Sobbing Children and Singing Shillings

Picture a man climbing the stairs of the Royal Exchange in London—this is in the old days of the grand stone building, before it burned down, in 1838—and imagine him ascending to the high gallery, up among the lottery booths, the mathematical-instrument makers, the Merchant Seaman’s Office and the Lloyd’s Subscription Coffee House. Over the railing and down in the quadrangle below, around the courtyard statue of Charles II, are moneylenders and merchants of the exchange: noise roils up from them.

Our observer in the gallery is a diminutive man, with a searching look, and he may be scratching his curly white locks as he listens; he may be wearing his old favorite frilly-fronted shirt. And he focuses intently—not on stock tips or on any specific words at all, but rather on the aggregate sound.

And he may note it as part of his ongoing project—the notes he is taking for his book—labeled The Music of Nature.

This crowd, he decides, is in the key of F.

There is no accounting, really, for a mind like William Gardiner’s. He was born to a Leicester hosiery-maker, and raised to take over his family trade; one of his earliest recollections was going to an immense orchestral benefit concert in 1774, at the age of four, and being taken into the orchestra by his indulgent father. The boy sat by the fourth Earl of Sandwich—yes, that one—and was transfixed as the Lord walloped enthusiastically at some kettledrums. The boy’s course for the next seventy­ years was now set: his living would be making stockings, but his life was in making music.

When Gardiner is remembered today, it’s for a fortuitous act of musical appreciation: In 1794, Abbé Döb­ler, a musician in political exile­ from Cologne, was sheltering in Lei­cester and stopped by to see the young stocking-maker. He’d heard Gardiner was a great music-lover, and showed him a violin trio in E-flat written by a still-obscure young acquaintance back home. Gardiner was so utterly taken with it that he arranged a local performance. The unknown composer was Ludwig van Beethoven—and the performance was quite possibly the first of his work outside his native country.

But if the young stocking-maker had been one of the first to stumble onto the landmark genius of his age, haunting the galleries of the Royal Exchange was a more deliberate project—a different sort of musical appreciation altogether.

For William Gardiner wanted to change not whom we hear, but how we hear.

Gardiner’s magnum opus, published in 1832, gives you a clue to its peculiarity the moment you open it: a hand-tinted frontispiece represents, through a...