Just intonation is a tuning system that is based on the proportions of natural numbers. It is characterized by large frequency differences between notes.
Just intonation is different from the twelve-tone equal temperament which frequently used in the modern keyboard instruments (e.g.: piano). Just intonation allows for larger frequency differences between notes while twelve-tone equal temperament limits the frequency ratios between notes. These differences can be discerned by the human ear.
Just intonation has been used since ancient Greece, where many musicians and philosophers believed that the essence of music lies in its adherence to mathematical principles found in nature. This tuning system is still used in the modern time by many musicians and composers.
Writer: Frankie Chan
Ludwig van Beethoven, German composer, the predominant musical figure during the transition between the Classical to Romantic eras. He occupies an unprecedented dominance in the history of Western music history, and has been widely regarded as the greatest, most influential and most popular musician who ever lived.
Beethoven's music inherited the artistic atmosphere of Haydn and Mozart, penetrated the desire for dignity, vented the anger tortured by fate, and demonstrated his determination to fight with fate.
Compared to other musicians, Beethoven is effectively to interact the philosophy of life with audience through music. Although he was not a romantic, he had become the object followed by other romantics.
As a musician, Beethoven suffered from ear diseases. However, he was unwilling to succumb to fate, vowing to take fate by the throat, and continue to complete his career. In the last ten years of his life, without hearing any sound, his compositions influenced the development of music for nearly two hundred years.