An octave is a specific interval or distance between two pitches.
In musicology, an octave is a distance between two pitches. In which, one pitch has a frequency that is twice the other (2:1). For example, a string that vibrates at 880 times per second produces a pitch that is an octave higher than a string that vibrates at 440 times per second.
Because of this "twice as fast" frequency relationship, when we hear two pitches that are an octave apart, we perceive them as being very similar, and therefore, they are given the same letter name. For example, a pitch produced by a string vibrating at 440 times per second is called "A", and another pitch produced by a string vibrating at 880 times per second is also called "A".
Since modern musical notation typically uses seven letters of the alphabet (and accidentals) to represent different pitches, the cycle starts again after the eighth. Therefore, pitches that are named with the same letter are part of the same "pitch class", or simply "octave".
Octaves are used in most of the music systems, such as tonal music (major and minor keys), pentatonic music, and serial music (twelve-tone technique).
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.