tasasointi

Tasasointi, often translated as harmonization or equal temperament, is a tuning system that divides the octave into a specific number of equal steps. In the most common form, the twelfth root of two is used as the frequency ratio between adjacent semitones, resulting in twelve equal semitones within an octave. This system is prevalent in modern Western music as it allows for playing in any key without significant pitch distortion.

Historically, various tuning systems existed, such as meantone temperament and well temperament, which favored certain keys over others. These systems often produced purer intervals in some keys but made modulation to distant keys sound dissonant. The development of equal temperament was a gradual process, with theoretical discussions dating back centuries. Its widespread adoption was facilitated by the increasing complexity of musical compositions and the desire for greater harmonic freedom.

The mathematical basis of equal temperament is that the frequency ratio of an octave is 2:1. Dividing this octave into twelve equal logarithmic steps means that the ratio between any two adjacent notes is the twelfth root of two (approximately 1.05946). This precise mathematical division, while making all intervals slightly impure compared to their just intonation counterparts, provides a consistent and predictable tuning across all keys. This consistency is crucial for instruments with fixed pitches like pianos and guitars, and for the practice of modulation in orchestral and chamber music.