1 Introduction

One of Turing’s contributions to the Digital Age that has largely been overlooked is his pioneering work on transforming the computer into a musical instrument. It’s an urban myth of the music world that the first computer-generated musical notes were heard in 1957, at Bell Labs in America.Footnote 1 In fact, about nine years earlier, computer-generated notes were heard in Turing’s Computing Machine Laboratory at Manchester University.

This chapter analyzes Turing’s groundbreaking work at Manchester, and also describes how Christopher Strachey, later Oxford University’s first professor of computing, used and extended Turing’s note-playing routines to create computer-generated melodies. Computer-generated music was recorded in Turing’s Manchester Laboratory by the British Broadcasting Corporation (BBC) in 1951.Footnote 2 We outline the techniques of digital archaeology, and the sheer detective work, which led to our reconstruction of the routines that were used to play the music in this recording, and led also to our restoration of the recording. To set the scene, we begin with an overview of the historic Manchester computer and of the characters involved in our story. Then we turn to Turing’s own programming manual for the Manchester machine—the first ever written for a stored-program computer. We clarify his notation for the machine’s instructions, and trace in detail how his lines of code were actually transformed into computer-generated notes. We describe the computer-assisted search that helped us to reverse engineer the Turing-type melody-playing algorithms used to produce the music in the recording—algorithms that ushered in the field of computer music. Our analyses establish Turing’s pioneering role in the history of computer music.

2 The Hardware

The world’s first electronic all-purpose stored-program computer—the first electronic universalFootnote 3 Turing machine—ran its first program in June 1948 (Copeland 2011a, b). Called simply “Baby”, this historic machine was tiny, rough and ready, and almost entirely lacking in the facilities needed for serious computing. Programs were entered bit by painstaking bit, using a panel of hand-operated switches to plant each bit in memory. Output was in the form of bright dots on a tiny glass screen. Baby was designed by two brilliant engineers, Freddie Williams and Tom Kilburn , to test their new groundbreaking high-speed electronic memory, the Williams tube. Around an array of three Williams tubes they wired together the simplest stored-program computer they could think of (Fig. 8.1).

Fig. 8.1
figure 1

Baby, the first electronic stored-program computer. Baby came to life in June 1948. The proud parents: Tom Kilburn is on the left, Freddie Williams on the right (Courtesy of the University of Manchester School of Computer Science)

In later life Kilburn was at pains to deny that Turing had contributed anything to the Baby (Copeland 2011b). This was highly misleading. For one thing, Turing contributed the fundamental concept, the very idea of a universal machine that stores programs of symbolically-coded instructions in its memory. Summarizing his pre-war work, Turing wrote in 1947:

Some years ago I was researching on what might now be described as an investigation of the theoretical possibilities and limitations of digital computing machines. I considered a type of machine which had a central mechanism, and an infinite memory which was contained on an infinite tape. ... [D]igital computing machines ... are in fact practical versions of the universal machine. There is a certain central pool of electronic equipment, and a large memory, [and] the appropriate instructions for the computing process involved are stored in the memory (Turing 1947).

Kilburn had stepped into Turing’s world at the end of 1946, when he entered a dingy London lecture room and sat down to listen to Turing explaining how to build a computer.Footnote 4 Williams had recently succeeded in storing a single binary digit on the face of a cathode ray tube, proving that his computer memory idea worked in principle; and so, as Williams said, “the point now had been reached where we’d got to find out about computers”.Footnote 5 They heard that Turing was giving a series of lectures on computer design in London, and it was decided that Kilburn would attend.Footnote 6 The lectures ran from December 1946 through to February 1947, and were held in a conference room at the Adelphi Hotel in the Strand.Footnote 7 Kilburn was a good pupil, quickly progressing during the lectures from not knowing (as Williams put it) the “first thing about computers”Footnote 8 to the point where he could start designing one himself. Kilburn’s initial design (later superseded) for what would eventually be the Manchester computer followed Turing’s principles closely, and Kilburn’s written reports made extensive use of the terminology Turing had taught him in the Adelphi lectures.Footnote 9 When asked where he had got his basic knowledge of the computer from, Kilburn usually said, rather irritably, that he couldn’t remember.Footnote 10 In a 1993 interview, he commented vaguely “Between early 1945 and early 1947, in that period, somehow or other I knew what a digital computer was”, adding “Where I got this knowledge from I’ve no idea”.Footnote 11 There is in fact no mystery about where Kilburn got his basic knowledge of the computer from—Turing taught him.

A few weeks after Baby ran its first program, Turing accepted the offer of a job at Manchester University. At last he could get his hands on a universal Turing machine in hardware. Turing improved on the bare-bones facilities, designing an input-output system based on wartime equipment used at Bletchley Park. Williams and Kilburn themselves knew nothing of Bletchley Park and its nine gigantic Colossus computers.Footnote 12 The ultra-secret Colossus was the world’s first large-scale electronic computer, although it was not all-purpose and did not incorporate Turing’s stored-program concept.Footnote 13 Turing based his input-output system for the Manchester computer on the same teleprinter tape that ran through Colossus.Footnote 14 His tape reader converted the patterns of holes punched across the tape into electrical pulses, and fed these pulses to the computer. The reader incorporated a row of light-sensitive cells which read the holes in the moving tape—exactly the same technology Colossus had used.

As the months passed, a large-scale computer took shape in the Manchester Computing Machine Laboratory (Fig. 8.2). Turing called it the Manchester Electronic Computer Mark I.Footnote 15 A broad division of labor developed that saw Kilburn and Williams working on the hardware, and Turing on the software. Williams concentrated his efforts on developing a new form of supplementary memory, a rotating magnetic drum, while Kilburn took the leading role in developing the computer proper. Turing designed the Mark I’s programming system, and went on to write the world’s first programming manual.Footnote 16 The Mark I was operational in April 1949, although additional development continued as the year progressed.Footnote 17 Ferranti, a Manchester engineering firm, contracted to build a marketable version of the computer, and the basic designs for the new machine were handed over to Ferranti in July 1949.Footnote 18 The first Ferranti computer was installed in Turing’s Computing Machine Laboratory in February 1951, a few weeks before the earliest American-built marketable computer became available, the UNIVAC I (Fig. 8.3).Footnote 19

Fig. 8.2
figure 2

Baby grows into the Mark I (Permission: University of Manchester School of Computer Science)

Turing referred to the new machine as the Manchester Electronic Computer Mark II, while others called it the Ferranti Mark I. Turing’s nomenclature will be followed here. His programming manual was written in anticipation of the Mark II’s arrival, and is titled Programmers’ Handbook for Manchester Electronic Computer Mark II (c. 1950), but it was the outcome of his programming design work undertaken on the Mark I.Footnote 20

Turing’s Handbook contains what is, so far as is known, the earliest written tutorial on how to program an electronic computer to play musical notes.

Fig. 8.3
figure 3

Turing at the console of the Mark II computer (Permission: University of Manchester School of Computer Science)

3 Programming Notes

The Manchester computer had a loudspeaker—the “hooter”, it was called—that served as an alarm to call the operator when the machine needed attention.Footnote 21 With some simple programming, the loudspeaker could be made to emit musical notes.

The computer’s “hoot instruction” worked like this. There was an electronic clock in the computer synchronizing all the operations. This clock beat steadily, like a silent metronome, at a rate of thousands of noiseless ticks per second. Executing the hoot instruction a single time caused a sound to be emitted at the loudspeaker, but the sound lasted no longer than a tick, a tiny fraction of a second. Turing described this sound as “something between a tap, a click, and a thump”.Footnote 22 Executing the hoot instruction over and over again resulted in this brief sound being produced repeatedly, on every fourth tick: tick tick tick click, tick tick tick click.Footnote 23

If the clicks are repeated often enough, the human ear no longer hears discrete clicks but a steady note. Turing realized that if the hoot instruction is repeated not simply over and over again, but in different patterns, then the ear hears different musical notes. For example, if the pattern tick tick tick click, tick tick tick tick, tick tick tick click, tick tick tick tick is repeated, the note of C5 is heard. (The subscripted number indicates the octave in which the note occurs. Turing described C5 as middle C, as musicians sometimes do, especially if playing an instrument with a very high register; however, it is more usual to call C4, which is an octave below C5, middle C.Footnote 24) Repeating the different pattern tick tick tick click, tick tick tick click, tick tick tick tick, tick tick tick click, tick tick tick click, tick tick tick tick produces the note of F4—and so on. It was a wonderful discovery.

Turing himself seems not to have been particularly interested in programming the machine to play conventional pieces of music. The different musical notes were used as indicators of the computer’s internal state—one note for “job finished”, others for “error when transferring data from the magnetic drum”, “digits overflowing in memory”, and so on.Footnote 25 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 Turing put it) to what the program was doing. He left it to someone else, though, to program the first complete piece of music.

4 God Save the King

One day Christopher Strachey turned up at the Computing Machine Laboratory (Fig. 8.4). Before the war, he had known Turing at King’s College, Cambridge. Strachey was soon to emerge as one of Britain’s most talented programmers, and he would eventually direct Oxford University’s Programming Research Group. When he first strode into the Manchester Computing Machine Laboratory he was a mathematics and physics master at Harrow, one of Britain’s foremost schools. Strachey felt drawn to digital computers as soon as he heard about them, in about January 1951, and taking the bull by the horns he wrote to Turing in April.Footnote 26 Turing sent a copy of his Handbook (c. 1950) and Strachey studied it assiduously.Footnote 27 This was “famed in those days for its incomprehensibility”, Strachey said.Footnote 28 An ardent pianist, he appreciated the potential of Turing’s terse directions on how to program musical notes. Strachey first visited the Computing Machine Laboratory in July 1951; Turing decided to drop him in at the deep end and suggested he try writing a program to make the computer check itself.Footnote 29 When Strachey left the Laboratory, Turing turned to his friend Robin Gandy and said impishly, “That will keep him busy!”Footnote 30

It did keep him busy, during the school summer holidays of 1951.Footnote 31 Strachey was a precocious programmer and when he “trotted back to Manchester”, he recollected, he had with him twenty or so pages covered in lines of programming code—at that time by far the longest program to be attempted.Footnote 32 “Turing came in and gave me a typical high-speed, high-pitched description of how to use the machine”, Strachey recounted.Footnote 33 Then he was left alone at the computer’s console until the following morning.

“I sat in front of this enormous machine”, Strachey said, “with four or five rows of twenty switches and things, in a room that felt like the control room of a battle-ship.”Footnote 34 It was the first of a lifetime of all-night programming sessions. He worked on debugging his monster program, which he called “Checksheet”.Footnote 35 The name was a variation on a term Turing had used, in his Programmers’ Handbook, for a hand method of checking programs. Turing called his method “Check Sheets”. The method was “done on paper with quarter inch squares on which vertical lines are ruled in ink”, Turing explained in the Handbook.Footnote 36

As well as spending the night struggling to debug Checksheet, Strachey prepared a surprise. He managed to debug and get running another program that he’d brought with him. To the astonishment of onlookers, the computer raucously hooted out the British National Anthem.Footnote 37 A budding programmer could hardly have thought of a better way to get attention. A few weeks later, Max Newman , Professor of Mathematics at Manchester and founder of the Computing Machine Laboratory, heard the computer grinding out “God Save the King”. Newman quickly wrote a letter to Strachey suggesting he might like a programming job in the Lab.Footnote 38

Fig. 8.4
figure 4

Christopher Strachey sunbathing in the garden of his cottage “The Mud House”; the photo was taken in 1973, two years before his untimely death (Courtesy of the Bodleian Library and Camphill Village Trust)

Manchester’s musical computer also caught the attention of the popular press, with headlines like “Electronic brain can sing now”.Footnote 39 The accompanying article explained that “the world’s most powerful brain” was “given a coded version of the score”, from which it “constructed the necessary waveform”. The BBC sent a recording team together with a radio presenter from Children’s Hour, known as Auntie, to capture a performance by the computer.Footnote 40 As well as “God Save the King”, the BBC recorded a version of Glenn Miller’s “In the Mood”, a reedy and wooden performance of the famous hit. There was also an endearing, if rather brash, rendition of the nursery rhyme “Baa Baa Black Sheep”. The Mark II, still full of glitches, managed to crash in the middle of its Glenn Miller party piece. “The machine’s obviously not in the mood”, Auntie gushed.

The unedited BBC recording of the session conveys a sense of people interacting with something entirely new. “The machine resented that”, Auntie observed at one point. The idea of a thinking machine, an electronic brain, was in the air at Manchester. Turing merrily fanned the flames. He provocatively told a reporter from The Times that he saw no reason why the computer should not “enter any one of the fields normally covered by the human intellect, and eventually compete on equal terms”.Footnote 41

Max Newman lectured on the new computer music in 1952, to 250 professional musicians who were attending the annual conference of the Incorporated Society of Musicians. His lecture was reported in the national press.Footnote 42 After explaining that, to make the Manchester computer play melodies, “All you have to do is to send an instruction to the hooter with the frequency of the note you want it to play”, Newman described the discovery that the computer could be programmed to compose tunes for itself. So far these were, he admitted, “very bad tunes”. (Quite possibly the program used Turing’s random number generator, a standard hardware component of the Ferranti computers.) According to the Manchester Guardian:

The next step, said Professor Newman, would be to make a machine which could compose good tunes, but so far no method of bridging the gap had been devised.Footnote 43

The article continued:

Professor Newman ended with this note of comfort for the assembled musicians: “All this appears much more alarming and dangerous than it really is. When you see how it is done and how far it is from genuine composition, composers will realise they need not start taking steps to protect themselves against competition from machines.”

5 Turing’s Music Tutorial

Turing’s brief tutorial in his Handbook was typically compressed and demanding; yet, equally typically, his terse account told readers everything it was necessary to know in order to start writing note-playing programs. Turing called the hoot instruction /V, pronounced “slash vee”. The complete tutorial occupied little more than half a page:

The hooter . When an instruction with function symbol /V is obeyed an impulse is applied to the diaphragm of a loudspeaker. By doing this repeatedly and rhythmically a steady note, rich in harmonics, can be produced. This is used to enable the operator to be called to attend to the machine in some way. The simplest case is where the whole of a job is completed and it is required to clear the electronic stores and start something different. All that is then required is to repeat a cycle of instructions including a hoot, e.g.

$$ {\displaystyle \begin{array}{l} FS\kern1.5em NS/V\\ {} CS\kern1.5em FS/P\end{array}} $$

In this case every second instruction will put a pulse into the speaker. These pulses will occur at intervals of 8 beats i.e. 1.92 ms giving a frequency of 521 cycles (about middle C). Or one could use the loop of three instructions

$$ {\displaystyle \begin{array}{l}O@\kern1.875em /\mathrm{V}\\ {}G@\kern1.375em \mathrm{P}@/\mathrm{V}\\ {}M@\kern1.375em \mathrm{O}@/\mathrm{P}\end{array}} $$

[see our footnote]Footnote 44

which gives a slightly louder hoot a fifth lower in frequency. Single pulses applied to the loudspeaker are distinctly audible as something between a tap, a click, and a thump. This fact can be turned to good account. By putting hoot instructions into programmes at suitable points one is enabled to “listen in” to the progress of the routine. Some indication of what is going on is given by the rhythm of the clicks that are heard. Footnote 45

In these two loops, one consisting of two instructions and one consisting of three, Turing has used international teleprinter code to abbreviate the instructions. At the level of “machine code”, the instructions consist simply of strings of binary digits (bits). Teleprinter code associates keyboard characters with strings of 5 bits; for example, A is 11000 and B is 10011. Teleprinter code was well known to engineers in that era, and was very familiar to Turing from his wartime work at Bletchley Park on the “Tunny” teleprinter code, used by Hitler and his generals. To Turing, teleprinter code must have seemed a natural choice for abbreviating the Manchester computer’s bitcode. This system’s main defect, that the abbreviations give no intuitive sense at all of what is being abbreviated, is one reason why his Handbook was such heavy going.

Let us unpack what Turing wrote down, in order to clarify its importance in the history of computer music. First, we explain Turing’s notationally formidable subroutines, simplifying his notation and spelling out the connection between his sequences of coded instructions and perceived musical sounds. Then we report the results of our computer-assisted analyses of the BBC’s 1951 recording of the Manchester computer’s music. From these results, we extract our account of how others at Manchester extended Turing’s note-playing subroutines, so enabling the Mark II to play its first melodies. We also provide a series of tables that allow the reader to see not only how these melodies were produced but also, more generally, how the computer itself can be used in historical detective work about computers.

In teleprinter code, / is 00000 and V is 01111; thus /V is the teleprinter code abbreviation of the Mark II’s 10-digit hoot instruction, 0000001111. Turing’s /P is also an instruction; instructions always began with /, or T (00001). The other symbols in Turing’s two sample subroutines, NS, P@, FS, CS, O@, G@ and M@, are memory addresses: each pair of symbols abbreviates a 10-digit address in the computer’s Williams tube memory.

Instruction /P (unconditional transfer of control) tells the machine to obey next the instruction stored at a location specified via the address immediately to the left of the /. In effect the second line of the first loop sends the machine back to the first line (but see our footnote); and the final line of the second loop again sends the machine back to the first line.Footnote 46 The computer will continue to loop until an instruction from elsewhere in the program terminates the loop after n repetitions.Footnote 47 The programmer selects the number n, so determining how long the note is held, as required by the rhythms of the melodies.

Our analysis of the BBC’s recording of the Mark II playing “God Save the King”, “Baa Baa Black Sheep”, and “In the Mood”, showed that the durations of the played notes varied between 80 milliseconds and 1100 milliseconds. The analysis also revealed that very short pauses were programmed between each consecutive note, presumably by means of “silent” loops—short loops containing no hoot instruction. The duration of these inter-note pauses is between 40 and 50 milliseconds (exact measurement was difficult because the pauses are blurred over by reverberation from the room housing the computer). The inter-note pauses help to define the beginning of each note, and are essential if a sequence of several notes of the same pitch is played. Without a gap between the individual notes, a single long note would be heard.

The occurrence of NS to the left of /V in Turing’s first subroutine can be ignored for the present purposes, and so can the P@ to the left of /V in the second subroutine. These terms create special effects to do with the computer’s visual display, and have no role in the production of musical notes. The effect produced by including the address NS in line 1 of the first subroutine is that the information stored at NS momentarily brightens on the monitor display as the machine hoots.Footnote 48 This provides a visual prompt to assist the operator. Similarly, the effect of P@ in the second instruction of the three-line subroutine is to cause the information stored at P@ to brighten on the display as the hooter sounds. The two note-playing subroutines can be written more cleanly without these special effects:

$$ {\displaystyle \begin{array}{l}\mathrm{FS}\kern3.375em /\mathrm{V}\\ {}\mathrm{CS}\kern2em \mathrm{FS}/\mathrm{P}\end{array}} $$
$$ {\displaystyle \begin{array}{l}\ \mathrm{O}@\kern2.75em /\mathrm{V}\\ {}\ \mathrm{G}@\kern2.75em /\mathrm{V}\\ {}\ \mathrm{M}@\kern0.75em \mathrm{O}@/\mathrm{P}\end{array}} $$

Taking clarity a step further, we might replace the teleprinter-coded addresses with simple line-numbers:

$$ {\displaystyle \begin{array}{l}1\kern1.75em /\mathrm{V}\\ {}2\kern1.25em 1/\mathrm{P}\end{array}} $$
$$ {\displaystyle \begin{array}{l}1\kern1.75em /\mathrm{V}\\ {}2\kern1.75em /\mathrm{V}\\ {}3\kern1.5em 1/\mathrm{P}\end{array}} $$

As Sect. 8.3 mentioned, the /V instruction takes four ticks to complete—four beats in the Manchester jargon—with the actual hoot occurring on the fourth beat.Footnote 49 /P also takes four beats to complete. As Williams and Kilburn put it, the basic rhythm of the Manchester computer was “four beats to the bar”.Footnote 50 Thus, running through Turing’s two-line subroutine once produces: tick tick tick click, tick tick tick tick; and looping repeatedly through the subroutine produces the first of the two sequences discussed in Sect. 8.3. Similarly, running through the three-line subroutine once gives: tick tick tick click, tick tick tick click, tick tick tick tick; and looping repeatedly gives the second sequence in Sect. 8.3.

The precise duration of a single beat was 0.24 milliseconds (ms). The first subroutine produces one click every 8 beats, which is to say every 1.92 ms. Thus, the frequency with which clicks are produced, as the machine loops repeatedly through the subroutine, is (1 ÷ 1.92) clicks per ms—0.52183 clicks per ms, or 521.83 clicks per second. In standard units, the frequency of the clicks is said to be 521.83 Hertz (Hz). This is close to C5, whose assigned frequency in the ‘Equal Tempered’ scale is 523.25 Hz. The Equal Tempered scale is the standard scale for keyboard instruments, with adjacent keys playing notes heard as equidistant from one another.Footnote 51

Table 8.1 shows the Equal Tempered frequencies of all the notes occurring in the fragments of the scores of “God Save the King”, “In the Mood” and “Baa Baa Black Sheep” that were performed in the BBC recording. Later tables show the actual frequencies that the computer produced.

Table 8.1 The Equal Tempered frequencies of the notes from those parts of the scores of “God Save the King”, “In the Mood” and “Baa Baa Black Sheep” that were performed in the 1951 BBC recording

By dispensing with any reference to memory addresses, and abstracting from which particular instructions are employed, Turing’s note-playing subroutines can be represented very transparently by means of what we call note-loops. The note-loop corresponding to Turing’s C5 routine is:

$$ \mathrm{START}\hbox{--} \hbox{--} \hbox{--} \mathrm{H}\hbox{--} \hbox{--} \hbox{--} \hbox{--} \mathrm{REPEAT} $$

Each “–” represents a single beat, with “H”, the hoot, occurring on the fourth beat of the first bar. Representing this more economically still, the note-loop is simply:

$$ <3\mathrm{H},4>. $$

6 Exploring the Mark II Notes

Subroutines for playing lower notes require the addition of further instructions, since this has the effect of adding extra blocks of 4 beats between the hoots, so lowering the frequency. Conveniently, one of Turing’s instructions, /L, served to waste time: its execution took up 4 beats but it did nothing. (Strictly, the instruction did nothing unless a “dummy stop” switch had been set manually at the control console before the program started, in which case /L caused the machine to pause. We discuss dummy stops in Sect. 8.8.) /L is ideal for creating lower-frequency notes.Footnote 52 For example, the note-loop <3H, 4, 4> produces a frequency of 347.22 Hz, approximately F4 (349.23 Hz), a fifth lower than C5.

<3H, 4, 4> produces the same note as Turing’s second example of a loop, which in our notation is <3H, 3H, 4>. Adding the second pulse of sound at the same frequency does not alter the note, but (as Turing said) has the effect of making the note louder. We call note-loops that play the same frequency equivalent.

Some further examples of note-loops are <3H, 4, 4, 4, 4, 4, 4, 4>, producing a frequency of 130.21 Hz, fairly close to C3 (130.81 Hz), and <3H, 4, 4, 4, 4, 4, 4>, producing a frequency of 148.81 Hz, lying between D3 (146.83 Hz) and D3 sharp (155.56 Hz). Both these note-loops produce a quiet sound. The same notes are played more loudly if extra hoots are added to form equivalent note-loops, such as <3H, 3H, 3H, 3H, 4, 4, 4, 4> and <3H, 3H, 3H, 3H, 4, 4, 4> respectively. We call a note-loop containing only one hoot the primary form, and equivalent note-loops containing more than one hoot padded forms of the loop. Padded note-loops typically produce notes with a different timbre or tone-color from the note produced by the loop’s primary form. Timbre is manifested by differences in the shape of waveforms of the same frequency. (If a violin and a flute play exactly the same note at exactly the same volume, the sounds are nevertheless instantly recognizable as different, because of their different timbres.)

We built a simulator in order to investigate the effects of padding note-loops, and also to establish that our calculated note-loops really do play the correct notes. Our simulations of the Mark II playing “God Save the King”, “In the Mood” and “Baa Baa Black Sheep” can be heard at www.AlanTuring.net/MarkII_music_simulations.mp3. An Atmel ATmega168 microcontroller was used to create a functional computer simulation of the Mark II as a note-playing device. We connected a small loudspeaker directly to one of the digital output pins. Microcontroller programs using pulses and delays reproduced the beat-structure of the Mark II and emulated the effects of the Mark II’s music routines. We found that primary note-loops produce relatively thin-sounding notes while their padded equivalents produce somewhat louder, fuller-sounding notes. Over-padding is possible, however. The simulator revealed that including too many hoots adds a high overtone, especially with lower notes containing more beats. Because an uninterrupted sequence of hoot instructions generates the Mark II’s highest achievable note of 1041.67 Hz (somewhere in the vicinity of C6), the result of over-padding a note-loop is that the ear tends to hear not only the intended note but also this maximum note as a high overtone.

The BBC recording indicates that the programmer most likely used padding. If only unpadded loops are used, lower notes are quieter than higher notes, since in a lower note there are longer gaps between the hoots. This is not observed in the recording, and in fact some lower notes are louder than some higher notes. However, because of the poor quality of the recorded material, the analysis described here did not reveal the number of hoots used in each individual note-loop. Our reconstruction of the note-loops in Sect. 8.12 retrieves the primary form of the note-loops only.

Although the normal rhythm of the Manchester computer was 4 beats to the bar, some instructions took 5 beats to execute. Incorporating a suitable 5-beat instruction in note-loops (e.g. Turing’s instruction TNFootnote 53) extends the number of playable notes. For example, adding 10 extra beats to either the primary or the padded form of the 148.81 Hz note-loop displayed previously results in a loop that plays 109.65 Hz, very close to A2 (110 Hz); the primary form is <3H, 4, 4, 4, 4, 4, 4, 5, 5>. The following loop plays the low note F2 sharp (F#2): <3H, 4, 4, 4, 4, 5, 5, 5, 5, 5>. This loop produces 92.59 Hz, fractionally higher than the note’s Equal Tempered frequency of 92.5 Hz.

In what follows, note-loops are sometimes written in an abbreviated form. For example, <3H, 4×7> replaces <3H, 4, 4, 4, 4, 4, 4, 4> and <3H, 4×4, 5×5> replaces <3H, 4, 4, 4, 4, 5, 5, 5, 5, 5>. Table 8.2 shows the full range of frequencies, down to 96.9 Hz, that the Mark II could produce by means of note-loops containing 4- or 5-beat instructions.

Table 8.2 The frequencies that the Manchester Mark II was able to play by means of loops containing 4-beat instructions or mixtures of 4- and 5-beat instructions (down to the lowest frequency in the 1951 BBC recording)

7 Hoot-Stop and Radio Stop

As Turing explained in his tutorial, a fundamental use for <3H, 4> was the so-called “hoot-stop”. If the two lines of code displayed in the tutorial were placed at the end of a routine (or program, as we would say today), then once the routine finished running, the computer would sound C5 continuously until the operator intervened. The intervention might take the form of pressing the “KEC” key at the control console—the “clear everything” key—in order to clear out the completed routine, in preparation for running the next.Footnote 54 Without the convenient hoot-stop facility, the operator was obliged to remain at the console, watching the indicators, in order to tell whether the routine had stopped running.

A very different solution to effectively the same problem was found in the case of BINAC, an early US computer. Herman Lukoff, one of BINAC’s engineers, explained that the technician whose job it was to monitor BINAC through the night, Jack Silver, had to spend all his time “looking at the flashing lights; it was the only way of knowing that the computer was working”. One night Silver switched on a radio to alleviate the monotony:

To Jack’s surprise, all kinds of weird noises emanated from the loudspeaker, instead of soothing music. He soon realized that the churning BINAC generated these noises because as soon as it halted, the noises stopped. … He put the computer-generated tones to good use. Jack found that by turning the volume up he was able to walk around the building and yet be immediately aware of any computer stoppage.Footnote 55

BINAC, built in Philadelphia by Presper Eckert, John Mauchly, and their engineers at the Eckert-Mauchly Computer Corporation, was the stored-program successor to the pioneering Eckert-Mauchly ENIAC. Eckert and Mauchly went on to build UNIVAC, one of the earliest electronic digital computers to enter the marketplace.

The first systematic use of the Manchester Mark I’s programmable hooter appears to have been to provide the hoot-stop facility.

8 First Hoots

In a section of his Handbook devoted exclusively to the Mark I machine, Turing made it clear that the programmable hooter predated the Mark II machine.Footnote 56 /V was Mark II notation; in the Mark I era it was the instruction K (11110) that caused the loudspeaker to sound. The Mark I, which was closed down in the summer of 1950,Footnote 57 was a slower machine than the Mark II; the duration of a beat was 0.45 ms, compared with the Mark II’s 0.24 ms. This considerably reduced the number of playable notes. For example, lengthening the beat to 0.45 ms causes the frequency of <3H, 4> (the highest-frequency loop) to drop from 523.25 Hz to 277.78 Hz, approximately C#4.

It is not known precisely when a programmable hooter was first added to the computer. Geoff Tootill’s laboratory notebook is one of the few surviving documents relating to the transition from Baby to Mark I.Footnote 58 In a notebook entry dated 27 October 1948, Tootill listed the K instruction 11110 among the machine’s 32 instructions, but indicated that it was unassigned at this time. Given Turing’s focus on the programming side, and the emphasis he placed on the use of the hoot instruction and pause-instructions, which he called “dummy stops”, for “testing”—i.e. debugging—new routines, it seems likely that the hooter was incorporated earlier rather than later.Footnote 59 The computer was running complex routines by April 1949, in particular a routine that searched for Mersenne primes (primes of the form 2n−1).Footnote 60 Most likely Turing’s debugging toolkit of hoots and dummy stops was introduced earlier than this. It also seems likely that the use of the K instruction, and the use of loops to increase the volume of the hooter’s native clicks, probably occurred more or less simultaneously. The loud note produced by the loop would have been more useful than the quiet click given by a single instruction. As Dietrich Prinz, a regular user of the Mark I, said, “By programming a simple loop containing this instruction … an audible ‘hoot’ is emitted”.Footnote 61

A table in Tootill’s notebook dated 28 November 1948, showing the machine’s instructions at that time, listed three different dummy stops, N, F, and C. The section of Turing’s Handbook dealing with the Mark I explained that, during the checking of a program, the dummy stops N, F, and C would be operated in conjunction with the hoot instruction K. By the time of the 28 November table, the K instruction had been assigned: Tootill listed its function as “Stop”. However, his table also contains another instruction labeled “Stop” (00010). Since the machine had no need of two ordinary stop-instructions, it seems very likely that K was being used for hoot-stop at this time. When execution of the program reached the point where the hoot-stop had been inserted, execution would pause and the hooter would play the note of C#4 (middle C sharp) continuously until the operator intervened. We conclude that the Mark I was playing at least one note in about November 1948.

9 Other Early Music

The Manchester Mark I was not the only zeroth-generation electronic stored-program computer to play music. Trevor Pearcey’s Sydney-built CSIRAC (pronounced “sigh-rack”) had a repertoire that included “Colonel Bogey”, “Auld Lang Syne”, and “The Girl with the Flaxen Hair”, as well as brief extracts from Handel and Chopin. Some of the music routines survived on punched paper tape, but seemingly no audio recordings were preserved. Australian composer Paul Doornbusch has recreated some of the music, using reconstructed CSIRAC hardware and the surviving programs.Footnote 62 CSIRAC, still complete and almost in working order, is in Melbourne Museum.

Doornbusch’s recordings and the BBC’s Manchester recording show that the programmers of both computers ran into the problem of “unplayable notes”—notes that could not be replicated or even closely approximated by means of an available note-loop. An example is the note of D3, which occurs 5 times in the BBC recording of “God Save the King”. This note’s Equal Tempered frequency is 146.8 Hz, but the closest that the Mark II can approach is the significantly different note of 148.81 Hz, discussed in Sect. 8.6. To judge from the Doornbusch recordings, F#2, G2, C#3, F#3, D4, E4, F4, G4, and A4 were particularly troublesome for CSIRAC. The Australian and British solutions to the problem of unplayable notes were distinctively different. The Manchester programmers opted to use the nearest playable frequency and tolerated the melody being less in tune (see Sect. 8.14 for a fuller discussion of this technique). CSIRAC’s programmers, on the other hand, attempted to mimic the unplayable frequency by rapidly moving back and forth between two playable frequencies that bracketed the note in question. The result was a melody in which tuning-related problems were replaced by timbre-related problems, with the Australian technique producing notes that sound grainy and unnatural.

An embryonic CSIRAC first ran a test program in about November 1949.Footnote 63 The computer seems to have been partially operational from late 1950, and in regular operation from about mid 1951. The date when CSIRAC first played musical notes is unrecorded; presumably this was in late 1950 or in 1951. The computer is known to have belted out tunes at the first Australian Conference on Automatic Computing Machines, held at Sydney University in August 1951.Footnote 64 A 2008 BBC News article, based on Australian sources, stated that CSIRAC was the first computer to play music.Footnote 65 The only evidence offered for this claim was that CSIRAC’s performance at the Sydney Conference allegedly preceded the date of the BBC recording of the Manchester computer (the recording described in Sect. 8.4). However, the date of the BBC recording is in fact unknown; and in any case the Manchester computer’s first performance of “God Save the King”—whose precise date is also unknown—would have occurred some days or weeks or even months before the BBC recording was made. Unfortunately, an Australian contribution to The Oxford Handbook of Computer Music also states, without evidence, that CSIRAC was “the first computer to play music”.Footnote 66 CSIRAC, however, was certainly not the first computer to play music.

There were American hoots too. BINAC was playing music before CSIRAC even ran its first test program. BINAC was completed in August 1949 (although it ran a 50-line test program in April of that year).Footnote 67 As Lukoff explained, a party was held to celebrate the machine’s completion:

It was held right at the BINAC test area one August evening. In addition to hors d’oeuvres and cocktails, the BINAC crew arranged a spectacular computer show. Someone had discovered that, by programming the right number of cycles, a predictable tone could be produced. So BINAC was outfitted with a loudspeaker attached to the high speed data bus and tunes were played for the first time by program control. The audience was delighted and it never occurred to anyone that the use of a complex digital computer to generate simple tones was ridiculous. … The crowning achievement of the evening came after a long, laborious arithmetic computation; the machine laid an egg! The engineers had programmed the machine to release a hard-boiled egg from its innards.Footnote 68

As far as can be ascertained, therefore, the first melodies to be played by a computer were heard at the Eckert-Mauchly Computer Corporation in the summer of 1949, and very likely individual musical notes were heard a few months earlier at Turing’s Computing Machine Laboratory, probably in November 1948. Effectively, the pioneering developments on either side of the Atlantic were roughly contemporaneous, with Australia entering the field a year or two later.

10 The BBC Recording

The BBC’s website offers an edited digitized version of the original BBC recording of the Manchester Mark II; and there is a full-length version of the same digitalization of the recording on the Manchester University website.Footnote 69 Upon pressing play, the listener is greeted by a thick wall of noise—a combination of hissing, humming, and rhythmically repeating crackles from the original acetate disc. Then a tone not unlike a cello cuts through this cacophony to give a mechanical-sounding rendition of the first two phrases of the National Anthem. The melody, though familiar enough, is somewhat out of tune, with some notes more distinctly out than others. Moreover, some notes are loud relative to their neighbors (most likely the result of padding). At the end of the second phrase, the performance is suddenly cut short by a glitch and nervous laughter.

The engineers restart the routine and this time the machine energetically plays its way through the entire first verse. Then, with scarcely a pause, it follows up with an unbroken performance of the first line of “Baa Baa Black Sheep”. For its third number the Mark II attempts “In The Mood”, but once again falls victim to an unknown error, causing it to sing out a high pitched beep. The recording team give the computer one more chance to make its way through “In The Mood”, and it proceeds admirably until the final line, when it yet again breaks down. Altogether, the recording lasts about 3 minutes.

The frequencies in the recording are higher than the ideal in-tune frequencies that would be heard if the same melodies were played on a modern synthesizer. Because the Mark II offered such a limited palette of notes, deviations such as this are to be expected. In scoring a melody for the Mark II, the musician had to try to ensure that the individual notes were as in tune with one another as possible. Whether or not notes were played at the ideal Equal Tempered frequency would necessarily have been a secondary consideration.

The waveform of the recording looks and sounds very unlike the square pulse-wave produced by a modern synthesizer. The early waveform is much rounder, with a lot less high-frequency energy. Its departure from the ideal square-wave is most likely a result of the Mark II’s pioneering digital electronics, together with the long and transformative signal chain between the original sound source and the final digital file. Obtaining clean pulse waves from early digital electronics was a challenge in itself; the pulses from the computer would have resembled trapezoids rather than perfect squares, and so would already be lacking some of the high frequency audio content of modern pulse waves. The hooter, the next element in the chain, may itself have transformed the sound somewhat, depending on the characteristics of the loudspeaker. Then the microphone used to record the performance and the amplifier used to boost the signal, as well as the room in which the performance took place, would all have colored the audio. Finally, the cutting mechanism, which gouged a groove in the rotating acetate disc, was a source of pitch instability and plenty of crackles and noise. Each of these stages provided generous opportunities for the introduction of unwanted noise, artifacts, pitch instability, and spectral alterations.

Two different acetate discs were cut during the recording session. One was taken away by the BBC and presumably used in a broadcast. It is unlikely that this disc survives, but a second disc was given to Manchester engineer Frank Cooper as a souvenir. It contained another recording made at Cooper’s request once the main recording session was over.Footnote 70 By that time, Cooper recollected, “the computer was getting a bit sick and didn’t want to play for very long”. Eventually he donated this 12-inch single-sided acetate disc to the Computer Conservation Society; and subsequently the National Sound Archive, now part of the British Library, made a digital preservation copy of the recording.Footnote 71 This further stage of processing may have added its own sonic characteristics.

11 The Paradox of the Impossible Notes

Despite the long chain existing between the original music-playing routine and the available recording, we decided to attempt to reverse-engineer the note-loops that the programmer had used. A frequency analysis of the digital recording told us the frequencies of the recorded notes, and where different recorded occurrences of the same note had different frequencies, we were able to gather information about error magnitudes. (The principal software used was iZotope RX for removing noise and artifacts, and Celemony Melodyne for carrying out the frequency analyses and pitch correction.)

Soon, however, we hit a fundamental problem. There were frequencies in the recording that could not possibly have been produced by the Mark II’s note-loops—impossible notes. An example is the recorded note corresponding to E3 (which occurs only once in the verse from the National Anthem). The measured frequency of the recorded note is 169.06 Hz, a thumping 4.25 Hz distant from the note’s Equal Tempered frequency of 164.81 Hz. 169.06 Hz is an impossible note for the Mark II. It is bracketed by a note-loop of 24 beats, producing a note of 173.61 Hz, and a loop of 25 beats, producing a note of 166.67 Hz (see Table 8.2). Whatever frequency it was that the computer had produced, this was certainly not the frequency we found in the recording on the BBC website.

We decided to move closer to the original recording, assuming that the problem lay in the transformative chain between the source and the digital file we were analyzing; and we obtained from the British Library an identical copy of their archived digital file. The recording we had analysed previously from the BBC website was in fact a digitized version of an analog recording that had been made by the National Sound Archive—using a cassette tape and Dolby B noise reduction—at the same time as the digital preservation copy was created.Footnote 72 (This cassette recording was subsequently digitized by a technician at Manchester University and put on the Internet as part of Manchester’s Digital 60 celebration of Baby’s 60th anniversary.) The digital file as we received it from the British Library did indeed exhibit differences from the previously analysed (cassette-based) recording—but not the differences we had hoped for. The new frequencies we measured were consistently higher than our previous measurements (indicating that the recording involving the cassette tape ran slower than the British Library’s preservation copy). However, the impossible notes were still present, as Table 8.3 shows. E3 is the most troubling case but the high notes C#3, D3, F#3, and G3 all stand out as being quite far off the playable frequencies shown in Table 8.2.

Although the software used for our frequency analyses is very reliable, the measured frequencies in Table 8.3 nevertheless have a significant margin of error. This is because of a wobble in the speed of the recording that was most likely introduced by the disc-cutting process. This wobble caused some notes in the recording to bend slightly throughout their duration, and the wobble also resulted in the measured frequency of different occurrences of a note being different from one another. The maximum difference between two readings of the same note from different parts of the recording was one fifth of a semitone (20 cents, in the unit of measurement introduced below). The frequencies shown in Table 8.3 are the midpoints of the range of frequencies measured for the note’s various occurrences. However, the margin of error in the measured frequencies created by the wobble (±20 cents) is not large enough to explain the presence of the impossible notes. A more probing analysis was needed.

Table 8.3 The measured frequencies of the notes in the National Sound Archive digital copy of the BBC recording, prior to correction

12 Searching for the Right Speed

The difference in speed and consequently in pitch between the two analysed recordings is in fact the clue to the impossible notes. If the speed of the archived recording were itself fast or slow, this could account for the presence of impossible frequencies. For example, if the turntable in the BBC recording van were running slightly too fast as the acetate disc was cut, the frequencies would be shifted systematically upon playback at the standard speed of 78 rpm.Footnote 73 (Achieving speed constancy was a problem with the BBC’s standard mobile recording equipment.Footnote 74) Only when we know the true speed S0 at which the recording should be played can we measure the frequencies actually produced by the computer.

Therefore we set out to determine the true speed of the recording. The basic question was whether some small increase or decrease in the overall speed of the recording would result in frequencies that correlated acceptably with the playable frequencies in Table 8.2. Our initial approach to the question was to nudge the speed up or down a bit and see what frequencies emerged. The result was always the same: some frequencies matched well but other frequencies that had matched at a speed investigated previously now no longer matched. How to get the carpet to fit into all the corners of the room at once? We wrote a command-line program to conduct a brute-force search for the optimum global fit. The program (written in C) incremented the speed of the recording in tiny steps and at each increment calculated the new notes, by appropriately tweaking the notes we had measured. We call the notes calculated at each increment the calculated notes, the notes that the computer is actually capable of producing the playable notes (shown in Table 8.2), and the notes that we measured from the BBC recording the measured notes (shown in Table 8.3).

The exhaustive search commenced at 79.5% of the native speed of the recording, an arbitrary point well below the native speed, and progressed through 80,000 increments to 126% of the native speed. At each step, the program computed the ‘distance’ between each calculated note and its most closely neighboring playable note. The program averaged these distances to produce ΦS, the closeness-of-fit parameter for speed S; and then the process repeated, with the program incrementing S by a small fixed amount δ and calculating ΦS.

Our program expressed the distance between a calculated note and the nearest playable note in musical units called “cents”. Cents were also the units of ΦS. One cent is one-hundredth of the distance between any two adjacent keys on the piano keyboard. To the human ear, the distance between, say, the notes C4 (261.64 Hz) and C5 (523.28 Hz), which are one octave apart, is musically the same as the distance between C5 and C6 (1046.56 Hz), which are again one octave apart. Working in Hertz, however, these distances are far from the same: the distance between C4 and C5 is 261.64 Hz, whereas the distance between C5 and C6 is 523.28 Hz. Musically, the distances are the same, but the frequency of the notes is doubling. If these distances are expressed in cents, on the other hand, they are indeed identical. Since C4 and C5 are 12 notes apart on the keyboard, as are C5 and C6, the distance is 1200 cents in each case. In fact, not only distances between notes but also the individual notes themselves can be expressed in cents, e.g. by somewhat arbitrarily taking C0 (16.35 Hz) to be the zero-point, so that C1 is 1200 cents, C2 is 2400 cents, and so on.

The program expressed all values in cents rather than Hertz, a procedure that yields a simpler algorithm, since each increment in speed has a uniform effect on the notes if the units are cents, whereas the formula is more complex if the units are Hertz. Moreover, if the notes are expressed in cents, the distance between two notes can be calculated simply by subtracting the smaller value from the larger, whereas matters are more complicated if the notes are expressed in Hertz, as our examples show. A calculated note could be, say, 10 Hz higher than the nearest playable note (100Hz, say), while at a higher speed, a calculated note could be 20 Hz higher than its nearest playable note (say 200 Hz), and yet each of the two notes be equally close to its nearest playable note, since differences in frequency are magnified as the speed becomes higher.

The object of our search, the smallest ΦS, turned out to be just 37.7 cents, and the associated speed, the calculated true speed S0, was just 2.2% faster than the native speed of the recording. If the speed of the recording is increased by this small percentage—or, equivalently, if our previous measurements of the notes are corrected by adding 37.7 cents to each measured note—then all the notes lie within 9.67 cents of playable notes, well within the margin of error of ±20 cents. In fact, the situation is even better than this. If A3 is disregarded, all the notes are within 3.52 cents of playable notes. (There are only four samples of A3 in the entire recording, all in quick succession at the end of “In the Mood”.)

The “impossible” notes have disappeared. They were artifacts, caused by the recording becoming slightly slowed down at some point in the transformative chain—most likely in the cutting of the original acetate disc.

Table 8.4 shows the measured notes after adjustment for the calculated true speed. Having discovered the true frequencies, with a margin of error of only a few cents, we were able to conclude that the routines used to play the versions of “God Save the King”, “Baa Baa Black Sheep” and “In the Mood” recorded by the BBC must have used note-loops whose primary forms are shown in Tables 8.5 and 8.6. As Sect. 8.6 explained, the programmer(s) probably used padded forms of the primary loops, but our analysis as described here retrieved only the primary forms.

Table 8.4 The frequencies played by the Mark II once the speed of the 1951 BBC recording is corrected
Table 8.5 The primary note-loops used to play the version of “God Save the King” recorded by the BBC, as indicated by our frequency analysis
Table 8.6 The primary note-loops for additional notes in the melodies “Baa Baa Black Sheep” and “In the Mood”

13 The Question of Authorship

The question of the authorship of the three routines that played the melodies recorded by the BBC is open. In the wake of Strachey’s tour de force a number of people in the computing lab started writing music programs: Cooper related that “everybody got interested—engineers started writing music programs, programmers were writing music programs”.Footnote 75 Nothing about the BBC recording settles the question of authorship: even the routine that played the National Anthem in the recording may have been a retouched version of Strachey ’s original.

However, it can at least be said that the programmer(s) of the routines for “Baa Baa Black Sheep” and “In the Mood” used the same key signature as the programmer of “God Save the King”; and also used the same primary loops as those selected for “God Save the King”: new loops were introduced only for notes that do not occur in the Anthem. This was so even though some alternative primary loops were available, and in fact it is arguable that some of these choices would have produced frequencies that sounded more in tune (see Sect. 8.14).

We expect that a more refined analysis currently underway will reveal information about the use of padding in the recorded melodies: this may help to clarify aspects of the authorship issue.

14 Tuning Puzzles

There are puzzles about some of the frequencies selected by the programmer(s) and so we end with a discussion of tuning.

While there are always differences between the Equal Tempered frequency of a note and the note actually played by the Mark II, these differences do not produce a general out-of-tune-ness in the performance. Certainly if the computer were playing together with some other instrument that was tuned in accordance with the Equal Tempered scale, the computer would sound conspicuously out of tune. However, with the computer playing solo, what matters more than the absolute frequencies of the notes is the extent to which the performed notes are in tune with one another, and in fact the relative tuning of the notes is quite acceptable, actually closer to the key of G# major than G major, the usual key of the National Anthem. In programming the National Anthem, the programmer seems to have picked frequencies with a view to their overall relationships, rather than trying to hit the Equal Tempered frequencies as closely as possible.

Nevertheless, some notes in the recording are sufficiently out of tune to make anyone with a musical ear cringe. Examples are the sequence of occurrences of D3 at notes 17 to 20 of “God Save the King” and the final occurrence of D3 at note 36. These notes would sound more in tune if a 27-beat loop <3H, 4×2, 5×3> had been used instead of the 26-beat loop selected by the programmer <3H, 4×3, 5×2>—as Fig. 8.5 indicates: the “difference line” at the foot of the graph would be flatter if the 27-beat loop were used. In fact, the preferable 27-beat loop even produces a frequency closer to the note’s Equal Tempered frequency of 146.83 Hz (154.32 Hz as opposed to the 26-beat loop’s frequency of 160.26 Hz). Why the programmer chose the excessively high 26-beat loop is puzzling.

Fig. 8.5
figure 5

Comparing the notes in the National Anthem’s score with the notes actually played by the computer in the BBC recording. The line at the foot of the graph, the difference line, shows the displacement between the other two lines. The straighter the difference line, the more in tune with one another the notes sound. Here, the line shows that the performance sounds most out of tune in the middle and again almost at the end. In both places, the culprit is the computer’s rendition of the note D3, which the programmer pitched a little too high

Another puzzling example of poor tuning, this time from “In the Mood” is A3, a note that does not feature in the other two melodies. Substituting an 18-beat loop in place of the 17-beat loop used by the programmer brings an improvement in relative tuning, and again produces a frequency closer to the note’s Equal Tempered frequency of 220 Hz (231.48 Hz as opposed to 245.1 Hz in the case of the 17-beat loop). Once again, an excessively high frequency has been selected, to the detriment of the relative in-tune-ness of the notes.

15 Conclusion: Restoring the Recording

To put our findings to some practical archival use, we restored the British Library’s recording. We increased the speed of the recording to match the original and used pitch-correction software to remove the effects of the wobble. We also filtered out extraneous noise from the recording.

Nobody had heard the true sound of the computer since the early Ferrantis were scrapped more than half a century ago. A German researcher David Link attempted to recreate the sound, by programming his emulation of the Mark II.Footnote 76 But an emulation is far from being the real thing, and without the original physical components, including of course the hooter, an emulation cannot recapture the actual sound. But now, thanks to an improbable meeting—in New Zealand—of the 1951 recording and modern analytical techniques, we really can listen to Turing’s Mark II.

Our restoration is now in the British Library (reference number H3942) and can be heard at www.AlanTuring.net/historic_music_restored.mp3.