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3. Prelude and Fugue in C sharp major from Book 1




THROUGH THE WORLD               Try speaking this in the rhythm of the opening of the Fugue subject

In one way, numbers appear to offer a limited number of possibilities. After all, including zero, there are only ten of them : 0 1 2 3 4 5 6 7 8 9 Every other number is formed from this finite simple group, even such exotic numbers as 3/4 to the power 5/2. But from a different perspective in the human mind there are an infinite number of possibilities in the number world. There are even an infinite number of very special numbers like prime numbers and Fibonacci numbers. When it comes to music we find a similar paradox. It seems at first glance - or maybe first hearing - that there are only twelve different notes, and all the pieces of music in the world are simply different combinations of those same twelve notes. For the vast majority of Western music this is in the theoretical sense true. But in a more subtle sense you only have to talk to a violinist to learn that an A sharp in the key of B is not the same sound as a B flat in the key of F. For the pianist maybe, but not for anyone able to use their ear to create different pitches on their voice or instrument. Sound is physical vibration - notes sound ‘good’ together, what music theorists call consonant, because their vibrations match up mathematically. Notes sound ‘bad’ together, or what music theorists call dissonant, because their vibrations do not match up mathematically. Harmony is created out of different combinations of consonance and dissonance. If you play a major seventh interval, e.g. C and the B above, together on the piano the energy of the sound is harsh and is interpreted by many, perhaps most, people as being quite unpleasant. But now if you add the E and the G in the middle and play all four notes together the sound is quite different. The major seventh chord which results is a familiar jazz harmony and is interpreted by many people as mellow, cool, sophisticated. Many people who insist that they cannot understand or enjoy ‘modern music’ (which sadly for some includes most of the last 100 years) because of the dissonance will nonetheless accept and enjoy the ‘same’ dissonance, e.g. a minor ninth, in Bach or Beethoven. In other words, context is everything. Numbers, like musical notes, do not fascinate in isolation but in the way that they combine together, the way they hold memories, the way they make promises for the future. People belive in lucky numbers, they will choose birthday and anniversary date numbers for lottery tickets. They also believe in unlucky numbers - I was fascinated as a young child in suburban Birmingham by the absence of the number 13 from the house numbers in every road. Some numbers gain mythic significance very rapidly in the modern world. What do you first think of in relation to 42.................... 13 3/4 ............ 9 3/4............. 9/11............... * Equally some numbers can have multiple signifiers - does the number 111 make you think first of cricket or Beethoven? The two images for me - one of the cricket umpire David Sheppard standing on one leg until the batsmen scored another run; the other the extraordinary use of unusual time signatures like 12/32 in Beethoven’s last piano sonata - are both strongly connected to the number 111.

It has often been suggested that musical and mathematical ability go together, but in some ways they seem to come from very different areas of the brain. In my experience it is often the case that people who are very competent at sight reading and music theory are also good at mathematics. But these skills in themselves do not guarantee that someone is really musical. A good ear for music in terms of awareness of sound, pitch pulse, dynamic, articulation and phrasing does not appear to come from the same part of the brain. The result is that it is possible to be really musical whilst still finding the more mathematical skills of sight reading and music theory quite elusive.


*  My guess is for most Westerners : Hitch Hiker’s Guide to the Galaxy; Adrian Mole; Harry Potter train platform; New York 2001