In the days when I was a violinist, I would often be exasperated as to how long it could take me to tune the damn instrument satisfactorily. Sometimes something similar happens when I tune a guitar. There could be several reasons for this, most of them revolving around the central fact of my own incompetence, but there is one intriguing possibility: that my ear is perhaps too sensitive.
For the most striking anomaly in the world of music is that the notes of the musical scale do not, so to speak, add up. If you progress in a cycle of pure fifths (where the notes have a ratio of 3:2, as imagined, say, by the length of the strings plucked) from a starting note of C, when you next end up at a C, you end up a quarter of a semitone too high. This might not seem too disastrous, but it doesn't sound good - "an excruciating discrepancy", as Professor Duffin puts it.
He knows that he is dealing with what may superficially look like an abstruse subject. And, looked at one way, it is: for the past 200 years or so, musicians have been nudged towards the orthodoxy of Equal Temperament (ET), until its almost complete ubiquity in the 20th century. Most audiences of the western canon (and this means pretty much everything we hear in Britain apart from some of the more far-flung world music on Radio 3) are hearing notes played from a scale where everything has been flattened ever so slightly in order to even out the differences. So it is, in a sense, a non-problem - in the way that the elephant, safely ignored in the corner of the living room, is also a non-problem.
But look at the fingerboard diagram from Peter Prelleur's The Modern Musick-Master (1730-31) and you will notice that C sharp comes before D flat; and E sharp is pitched higher than F flat. (We don't even have a note called F flat any more.) In 1797, another fingerboard diagram is still saying that F sharp is higher pitched than G flat, and so on. For a piano to work without ET, it would have had to have split-key accidentals: 17 keys to the octave rather than the 12 we are familiar with.
I used to have a very glancing acquaintance with this problem, but assumed, like many others, that the business had been sorted out around the time when Bach composed The Well-Tempered Clavier. Wasn't that what the very title of his work meant? No, says Duffin: it was written for an irregular temperament that worked in a wide variety of keys, and one which meant you didn't have to retune the instrument whenever you changed keys - but it was not ET. (Duffin cites evidence that Bach's son Johann Christian was importing split-key pianos in 1766, which suggests that his father had not abandoned them.)
Haydn, in 1802, made an explicit note in the autograph score for his Op 77 No 2 Quartet that a cello's E flat is to be played as if it were a D sharp - more evidence that this was by no means common practice. And when Beethoven started going deaf, was he still hearing his compositions in the old style, or in newfangled ET?
As I say, you might find this an abstruse subject, but Duffin goes out of his way to make it accessible to as many people as possible: short, punchy, and interspersed with potted biographies of musicologists and, should you need them, cartoons.
If I may propose an analogy of my own: ET is like pasteurised cheese, which means it's easier to make and more people can eat it; but it doesn't have as rich a flavour. Similarly, ET was born from the need to supply the expanding middle class with instruments they could play among themselves with the minimum of difficulty. (And the increasing use of vibrato may well have been used to mask some of the ensuing small crashes of harmony when string players accompanied keyboard instruments.)
Duffin knows what he's talking about - and you won't think about music in the same way again.
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