S/N for a cassette is variously given as 50dB, 58dB or 67dB [1,2]. Bandwidth is given as 12kHz (standard), 16kH (medium Fi), 19kHz (HiFi) for different quality cassette systems [3]. Let's simplify by assuming the frequency cutoff is a brick wall and the S/N is constant across the band.
The maximum channel capacity for a cassette can be calculated using Shannon's Theorem [4]: C = B*log2(S/N+1)
Cheap and cheerful (S/N=50dB, B=12kHz): C= 199kbit/s
Mid range (S/N=58dB, B=16kHz): C= 297kbit/s
Hi Fi (S/N=67dB, B=19kHz): C= 422kbit/s
Modern coding (LPDC) can achieve within a fraction of a dB of the Shannon Bound, so those numbers will be close to what a state-of-the-art encoding could do with a cassette. (A new hobby for someone?)
My guess is the the Shannon based predictions are realistic, as they are lower than the same rates as achieved by specialised data recording systems. They are also a bit better than what a narrow band radio system can achieve, and a cassette will be a better channel than a typical radio channel.
There's also stereo to consider, right? So you could get up to 2X bandwidth. (Channel separation issues might mean less than 2X in practice, though.)
If you want to stretch the definition of "cassette", tapes are two-sided, and there were 4-track recorders that used all 4 tracks in one direction. They weren't anything too exotic. Musicians used them for cheap recordings for demos and such.
The maximum channel capacity for a cassette can be calculated using Shannon's Theorem [4]: C = B*log2(S/N+1)
Cheap and cheerful (S/N=50dB, B=12kHz): C= 199kbit/s
Mid range (S/N=58dB, B=16kHz): C= 297kbit/s
Hi Fi (S/N=67dB, B=19kHz): C= 422kbit/s
Modern coding (LPDC) can achieve within a fraction of a dB of the Shannon Bound, so those numbers will be close to what a state-of-the-art encoding could do with a cassette. (A new hobby for someone?)
[1] http://www.tapeheads.net/showthread.php?t=35390
[2] http://www.muzines.co.uk/articles/choosing-a-cassette-tape/1...
[3] https://arstechnica.com/civis/viewtopic.php?t=848978
[3] https://en.wikipedia.org/wiki/Shannon%E2%80%93Hartley_theore...
Edit: Here's a dose of reality from another forum:
https://dsp.stackexchange.com/questions/70700/why-can-so-lit...
My guess is the the Shannon based predictions are realistic, as they are lower than the same rates as achieved by specialised data recording systems. They are also a bit better than what a narrow band radio system can achieve, and a cassette will be a better channel than a typical radio channel.