Equal temperament
Equal temperament is a musical tuning system in which the octave is divided into 12 equal semitones, with each semitone having a specific frequency ratio to the one below it. This system allows for Modulation and Chord progression to be used in a variety of keys without the need for retuning instruments. The use of equal temperament has become widespread in Western music, particularly in the context of Classical music and Jazz. It was first proposed by Zhu Zaiyu, a Chinese prince and musician, in the 16th century. The system is based on a mathematical division of the octave, using the Dirac delta function to calculate the frequency ratios between notes. Equal temperament has had a significant impact on the development of Western music, enabling the creation of complex Harmony and Melody.