Just Intonation

Any musical tuning in which the frequencies of notes are related by whole number ratios. Any interval tuned in this way is called a just interval. Thus, although in theory, two notes tuned in the frequency ratio 1024:927, might be considered justly tuned, in practice, only ratios using quite small numbers such as 3:2, 5:4 or 7:4; or in which all pitches are based on the harmonic series, which are all whole number multiples of a single tone. Such a system may use two different ratios for what is the same interval in equal temperament depending on context; for instance, a major second interval may be either in the ratio 9:8 or 10:9 tend to be called “just.” The reason that just intonation is not used much is because for many instruments tuned in just intonation, you can’t change keys without retuning your instrument. It was Johann Sebastian Bach who is credited with establishing the use of equal temperament in western art music.