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Wax cylinders were used at the dawn of the phonograph to store audio recordings. This was long before the codec or compression, and they only had space for approximately two minutes of sound.

I'm working on a game at the moment in which they're going to be particularly common, along with the vinyl record, and are kind of plot central. I'm led to wonder what other data could have been stored on them. A central question to this is:

Given an agreed on encoding, how much binary data could reliably be stored on such a cylinder?

I know that wax is generally a smooth and malleable medium, and needle sizes could also vary along with amplification techniques, so there's likely going to be some margin for error here.

Using analog media for digital storage isn't unheard of; we used tape drives all the time in the 1990s. They were incredibly slow, but you could fit a few gigabytes on them. On top of this, the peak use of the wax cylinder was well after the creation of the Jacquard loom and the beginning of mechanical computing around 1850, wasn't it?

Unfortunately they're about as common as 8-tracks these days, or I'd just experiment and find out.

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    $\begingroup$ What are you using to convert from wax cylinder to some other format? Generally this is goinng to be limited by the fidelity of that conversion. The degree to which you can get accurate reproduction over a wide frequency range will be the limiting step. $\endgroup$
    – Dan
    Feb 7 at 3:02
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    $\begingroup$ We are still using tape drives. It's just that their use has moved into the large data centers which consumers call the cloud. Tape drives are not slow at all, and never were. You may be thinking of audio cassettes, but those were slow only because they were used off-label, to do something they were not designed to do. An ordinary LTO-7 tape drive writes 300 MB/s and stores 6 TB of data (both without using the native compression capabilities). What tapes cannot do is provide fast access to random data -- they are sequential devices. $\endgroup$
    – AlexP
    Feb 7 at 8:31
  • $\begingroup$ How are you proposing to get data on and off the storage device? $\endgroup$ Feb 7 at 12:57
  • $\begingroup$ We still use tape drives, they just aren’t analog anymore. See en.wikipedia.org/wiki/Linear_Tape-Open. $\endgroup$ Feb 7 at 13:07
  • $\begingroup$ @StarfishPrime presumably through the typical automated-cut encoding that sound is recorded with. I'd have one kind of groove for zeroes and another for ones. It could be read in much the same way, but rather than going through an amplifier it would feed into a static computer of some kind. $\endgroup$ Feb 7 at 14:47

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In order to encode data onto an analog recording device, you'd need something like early telephone modem encoding... without the handshaking, of course. You'd probably get something equivalent to 300 baud, i.e. 300 bits per second. You'd also be advised to have a couple of extra bits per byte for error correction, so assuming 8 bits per byte, you'd get 30 bytes per second, for about 3600 bytes total.

Since wax cylinders are are a recording medium which has an innately high level of background noise, it is unlikely that any higher data rate would be sufficiently reliable.

Wax is also not particularly strong. Recording at too high a frequency may lead to reduced playback lifespan, and attempting to record quarter-wave data may well lead to the wax breaking where there are big jumps between the wave phases. Additionally, the frequency response of the wax cylinder phonograph is unlikely to allow a much higher bit rate.

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    $\begingroup$ To store data really "reliably" you also need a error correcting code, for example Hamming code, which requires more than $log_2(D)$ bits, where $D$ is the length of binary data. $\endgroup$ Feb 7 at 5:30
  • $\begingroup$ You're spot on with this Kansas City Standard at 27 3/11 bytes per second. Actual data amount will depend on how widely spaced the grooves are and how big the cylinder is and recording speed. $\endgroup$
    – elemtilas
    Feb 7 at 13:16
  • $\begingroup$ @elemtilas OP stated 2 minutes per cylinder. $\endgroup$
    – Monty Wild
    Feb 7 at 13:18
  • $\begingroup$ That's only one kind of cylinder. It does happen to be the most common type that has survived. I read that more as a general description of the media type than a specific of the media that's actually being used in the story. $\endgroup$
    – elemtilas
    Feb 7 at 13:53
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Modern dial-up modems typically have a maximum theoretical transfer speed of 56 kbit/s (using the V.90 or V.92 protocol), although in most cases, 40–50 kbit/s is the norm.

Recording time of a wax cylinder is 2 minutes (120 s).

40 kbit/s x 120 s = 4800 kbits = 600 kbytes

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    $\begingroup$ I disagree with the assumption that wax cylinders have the same frequency range as a landline. According to this paper, audio stored on a wax cylinder only has a frequency range of 250..2600 Hz, while a POTS landline has 300..3600 Hz. So, one third of the range is missing, especially the higher frequencies, so I'd say that you have to at least halve your result. $\endgroup$
    – orithena
    Feb 7 at 12:53
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    $\begingroup$ The biggest issue is the bandwidth of the phonograph is going to be lower than that of a modern phone line, probably quite a lot lower. You can hear the loss in fidelity in the recording and playback demonstration on the wikipedia page linked from the OP. Monty Wild's guess at 300bps is probably a lot more plausible than tens of kilobits. $\endgroup$ Feb 7 at 12:54
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    $\begingroup$ @orithena hah, beat me too it, and with some quantifiable references too. $\endgroup$ Feb 7 at 12:56
  • $\begingroup$ @StarfishPrime I'd think that the 300bps is a lower bound, probably you can go higher. Especially when you use a better cutting machine than Edisons Phonograph while recording (one that does not use a flexible membrane to vibrate the needle) and a contactless reading machine (e.g. laser-based, like reading a compact disc) to avoid degradation of reliability with each reading process. I only just realized that one might improve the frequency range that way to even surpass a POTS landline... $\endgroup$
    – orithena
    Feb 7 at 13:12
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    $\begingroup$ @MichaelMacha In case of CDs, the error correction used is called Reed-Solomon-Code. To get an idea of how error correction works in principle, there's a video by 3Blue1Brown about the earlier Hamming Codes. $\endgroup$
    – orithena
    Feb 9 at 9:36

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