Middletuned

Middletuned refers to a specific type of musical temperament, a system for tuning musical instruments, particularly keyboard instruments and fretted instruments. Unlike equal temperament, which divides the octave into twelve perfectly equal semitones, or just intonation, which relies on simple frequency ratios derived from the harmonic series, middletuning aims for a compromise. It typically involves tuning some intervals precisely according to pure, simple ratios found in just intonation, while others are slightly adjusted or "tempered" to avoid the harshness of wolf intervals.

The term "middletuned" is not as strictly defined as other temperament names. It generally describes systems that fall between the purity of just intonation and the evenness of equal temperament. The goal is to achieve a pleasing sound for a subset of keys and intervals, acknowledging that some other intervals may be less accurate. Historically, various forms of "meantone" temperaments, which tempered the major third, could be considered a precursor or a specific instance of what might broadly be termed middletuned.

The advantage of middletuning systems is that they can produce beautiful-sounding consonances, particularly major and minor thirds, which are often considered more pleasing than their tempered counterparts in equal temperament. However, this comes at the cost of creating some intervals that are significantly out of tune, leading to the characteristic "wolf" intervals in some temperaments. The specific intervals that are pure and those that are tempered vary depending on the precise middletuning system employed.