12edo

12EDO, also called 12-TET (twelve-tone equal temperament), is a musical tuning system in which the octave is divided into twelve equal parts. The frequency ratio between adjacent semitones is the twelfth root of two, approximately 1.059463, and the octave spans a 2:1 ratio. Each of the twelve pitch classes within an octave is assigned a fixed frequency, so notes such as C sharp and D flat are the same pitch in 12EDO. By design, there are 12 equal steps per octave, corresponding to a 1200-cent octave, with each semitone measuring 100 cents.

In 12EDO, the chromatic scale is uniformly spaced, which makes transposition and modulation between keys straightforward. It provides a practical framework for keyboard and fretted instruments, where fixed pitch makes alternative tunings more complex. The system is independent of absolute pitch reference; in modern practice, A4 is commonly tuned to 440 Hz, though other reference standards exist.

Historically, Western music used various tolerances (temperaments) that altered intervals to favor certain keys. 12EDO emerged as a practical standard in the 18th and 19th centuries, enabling near-uniform intonation across all keys and becoming the dominant tuning in most Western music, including classical, jazz, and popular genres. It is a tuning convention rather than a scale, providing a common framework for notation and performance.

Limitations of 12EDO include the regular compromise of intervals that are simple in just intonation, such as major thirds and perfect fifths, which deviate from their pure ratios. Other tunings, microtonal systems, and historical temperaments exist for specialized aims, but 12EDO remains the default tuning in much of Western music today.