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"There's a new band in town, but you can't get the sound from the pages of a magazine", goes a Billy Joel song.

Or, in this case, from this useless story with no link to any audio.

Yeah, link "New Zealand" to your New Zealand topic roster: way relevant there, Guardian. Let's see, "Angry French hitchhiker charged with stealing sleeping bag in New Zealand". Nope, no Alan Turing computer audio there! How about, "The coffin club: elderly New Zealanders building their own caskets". Guess again!

There is an embedded soundcloud widget.
It never came up for me; I assume something blocked it as an ad.
Ghostery hid it from me, but it had a button for "play one time" that worked perfectly.

It sounds a little like a scratchy cello.

The ironic thing is that it actually sounds better than the cello patches of some synthesizers from several decades later.
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How does this relate to this clean recording form 51? http://news.bbc.co.uk/2/hi/technology/7458479.stm
From the other article linked elsewhere in this thread:

"Today, all that remains of the recording session is a 12-inch single-sided acetate disc, cut by the BBC's technician while the computer played. The computer itself was scrapped long ago, so the archived recording is our only window on that historic soundscape. What a disappointment it was, therefore, to discover that the pitches were not accurate: the recording gave at best only a rough impression of how the computer sounded."

More here: http://blogs.bl.uk/sound-and-vision/2016/09/restoring-the-fi...

"The Manchester computer had a special instruction that caused the loudspeaker—Turing called it the 'hooter'—to emit a short pulse of sound, lasting a tiny fraction of a second. Turing said this sounded like 'something between a tap, a click, and a thump'. Executing the instruction over and over again resulted in this 'click' being produced repeatedly, on every fourth tick of the computer's internal clock: tick tick tick click, tick tick tick click. Repeating the instruction enough times like this caused the human ear to hear not discrete clicks but a steady note, in fact the note C6, two octaves above middle C. ...

Turing was not very interested in programming the computer to play conventional pieces of music: he used the different notes to indicate what was going on in the computer—one note for 'job finished', others for 'digits overflowing in memory', 'error when transferring data from the magnetic drum', and so on. Running one of Turing's programs must have been a noisy business, with different musical notes and rhythms of clicks enabling the user to 'listen in' (as he put it) to what the computer was doing. He left it to someone else, though, to program the first complete piece of music."

I had something similar-ish with a desktop PC: when I plugged headphones into my amp and that into motherboard sound output, I could hear all sorts of faint squelchy noises that seemed to correlate both with what is going on on the screen as well the CPU. Some things always sounded the exact same (like running a certain command etc.)... it was both very fascinating and annoying. If a program sometimes ran fine and sometimes crashed, I could tell by ear right when either happened, etc.
Back in the days when CPU speed was measured in single digit MHZ (e.g. Amiga 68000 at 7mhz, ZX Spectrum at 6Mhz?), I had a hard time hearing anything other than CPU noise on standard FM radios. You could indeed hear algorithms running very clearly, it's something I considered to be useful during a time when I was learning about CPUs and computer programming.