In a sly joke, the deity who invented music made sure that the mathematical proportions of "pure" acoustic intervals don't quite add up properly. So in order to play harmonically rich music in different keys, you have to skew the tuning in one way or another. Our current method is called "equal temperament", which is what modern pianos have, and in which the major thirds are sharp and the fifths are flat. Lots of people think that Bach's Well-Tempered Clavier was propaganda for equal temperament, and that everyone settled on it soon thereafter. But, as Duffin's scholarly and enjoyably pugnacious book shows, that's not the case: Bach used a different temperament, which slightly favoured some keys over others. Equal temperament was not universally adopted until the 20th century, and Duffin thinks it should still not be the default. He offers cute capsule biographies of major thinkers in the tuning debates and arguments, based on score markings and other evidence, about what composers such as Haydn or Beethoven would have expected. He even imports early records into a software program to analyse the pitches and find out how people were tuning their violins. Most controversial is his argument that string players should play leading notes flatter than in equal temperament (in order to favour harmonic consonance over melodic shape), rather than sharper, as they have traditionally done. None the less, his fine book should make any contemporary musician think differently about tuning.
The Original Accident, by Paul Virilio (Polity, £14.99)
To invent the train, says Virilio, is to invent the train wreck. Our society is predicated on the industrial accident, which only recently leapfrogged the natural disaster in destructive power. From this spiky proposition, Virilio, the ludic French "dromologist" (student of speed), careers off on a kind of intellectual rollercoaster that takes in Aristotle, Chernobyl, the twin towers, genetic engineering, the privatisation of police forces, cosmology, Rabelais, killer asteroids, and a wonderful short story by Ursula Le Guin, written from the point of view of a tree. Virilio's breakneck pattern-recognition method is apt to spark new thoughts in some readers' heads, even if his images are sometimes hostages to pedantry: "If knowledge can be shown as a sphere whose volume is endlessly expanding," Virilio writes, "the area of contact with the unknown is growing out of all proportion." Does it matter that the surface-area-to-volume ratio actually shrinks, not expands, when a sphere grows? I leave it to you to decide.
What Is Your Dangerous Idea?, edited by John Brockman (Simon & Schuster, £12.99)
The results of the 2005 Question at edge.org, posed by Steven Pinker, are in. Apart from an exasperating section about "memes" (are they still fashionable?) and a few Eeyorish dullards, it's a titillating compilation. Physicist Freeman Dyson predicts that home biotech kits will become common; others posit that democracy may be a blip and "on its way out", that "heroism" is just as banal as evil, and that it will be proven that free will does not exist. There are also far-out but thought-provoking notions: that, given the decadent temptations of virtual reality, the only civilisations of any species that survive to colonise the galaxy will be puritan fundamentalists; or that the internet may already be aware of itself. I particularly enjoyed cognitive scientist Donald D Hoffman's gnomic pronouncement that "a spoon is like a headache", and mathematician Rudy Rucker's robust defence of panpsychism, the idea that "every object has a mind. Stars, hills, chairs, rocks, scraps of paper, flakes of skin, molecules". Careful what you do with this newspaper after you've read it.