Background Information
Pythagoras' discovery
Man's relationship with music is rooted in nature. The ancient Greeks first started arranging notes into scales to create a pattern, and it was the mathematician Pythagoras (c. 580 B.C. –500 B.C.) who created the first real scale. His invention had a profound effect on early western music. He was passing a blacksmith's forge one day when he noticed the sounds of the metal being hammered and realised that the hammering made different regular notes. When he weighed the hammers, he discovered that they were all ratios of each other. The first was half the size of the next and another was two-thirds the size of the first, and so on. This demonstrated natural harmonics. One note played on, for example, a metal bar can produce many harmonics (higher notes). A bar half the size will produce a note an octave higher. A bar two-thirds the size will produce a note a fifth higher (the dominant note). The ratio of two-thirds is a naturally harmonious relationship in mathematics and it was this that caught Pythagoras' attention. He was also a mystic who believed that the universe made its own music by the movement of the planets. He felt music would be more powerful and mystical if it obeyed the natural laws of physics, so he set about making a scale of notes by dividing metal into simple ratios, thus creating a spiral of notes. However, when he came to the thirteenth note of the scale, he realised that it was slightly different to the first one and when the two were played together, the result sounded awful. This problem was later to be called 'the Pythagorean comma'. The notes were not equally apart all the way up the spiral. Pythagoras' solution was simply to abandon the thirteenth note and he was left with a twelve-note scale. To play safe, musicians kept to the first seven notes of the scale and along with the original note they had an octave. The average instrument could only cope with six notes anyway, and even up until the late thirteenth century music was kept as simple as possible.
Church music, however, required more sophistication, so composers introduced other lines to create more interesting sounds. Now the first and third notes of the scale sung together sounded fine. Also the first and fifth notes, but others didn't work. This is because the thirds and sixth notes came further up the Pythagorean spiral and sounded dissonant. Medieval music sounds rather austere to our ears as it lacks the warmth of thirds and sixths.
John Dunstaple
It was not until the fifteenth century that musicians started experimenting with thirds and sixths. One of the most influential composers at this time was John Dunstaple (died 1453) who, like Pythagoras, was fascinated by astrology. He kept away from writing keyboard music with its fixed intervals and experimented instead with the flexible and re-tuneable human voice. His compositions must have sounded very modern in their day. Dunstaple was invited to compose at the English court in France, where they loved his music and developed it, thus moving music out of the Dark Ages and into the Renaissance.
It was during the Renaissance that the relationship between the sciences, arts and mathematics was re-examined. Composers started writing for four and even more voices. This was possible as voices could tune themselves to make the sound pleasing to the ear.
Keys
Each note of the scale gives birth to a new family of notes. These families are called 'keys'. The problem caused by the Pythagorean comma is that very few of these families of keys can work well together in the same piece of music. Nearly all the music written up until the late Renaissance was composed in a single key, so the instruments were tuned to the key of that piece. However, composers started wanting to use more than one key in a piece. There then followed attempts to create a tuning system, but there were several different systems in use. Furthermore, a tuning that worked for one piece of music didn't work for another and using instruments with different tunings together in the same piece was unworkable, too. Composers realised that the ideal would be to create equal temperament: a single mathematical pattern of notes which would become the blueprint for all the keys and enable different keys to be used in the same piece of music. How could this be done?
The big bang
The man who would develop a solution to this problem and therefore change the course of musical history was the great J.S. Bach (1685–1750). In 1722, he produced the most important book of keyboard pieces ever written: 'The Well-Tempered Clavier". It comprises two series of preludes and fugues, each series including all the twelve major and all the twelve minor keys. This used equal temperament, which meant an adjustment in the tuning of the keyboard away from the 'natural' scale. Its publication was a critical turning point in the history of western music. Without it, the complex works of future composers could never have been written. Composers now had the tools to move easily from key to key.
Thanks to Victorian engineering, Bach's principles could be applied accurately to all other instruments, which were soon mass produced and exported all over the world. The accordion, invented in 1830, had a profound effect on ethnic and folk music. It was loud and forced other quieter instruments to tune to it. The old harmonies and chords of Eastern European folk music were soon replaced by the man-made tuning.
One culture, however, rejected this system of tuning in favour of the natural one. The Chinese had already worked out the system that Pythagoras developed, but rejected it. The relationship between man and nature was more important. They continue to use the first five notes of the ancient scale, which is known as the pentatonic scale. Perhaps as western music is heard more and more in their culture, their system may eventually be eroded.
