O-PEN THE DOOR
THE SE-CRET OF THE MIND
THE POR-TAL OF THE HEART
AND THERE IN-SIDE IS THE
GATE TO HEAVEN Try speaking this in the rhythm of the opening of the Fugue subject!
To some people there is a natural connection between mathematical and musical ability; to others maths and music seem to occupy very different parts of the brain. To someone who struggles with music theory but has an ear that can take a song in at one hearing and reproduce it note for note the maths will probably seem quite irrelevant. But to a composer fascinated by numbers the riches of mathematics are as infinite as the series of prime or Fibonnaci numbers.
I remember being astonished when I suddenly realised in the sixth movement of Messiaen’s great Quartet for the End of Time – the unison movement – that the apparently random collection of note lengths were actually composed and presented as a set of perfect palindromes. 3 + 5 + 8 + 5 + 3, 4 + 3 + 7 + 3 + 4, 2 + 2 + 3 + 5 + 3 + 2 + 2 and so on. In a totally different context, I remember the excitement of understanding that the well known West African bell pattern, which can be symbolised * - * - ** -* -* -* actually has the beat or pulse on every third note *--*--*--*--. When you hear these two together, there is this wonderful sense of two different metres being heard simultaneously even though the whole pattern can be understood easily enough in Western terms as a repeating pattern of twelve fast semiquavers. Try it for yourself and see – tap the bell pattern with your right hand on right knee, and the pulse with left hand on left knee. It’s fun!
For explaining the real difference between 3/4 and 6/8 time – which is something a lot of amateur students of music find quite confusing – there is no better example than the opening of the song America from Bernstein’s Westside Story. One bar in 6/8 with 2 beats followed by one bar in 3/4 with three beats. Same duration, but totally different feel. It’s always a great feeling as a teacher when you see someone suddenly understanding this directly. This is not paper knowledge, but real musical knowledge.
Many mathematicians through the ages have devoted years and years of their lives to discovering proofs which only a tiny number of people in the world understand., But for the wider population, surely the more important thing than proof is fascination. And one of the groups of people most fascinated by numbers are composers. This was as true in the medieval world as it is in the contemporary world. It is as true in the world of Indian music as it is in the West. The link between pattern in number and pattern in sound is a deep one in the human experience. Maybe it is a way of connecting with our own physical reality, the changing pulse rate of our material existence.