Pick up a telephone and press a key. What leaves the handset is two tones at once, one from a low group and one from a high group, and the pair identifies the digit. Everybody who has ever held a phone knows this, in the sense that everybody has heard it.

The interesting question is not why two tones. It is why those two tones. The answer is that around 1960 a group of engineers set out to design a sound that a human being cannot make by accident.

The first design worked by muting you

An earlier scheme for pushbutton dialling did four things when you pressed a key. It generated a tone identifying the digit. It generated a second tone identifying the party. It stepped down the direct current the set was drawing. And — this is the one that matters — it temporarily disabled the speech transmitter.

That last item is the entire original solution to the central problem. The danger in signalling with audible tones inside a voice channel is that the channel is full of a voice. Speech and music are loud, broadband and relentless; sooner or later a syllable or a note lands where a signalling tone is supposed to be, the equipment believes it, and a digit appears that nobody dialled. The Bell System had a name for this, and it is a good one: talk-off.

The first design defeated talk-off by switching off your microphone while the tone went out. You cannot interfere with a signal you have been muted for.

Then the requirement changed

That early plan only had to carry information from a handset as far as the local central office. But it would be far more useful, L. Schenker wrote in the Bell System Technical Journal in January 1960, to signal end-to-end — over any established connection that will transmit speech. Not merely to the exchange. Through it, and out the far side, to whatever is listening.

That single change of scope destroyed the original defence. If the tones must survive an ordinary voice connection all the way to a distant machine, they have to live inside the voice channel for the whole journey. And you cannot mute a customer at the other end of a call you do not control.

So the engineers lost the ability to silence the human, and were left holding the problem in its pure form: build a signal that speech and music will not produce by accident, across millions of calls, for decades.

Particularly difficult of imitation

Schenker's statement of the problem is one of the quietly confident sentences in engineering: since signals with a simple structure are prone to frequent imitation by speech and music, some form of multifrequency code particularly difficult of imitation is indicated. Immediately before it, he concedes the method — protection against talk-off must rely heavily on statistical tools.

There is no elegant circuit that can distinguish a tone from a voice on principle. There is only the observation that human sound has a shape, and the patience to go and find the places that shape does not reach.

The result is the four-by-four code. Four low frequencies — 697, 770, 852 and 941 hertz — and four high ones, of which 1209, 1336 and 1477 are the columns you have used and the fourth was reserved for purposes most people never encountered. Every digit is one tone from each group and never two from the same group, which by itself rules out an enormous class of accidents.

The frequencies were then chosen against the arithmetic of sound. No frequency in the set is a harmonic of another, so a note's overtones cannot be mistaken for a different note's fundamental. The second harmonic of 697 hertz is 1394 — which falls, conveniently for everyone, in the gap between 1336 and 1477, hitting neither. The sums and differences that two simultaneous tones inevitably throw off were checked as well, and steered into empty ground.

None of these numbers are musical. That is precisely the point. They were selected for being inconvenient to a voice.

What you are holding

The system went to a field trial with something like four hundred customers, and the customers liked it.

What survived is a keypad that has outlasted the switching equipment it was built for, the handset it was built into, and very nearly the telephone call itself. It is still in your phone. Automated systems on the other side of the world are still listening for it. It works because somebody accepted an unflattering premise about the medium and then designed honestly against it.

The premise is this. The channel is full of a human being; the human being is loud and unpredictable and can no longer be switched off; and the only way to be heard reliably through all of that is to say something a human cannot accidentally say.

You cannot whistle a phone number. Not because whistling is imprecise — a good whistler is very precise indeed — but because those particular pairs were chosen, out of the entire audible range, for sitting outside what a person is able to produce. The keys under your thumb are a small monument to the proposition that you are noise.