welltemperaments

A well-temperament, often referred to as a "well-tempered tuning," is a system of tuning a musical instrument, particularly a keyboard instrument like a harpsichord or organ, where the intervals are adjusted slightly from pure mathematical ratios. This adjustment is done to make all keys and harmonies sound reasonably good, avoiding the excessively harsh or out-of-tune intervals that would result from simpler tuning systems like meantone temperament when playing in more remote keys.

The concept of well-temperaments arose as composers began to explore a wider range of keys in their music. Older tuning systems, while producing pure intervals in certain common keys, would render other keys dissonant and unusable. A well-temperament system distributes these small imperfections across all keys, making them all playable and musically acceptable. This was a significant development, paving the way for the rich harmonic language of the Baroque and subsequent musical periods.

It is important to distinguish between well-temperaments and equal temperament. While both aim to make all keys usable, equal temperament divides the octave into twelve precisely equal semitones. This results in every interval being slightly out of tune compared to its pure acoustic counterpart, but it offers perfect symmetry and allows for seamless modulation between any keys. Well-temperaments, on the other hand, retain some intervals that are closer to pure ratios than others, giving each key a subtly unique character. The specific "well-temperament" can vary, with different historical systems offering different distributions of these slight deviations.