> I had heard that tape is still the best medium for storing large amounts of data.

well, "best" is always a reduction to a single set of optimization parameters (e.g. cost per bit, durability, ...) and isn't ever "universally true".

I can see, for example, that "large" is already a relative term, and for a small office, the optimum solution for backing up "large" amounts of data is a simple hard drive, or a hard drive array.

For a company, backup tapes might be better, depending on how often they need their data back. (Tapes are inherently pretty slow and can't be accessed at "random" points)

> So I figured I can store a relatively large amount of data on a cassette tape. 

Uh, you might be thinking of a Music Casette, right? Although that's magnetic tape, too, it's definitely not the same tape your first sentence referred to: It's meant to store an analog audio signal with low audible distortion for playback in a least-cost cassette player, not for digital data with low probability of bit error in a computer system.

Also, Music Cassettes are a technology from 1963 (small updates afterwards). Trying to use them for the amounts of data modern computers (even arduinos) deal with sounds like you're complaining your ox cart doesn't do 100 km/h on the autobahn.

> But after reading up about it for a bit it turns out that they can store very small amounts of data. With baud rates varying between 300 to 2400 something between ~200KB to ~1.5MB can be stored on a 90 minute (2x45min) standard cassette tape.

Well, so that's a lot of data for when music-cassette-style things were last used with computers (the 1980s). 

Also, where do these data rates drop from? That sounds like you're basing your analysis on 1980's technology. 

>These guys can store 90 minutes of audio. Even if we assume the analog audio quality on them was equivalent of 32Kbps that's about 21MB of data.

32 kb/s of what, exactly? If I play an [Opus Voice](https://opus-codec.org/static/examples/samples/speech_32kbps_fb.wav), [Opus Music](http://marcus.hostalia.de/opus_music_32kbps.opus) or MPEG 4 AAC-HE file with a target bitrate of 32 kb/s next to the average audio cassette, I'm not sure the cassette will stand much of a chance, unless you want the "warm audio distortion" that casettes bring – but that's not anything you want to transport digital data.

You must be very careful here, because audio cassette formulations are optimized for [specific audio properties](https://en.wikipedia.org/wiki/Compact_Cassette_tape_types_and_formulations#Electroacoustic_properties). That means your "perceptive" quality has little to do with the "digital data capacity".

> I have a hard time believing what I listened to was 300bps quality audio.

again, you're comparing apples to oranges.  Just because *someone* 40 to 50 years ago wrote a 300 bits per second modem that could reconstruct binary data from audio cassette-stored analog signals, doesn't mean 300 bps is the capacity of the music cassette channel.

That's like saying "my Yorkshire Terrier can run 12 km/h on this racetrack, therefore I can't believe you can't have Formula 1 cars doing 350 km/h on it".

>  I read about the Kansas City standard and I can't understand why the maximum frequency they're using is 4800Hz yielding a 2400 baud. Tape (according to my internet search) can go up to 15KHz. Why not use 10KHz frequency and achieve higher bauds?

Complexity, and low quality of implementation and tapes. I mean, you're literally trying to argue that what was possible in 1975 is representative for what is possible today. That's 35 years in the past, they didn't come *anywhere* near theoretical limits.

> Why do all FSK modulations assign a frequency spacing equal to baud rate? 

They don't. Some do. Most modern FSK modulations don't (they're minimum shift keying standards, instead, where you choose the spacing to be *half* the symbol rate). 

> In the Kansas example they are using 4800Hz and 2400Hz signals for '1' and '0' bits. In MFSK-16 spacing is equal to baud rate as well.

Again, 1975 != all things possible today.

> Why don't they use a MFSK system with a 256-element alphabet? With 20Hz space between each frequency the required bandwidth would be ~5KHZ. We have 10KHz in cassette tape so that should be plenty. Now even if all our symbols were the slowest one (5KHz) we would have 5*8 = 40000 baud. That's 27MB of data. Not too far from the 21MB estimation above.

Well, it's not that simple, because your system isn't free from  noise and distortion, but as before:

1975. Low cost. 

They simply didn't.

>  If tape is so bad then how do they store Terabaytes on it?

You're comparing completely different types of tapes, and tape drives:

This 100€ LTO-8 data backup tape

[![LTO-8 tape][1]][2]

vs this cassette tape type, of which child me remembers buying 5-packs at the supermarket for 9.99 DM, which, given retail overhead, probably means the individual cassette was in the < 1 DM range for business customers:

[![Audio Cassette][3]][4]


and this 2500€ tape drive stuffed with bleeding edge technology and *a metric farkton of error-correction code and other fancy digital technology*

[![LTO-8 tape drive][5]][6]

vs this 9€ casette thing that is a 1990's least-cost design using components available since the 1970s, which is actually currently being cleared from Conrad's stock because it's *so* obsolete:

[![Cassette player][7]][8]


  [1]: https://i.sstatic.net/XwlkM.jpg
  [2]: https://www.heise.de/preisvergleich/hp-ultrium-lto-8-rw-kassette-q2078a-a1815697.html?v=k&hloc=de
  [3]: https://i.sstatic.net/gzAEB.jpg
  [4]: https://en.wikipedia.org/wiki/Cassette_tape
  [5]: https://i.sstatic.net/NcKIH.jpg
  [6]: https://www.heise.de/preisvergleich/?cat=dat&xf=1202_LTO-8
  [7]: https://i.sstatic.net/a03Kb.jpg
  [8]: https://www.conrad.de/de/p/basetech-kw-118c-tragbarer-kassettenspieler-schwarz-1934371.html?hk=SEM&WT.srch=1&WT.mc_id=google_pla&s_kwcid=AL%21222%213%21423682525912%21%21%21g%21%21&ef_id=EAIaIQobChMIm6eXt6qd7AIVawiICR2QXAAYEAkYAyABEgI4rPD_BwE%3AG%3As&gclid=EAIaIQobChMIm6eXt6qd7AIVawiICR2QXAAYEAkYAyABEgI4rPD_BwE