The Distinction Between a Temperament and Tuning

When a conventional keyboard of an acoustic instrument is tuned, it is impossible for thirds, fourths, fifths, sixths, and octaves all to be tuned as perfect intervals (a perfect interval is one for which their frequencies are a ratio of simple whole numbers, e.g., a perfect fifth involves a 3:2 ratio). Thus, some of the above-mentioned intervals must be imperfect (octaves are always perfect). When a keyboard instrument is tuned, some methods use all intervals that are perfect (e.g., Pythagorean Tuning), others use some intervals that are perfect and some that are not (Meantone and Well Temperament), and still others use all imperfect intervals (Equal Temperament). If a tuning method involves all perfect fifths, it is called *a tuning*, but if it involves some or all imperfect fifths, it is called *a temperament*.