THERE ARE TWELVE KEYS MA-JOR,
TWELVE KEYS MI-NOR
AND FOR EV-ERY KEY
THERE ARE TWO PRELUDES AND TWO FUGUES Try speaking this in the rhythm of the opening of the Fugue subject!
There are twelve different notes in the chromatic scale, and then we return to the opening note again, an octave higher. The octave always sounds in harmony because the frequencies of the notes match up in simple mathematical ratios. Similarly the fifths in between the octaves. For instance : - //A 110 /E 165 /A 220 E/ 330 A/ 440 E// 660 Each of the twelve notes of the chromatic scale is the base note for two scales, one major and one minor. The Well-Tempered Clavier consists of two pieces - a Prelude and a Fugue - for each and every major and minor key. One collection of pieces was written in the 1720s; the other in the 1740s. In total, then, we have 12 x2 x2 x2 = 96 short pieces of music. But the collection is always known as the ’48’ because the Prelude and Fugue are always played consecutively as if they were different movements of a single piece. Other composers have written sets of pieces in all the twenty-four keys. For piano, the most famous are Chopin’s set of Preludes, Op 28 and Shostakovich’s sets of Preludes Op 34 and Preludes and Fugues, Op 87, inspired by the composer’s hearing the Bach ’48’ performed by Tatiana Nikoleyeva in 1950. But why not symphonies? No-one as far as I know has ever tried to write a symphony in all 24 keys. The largest collection of symphonies is that of Haydn, which at 104 is unlikely to be surpassed. There are, nonetheless, several keys that he left untouched. There are many practical difficulties tuning string and wind instruments together in more complex keys, and so the majority of symphonies in the classical and romantic eras were written in keys with no more than three sharps or flats. Meanwhile, the piano plays equally well in all keys - or equally badly in all keys if you happen to have the sort of perfect pitch that most of us are glad we don’t have! When I think of the number of symphonies written by famous composers I think immediately of 1,4,7,9,15,41 and 104. Of these numbers the 9 is famously important for proving an end point for several composers. Mahler, indeed, was so nervous about writing a 9th symphony in case it was his last that he famously titled his major symphonic work Das Lied von der Erde instead of Symphony No. 9. Now, in the spirit of making unlikely connections, if we take this special symphony number, 9, and multiply by the special chromatic scale number, 12, we arrive at one of the most powerful sacred numbers in all the world, 108. In the Tibetan tradition as indeed in many much earlier Asian traditions the number 108 takes on a special significance - the number of beads on a mala, the number of mantras chanted in one cycle of prayers. Astrologically, 108 is 9 Heavenly Bodies x 12 Signs of the Zodiac. It is 27 Lunar Mansions X 4 phases of the moon. In Buddhism it is also 6 (consciousnesses) x 3 (preferences) x 3 (times - past, present and future) x2 (virtuous or non-virtuous). It also happens to be the case that the distance between the Earth and the Sun is 108 times the Sun’s diameter, and the distance between the Earth and the Moon is 108 times the Moon’s diameter. The Sun’s diameter also happens to be 108 times that of the earth. Why are numbers so important to us? Clearly in some ways they correspond to things that we understand - or think that we understand - very dimly. They are a tool for creating patterns of order in the chaos; they give us a framework for seeing and interpreting the world.In other ways, they seem to correspond to material reality - there is this particular number of children, this particular number of musical keys. From a slightly different perspective, however, we can see that the numbers we think of as ‘normal’ are in fact the exception. On a sliding scale of all numbers, 1,2 and 3 are all extraordinary exceptions just as on the sliding scale of all musical vibrations, what we on the piano call C,D and E are extraordinary exceptions. A violinist can understand this more easily than a humble pianist, for the latter can only play the notes which are set in front of him/her whereas the violinist can make an infinite number of notes between for example the D/ and E/ of the piano. Where does his leave us? Maybe with a sense of wonder that we really understand so little. The numbers that we love to make sense of our lives are only a tiny fraction of the whole. Just as the physicists are discovering that the very stuff of the material cosmos is for the most part emptiness rather than solidity. Just as the mystics of all traditions have always known that the reality we think we understand is but a tiny fraction of the big picture.