The musical note that can trigger cold sweats and sightings of the dead

Imagine that all the frequencies nature affords were laid out on an extended piano keyboard. Never mind that some waves are mechanical, propagated through air or some other fluid, and other waves are electro-magnetic and can pass through a vacuum. Lay them down together, and what do you get?

The startling answer is a surprisingly narrow piano. To play X-rays (whose waves cycle up to 30,000,000,000,000,000,000 times per second), our pianist would have to travel a mere nine metres to the right of middle C. Wandering nine and a half metres in the other direction, our pianist would then be able to sound the super-bass note generated by shockwaves rippling through the hot gas around a supermassive black hole in the Perseus cluster – a wave that cycles just once every 18.5 million years.

Closer to home, how big do you think that piano would have to be for it to play every note distinguishable by the human ear? You’d have to add barely a single octave to either side of a regular concert grand.

Readers of Richard Mainwaring’s wonderfully titled book will fall into two camps. Some will want to hear what this ‘infinite piano’ conceit reveals about the natural world: about the (considerable) auditory abilities of spiders, say, or how 23 high-stepping fitness junkies caused a tremor that evacuated the 39-storey Techno Mart building in Seoul, South Korea.

Other readers, though entertained well enough by Mainwaring’s extraordinary clear and concise science writing, won’t be able to get that infinite piano out of their heads. It’s a metaphor so engaging, so intuitive, it’s quite as exciting as anything else in the book (for all that it features ghosts, whales, neolithic chambered cairns and Nikola Tesla).

Mainwaring is a musician and composer, and the business of music underlies even his most abstruse intellectual excursions.