In Perfect Harmony

I hugely enjoyed this book, which I think was only published this summer: a fascinating blend of music, physics and maths, by somebody who seems to have a real understanding of all three.

One mark of how good the book is that even in the sections where I already knew more or less what he was writing about, I learned more.

Amongst the random stories I found within it...

• I knew about Galileo's father, Vincenzo, being a professional lute player (a luthier?), but I hadn't read before about what a key figure he is in music history, establishing the relationship between the tension of a string and its frequency - and doing so by experimental methods, which was surely central to his son's later insistence on matching theory with experimental results.

• The lower temperatures found in Europe during the little ice age (1700s) hampered the normal growth of trees. This reduced the contrast between the softer wood that grows in summer and the denser growth of winter in Spruce and Maple trees, and this seems to be key to the particular tone produced by the violins manufactured by Stradivarius and others in that time.

• An MIT team in 2015 established that for violins, the loudness of the sound produced is proportional to the perimeter of the f-hole rather than its area.

• The history of the standard tuning of A = 440 Hz is covered in detail and its a mix of fascinating stories. (A is selected, for example, because most string instruments have an A string.) Prior to the 440 Hz standard, a mix of regional standards would apply - often determined by the tuning of local church organs: and as repairs over the years would often shorten the pipes of those organs, the regional tuning would have to adapt to match it. This became a problem in Germany in the 1700s - because singers were finding it increasingly difficult to match the slowly increasing pitch.

• Interestingly, the existence of tuning forks (again the 1700s) provides us with a historical reference point. We know that most of Handel's music for example, including the Messiah recital in Dublin in 1742, would be considered very flat to modern ears. His tuning fork still exists and corresponds to A at 422.5 Hz.

It is a mark of the times that I found myself noting at several points that 'there could be an AAC in this.'