"Equal Temperament" is a musical tuning system that divides the octave into equal intervals, ensuring that all half steps between adjacent notes have the same frequency ratio. This tuning system allows for consistent and flexible modulation between different keys, but it comes at the cost of sacrificing the purity of certain intervals.
Equal Temperament is a widely used tuning system, particularly in keyboard instruments like the piano and many modern instruments. In this system, the octave is divided into 12 equal parts, each representing a half step or a semitone. The frequency ratio between adjacent notes in Equal Temperament is the twelfth root of 2 (approximately 1.05946), which ensures that the distance between each half step is the same.
However, this uniform division of the octave comes with a trade-off. In traditional tuning systems like "Just Intonation", intervals are tuned based on pure integer ratios, resulting in perfectly harmonious intervals. In Equal Temperament, intervals are adjusted slightly to achieve equal spacing, which means that certain intervals are no longer pure. For example, the perfect fifth and major third intervals are slightly narrower in Equal Temperament compared to pure tuning.
Despite this compromise, Equal Temperament offers significant advantages. It allows for seamless modulation between different keys, as all keys have the same pattern of intervals. Musicians can play in any key without encountering jarring dissonances when transitioning between different tonalities.