Temperatio

Temperatio, from the Latin temperare meaning to temper or regulate, is a term used in historical Latin to denote tempering or moderation in various technical senses. In music theory and the history of tuning, temperatio designates the practice of adjusting or “tempering” pitch relationships to suit instruments with fixed pitches, such as keyboards or wind instruments. The problem arose because pure just intervals cannot be maintained across all keys without causing dissonance when switching keys; temperatio describes the solution: a system of temperament that compromises pure intervals to achieve workable tuning across a repertoire.

In medieval and Renaissance theory, temperatio was applied to describe tuning methods that adjusted fifths or thirds, balancing the Pythagorean and meantone approaches. Types of temperaments include Pythagorean temperament (fifths tuned to be pure, resulting in very out-of-tune thirds in most keys), and meantone temperament (fifths narrowed by a syntonic comma to improve thirds in common keys). Later, well temperament allowed all keys to be used, each with its own character; equal temperament, in which all semitones are equal, became dominant in the modern era, enabling uniform intonation in every key.

The concept extends beyond music to general ideas of tempering or moderating materials or processes, but in musicology it remains primarily tied to tuning systems. While the term temperatio can appear in older Latin texts, modern discussions typically use temperament or tuning to describe the same practice.