Symmetry in Music

Symmetric and asymmetric music chordsI recently came across the idea of applying set theory to musical analysis (which apparently has been around for some time, although I’d never heard of it before). For most people, who have a stronger intuitive grasp of music than mathematics, this must seem a pointless exercise, but for anyone like me who’s the other way around it’s really very illuminating.

Take symmetry, for example. In most areas of the arts and sciences, symmetry is seen as a good thing – but in music, that’s not the case. All the most popular chords are asymmetric in terms of interval content. You can see that in the left-hand image above, which shows the three notes of the C major chord on the chromatic circle. They’re separated by intervals of 3, 4, and 5 semitones.

In contrast, an augmented C chord, shown on the right, is perfectly symmetric, with all three intervals equal to 4 semitones. The problem (as far as musicians are concerned) is that it’s not very firmly tied to C major. It could equally well be A flat or E major. In the same way, the four-note symmetric chord C – E♭ – F♯ – A can be interpreted in four different ways: as Cdim7, E♭dim7, F♯dim7 or Adim7.

There’s even a completely symmetric two-note interval, in the form of the tritone, consisting of two notes 6 semitones apart (or 3 whole tones, which is how it gets its name). That’s exactly half an octave, for example from C to F sharp. But it’s also the distance from F sharp to C, so you really don’t know which key you’re in. That’s why composers spent centuries trying to avoid it. They called it diabolus in musica, or “the devil in music”.

Being a symmetry-loving scientist rather than a musician, I decided to try writing something that consisted only of symmetric chords. It’s a sort of canon, in the key of everything.

Here’s a link to a YouTube video, with added graphics depicting the various chords on the chromatic circle. Hopefully you’ll enjoy the graphics even if you don’t like the music!

Telescopic Tourist video

I’ve just belatedly produced a promotional video for my book The Telescopic Tourist’s Guide to the Moon, which came out last summer. Here it is:

The background “music” (actually just a sequence of spacey sounding chords) is my own composition!

Needless to say, The Telescopic Tourist’s Guide to the Moon is available from all good bookshops, as well as online retailers such as Amazon.com and Amazon UK.

Dirac on Einstein

I was going through some old audio cassettes I recorded from the radio when I was a student, and came across a really interesting little snippet. It’s the physicist Paul Dirac reminiscing about Einstein on a BBC programme, though I’m afraid I’ve no idea which one. The note I made at the time says “recorded in March 1979″ – when Dirac would have been 76 (he lived to 82).

Although the quote is very short, it’s really fascinating – and a Google search didn’t turn up any other references to it. So I made a little YouTube video of it, which hopefully the following link will take you to:

Here is my transcript of what Dirac has to say about Einstein:

He wasn’t merely trying to construct theories to agree with observation. So many people do that; Einstein worked quite differently. He tried to imagine “If I were God, would I have made the world like this?” – and according to the answer to that question, he would decide on whether he liked a particular theory or not.

And I can’t resist adding a couple of Amazon links for my own book about Einstein:

Einstein book covers