths: 3 samples per line x 490 usable lines per picture frame x 30 frames per second = 44100 samples per second!
And that's why we're stuck with 44.1kHz as the basic audio sample rate.
Amusingly, when Mr Sony went on to develop a European PAL (635 line/25 frame) version of the hardware, the ended up using the same 3 sample per line structure, but 588 active lines, so the sums are 3 x 588 x 25... which also equals 44.1 samples per second!
Later, when it came to sound on digital video recorders it became necessary to ensure a whole number of audio samples per video frame (to allow easy editing). Although 44.1 obviously works with 25 fps PAL and 30fps B&W NTSC, it doesn't work with 29.97 fps colour NTSC or 24fps film.
The next lowest available number that does work is 48kHz, which works perfectly with PAL, B&W NTSC and film. It still doesn't work with 29.97 colour NTSC but nothing practical will anyway... but there is an easy bodge where five frames of 29.97 hold a whole number of audio samples. So 48kHz became the standard sample rate for all things video.
It would have been so much better had the original CD audio sample rate been selected as 60kHz (which would work for all video formats in the same way as 48k does), as then we would have had no need for double (96k) rates etc.. but such is life!
As for the physical size of the CD, the limiting factor was a disc that would fit in a standard ISO-sized car hi-fi unit. The alleged requirement to accommodate sufficient play time for a Beethoven symphony was obvious, but probably secondary, and there was some wriggle room anyway in the choice of the linear rotational speed and data coding format!