Dodicesimi

Dodicesimi, also known as "twelfths," is a tuning system used in music that divides the octave into twelve equal semitones. This system, more formally called equal temperament, is the most common tuning in Western music today. The advantage of dodicesimi is that it allows for playing in all keys without significant intonation problems, which was a challenge with earlier tuning systems like meantone temperament.

In dodicesimi, the ratio between the frequencies of any two adjacent semitones is constant. This ratio is the twelfth root of two, approximately 1.05946. While this means that intervals like perfect fifths are slightly out of tune compared to their pure Pythagorean or just intonation counterparts, the difference is generally small enough not to be objectionable to most listeners. This slight compromise in interval purity allows for the seamless modulation between keys.

The development and widespread adoption of dodicesimi were gradual processes. By the Baroque era, composers were exploring its possibilities, and by the Classical and Romantic periods, it had become the standard. Many keyboard instruments, such as pianos and organs, are tuned using dodicesimi. String instruments and wind instruments often adjust their intonation slightly in performance, but the underlying tuning system is typically based on dodicesimi.