temperát

Temperát is a term used in music theory to describe a system of tuning where the intervals between notes are slightly adjusted or "tempered" from their pure mathematical ratios. This tempering allows for instruments like pianos, organs, and string instruments to play in all keys without sounding excessively out of tune. Without tempering, some keys would sound consonant and pleasant, while others would be noticeably dissonant, rendering them unusable.

The need for temperament arose from the limitations of just intonation, a tuning system based on simple whole-number frequency ratios. While just intonation produces pure intervals, it is not flexible enough for music that modulates or uses a wide range of keys. The development of temperament involved finding compromises that made the tuning of intervals acceptable across the entire chromatic scale.

Various temperament systems have existed throughout history, each with its own unique way of distributing the "wolf intervals" – the most dissonant intervals created by the tempering process. Early forms like Pythagorean tuning and meantone temperament were popular in different eras, but they favored certain keys over others. Equal temperament, where all twelve semitones in an octave are divided into mathematically equal intervals, has become the dominant tuning system in Western music today. This system allows for complete freedom in modulation and key choice, making it a cornerstone of modern musical practice.