4. Prelude for Max Penrose (3:15)This is a song without words, only three minutes long, but with the most intensive musical structure. It was inspired by my mentor Roger Penrose when he appeared on the BBC radio programme Desert Island Discs in 2000. He made Bach's B Minor Mass his principal choice, and emphasised Bach's emotional power.There is a simple explanation for the title of the Prelude: the piece has 69 bars of contrapuntal music, with a shift in harmonic style after 56 bars and a great surprise in the very last bar; you need only know that Roger was born in 1931, married Vanessa in 1988 and that Max was born to them in 2000. But there are other elements in the structure, related to the long, long development of Roger's twistor theory, which has continued with a time-scale unrelated to worldly expectations and in 2000 has come up with a surprise of great importance to me. One feature is that there are indeed 69 bars of time, but at three points they are suddenly interrupted by out-of-time sound, slow soft chords on vibraphone and solo strings. These have two effects I think — they make the busy work of the counterpoint seem oddly irrelevant and superficial when they resume, putting the ordinary measure of life and activity into question. But hear them another way and you cannot help seeing a ridiculous aspect — the way the music picks up and carries on after the interruption is just like a game of Musical Chairs. Sublime and ridiculous at once — this is rather how mathematicians' thought habits appear to those around them. Anyway, the 'timed' music has a fugal texture, based on a chromatic theme that is not unlike Bach's but developed with greater harmonic and instrumental freedom. The closeness of music to mathematics is well known, and the work of writing the counterpoint in this piece needs something like the total concentration of mathematical research. However this doesn't mean quite what many people would suppose: in both cases intuition and imagination are as important as careful calculation, and emotional involvement counts as much as the ability to hold a complex logical structure in one's head. (I would also say that music is a lot easier and much more fun than maths.) In the first 56 bars I have tried to convey by 'classical' means, without the use of romantic chord progressions, a sequence of episodes with different emotional tones. Like a sun moving behind a cloudy sky, there are moments suggesting enlightenment and breakthrough, and even a sense of continual progress, but nothing is completely resolved and clouds move over again; this reflects pretty accurately my own experience of continued mathematical research. This section culminates in a classical stretto over a prolonged pedal, but does not move towards a classical cadence. Instead, the following 12 bars recapitulate the theme in the bass, augmented by a factor of three, and a romantic dialogue of clarinet and bassoon develops. At this point the music of timelessness joins in , the vibraphone and solo strings providing the background. And then comes the surprise: classical form and expectations of Time are wholly discarded. The resulting discord (a minor ninth on C sharp) is resolved into G major by the opening of the next song, Gerry's Nightmare. © 2000 Andrew Hodges
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