Tech Tip:What Is "Just Intonation"?

Just Intonation, abbreviated JI, does not refer to a single tuning or scale. Rather, it refers to "any system of tuning in which all of the intervals can be represented by whole-number frequency ratios." (David B. Doty, The Just Intonation Primer).


To illustrate, the often-used tuning note, A440, vibrates 440 times a second, and its frequency is said to be 440 Hertz. An octave above A440 is A880, which vibrates 880 times a second, or 880 Hertz. The ratio between 880 and 440 is 2 to 1, written 2:1. A just-tuned perfect fifth above A440 is E660, a ratio of 3:2. The interval between any two notes in a just-tuned scale can be represented as a whole-number ratio. A major third is 5:4, a minor third is 6:5, and so on. Most musicians who use just-tuned scales prefer lower prime number ratios - numbers divisible by 2, 3, 5, 7, less often 11, 13, 17, 19, and higher.


Almost all popular and classical music from American and European countries is tuned in 12-note equal temperament, which is based on the twelfth root of two, an irrational number used to divide the octave (2:1) into twelve equal parts. So, other than the perfect octave, none of the intervals in 12-note equal temperament can be expressed as a whole number ratio, and these intervals sound different than their just-tuned counterparts. For example, the interval between the two notes in a 12-note equal-tempered major third is significantly wider than the interval between the two notes of a just-tuned major third.


Another difference between JI and 12-note equal temperament is that JI has an infinite number of pitches to draw from, whereas 12-note equal temperament has only 12 (granting expressive pitch inflections). JI is open-ended, and many possibilities remain to be discovered.


Just tunings are available in most keyboards and sound modules that are user-tunable. One or two just tunings may be included among the tuning presets, labeled "pure major", "pure minor", or similar.


If you're interested in JI, don't miss the Just Intonation Network site; the Just Intonation Primer is available there.


For exploring just-tuned guitar and other instruments, as well as many other microtonal music sites, many links are provided at John Starrett's Microtonal Music Page.