When a violinist tunes his instrument he is making sure that his four strings are tuned perfectly to G, D, A and E. Each string is wound around a peg near the top of the scroll, so that turning the peg changes the tuning. He may also have “adjusters” or “fine tuners” which are at the other end of the string where it is attached to the tailpiece. The adjusters make it easier to make small changes to the tuning. The violinist will make sure that the A is in tune, then the A and D can be played together so that they are exactly a fifth apart, then the D and G and finally the A and E are compared.
If they are not tuning to a piano, players of instruments sometimes use a tuning fork which gives an exact note (usually an A) so that they know they are in tune. There are also electronic tuning devices.
When an instrument such as the piano is tuned, the piano tuner has to know how to make each note relate correctly to the others. During the course of music history there have been several systems of doing this. These different "tuning systems" are all about the exact scientific relationship between the notes of the scale. There has been an enormous amount of discussion among musicians about how best to tune instruments.
When two notes are an octave apart the higher note is vibrating at twice the speed of the lower note. For example: if a string is vibrating at 440 Hz (440 times a second) the note we hear is an A (the A above Middle C on the piano). If the string is stopped halfway up (e.g. because the player presses it down with a finger) it will vibrate at 880 Hz and we will hear the note one octave higher.
The note which vibrates at 1 ½ times the frequency of the basic note will be the note a perfect fifth higher (an E).
If a piano tuner starts by tuning a C, then tunes a G so that it is exactly 1 ½ times the frequency of the C, he can continue tuning in fifths (a D, then an A etc.) until he arrives back at C again. However, he will find that, for mathematical reasons, the last C is not in tune with the first C. This was discovered long ago by Pythagoras and is called “the comma of Pythagoras”.
Musical tuning systems throughout the centuries have tried to find ways of dealing with this problem. From the 16th century onwards several music theorists wrote long books about the best way to tune keyboard instruments. They often started by tuning up a fifth and down a fifth so that these notes were perfectly in tune (e.g. C, G and F), then they would continue (tuning the D to the G and B flat to the F) until they met in the middle around F sharp. Sometimes old organs today are tuned by such a method. Playing in keys with very few sharps or flats (such as C, G or F) sounds very beautiful, but playing in keys with lots of sharps or flats sounds horribly out of tune.
In 1584, Zhu Zaiyu, a prince of Chinese Ming Dynasty, published the invention of equal temperament in his book "A New Account of the Science of the Pitch-Pipes." In 1585 Simon Stevin invented a similar system. Some scholars think one of these really invented this system. Others think both did, or neither.
Around 1700, based on this new system, the great composer Johann Sebastian Bach wrote two books of 24 preludes and fugues (called the "Well-tempered Clavier)" to prove that it was now possible to play in any key.
Here are some of the main ways of tuning the twelve-note chromatic scale which have been developed in order to get round the problem that an instrument cannot be tuned so that all intervals are "perfect":
List of members of the Red Army Faction
This is a list of Members of the Red Army Faction. After Andreas Baader escaped from jail in 1970, the media began referring to the "Baader-Meinhoff Gang". When Baader and Meinhof were arrested, they became known as the Red Army Faction.
These are the earliest members, from the late 1960s. The most important had all been arrested by 1972.
Other young terrorists available to swell the shrinking ranks of the Gang. Like the first generation they were mostly middle class and a lot of them were students. A lot of them were terrorists who joined the Gang after their own groups dissolved (e.g. the Socialist Patients' Collective (SPK), J2M).
This generation was active mostly throughout the 1980s and early 1990s. More vicious than their predecessors, they did not have as much cause as the earlier generations to rebel.
Captain of Köpenick
The Captain of Köpenick (born Wilhelm Voigt on February 13, 1849 - January 3, 1922) was a German shoemaker, criminal and impostor who became world-famous in 1906 for a trick he played in Berlin when he pretended to be a Captain in the army.
Voigt was born in Tilsit, a town which was then part of Germany but is now called Sovetsk near Kaliningrad, Russia. In 1863, aged 14, he was sent to prison for 14 days for stealing. He was expelled from school.
Voigt’s father taught him how to make shoes. However, Voigt continued to steal and forge and was often sent to prison. Eventually he was let out of prison in 1906.
Voigt travelled around until he went to live with his sister who lived near Berlin. He worked briefly as a court shoemaker until, on August 24, 1906, police expelled him from Berlin as an “undesirable” (someone who is not wanted). Although he was supposed to have gone to Hamburg he stayed in Berlin. He could not get a job because he was an unregistered citizen, but he could not register to live in Berlin because he had no job.
On October 16 1906 Voigt was ready for the big adventure that made him famous. He had bought parts of a captain's uniform from different shops. He had resigned from the shoe factory ten days before. He put on the captain’s uniform and went to the local army barracks, stopped four grenadiers and a sergeant on their way back to barracks and told them to come with him.
These soldiers had been taught to obey officers without asking any questions, so they did what they were told. He told the commanding sergeant to report to his boss, and told 6 more soldiers to come with him. Then he took a train with the soldiers to Köpenick, east of Berlin, occupied the local city hall and told the soldiers to guard all the exits.
He told the local Police to go and look for people breaking the law, and told the local Post Office not to let anyone make telephone calls to Berlin for an hour (this was in the early days of the telephone when people could not dial numbers automatically: they had to ask the Post Office to make the connection).
He arrested the town secretary and the mayor, saying that they had been taking money from the town hall, and he took a large amount of money: 4002 marks and 37 pfennigs, signing a receipt for it, but using the name of the governor of the jail where he had been.
Then he stopped two carriages and told the grenadiers to use them to take the mayor and the treasurer to the police so that they could be questioned. He told the remaining guards to stand in their places for half an hour. Then he went to the train station. Later he changed back into ordinary clothes and disappeared.
During the next few days the newspapers around the world reported what had happened. Everybody seemed to think it was a very amusing joke.
Voigt was arrested on October 26 and on December 1 he was sentenced to four years in prison for forgery, impersonating (pretending to be) an officer and wrongful imprisonment. However, so many people seemed to have sympathy with Voigt. Even the Emperor Wilhelm II was probably amused by it and he pardoned him on August 16, 1908.
In England everybody thought the whole story was funny. The English people thought it showed that the stereotype (idea) they had about Germans was right, i.e. that they were taught to obey orders and not to think.