Just Intonation is any system of tuning that uses the naturally occurring Harmonic series as a basis. When we hear a note produced by a plucked string, a voice, etc., we are actually hearing an array of harmonics along with the fundamental. If two singers sing the same note, they will sound different from each other because each voice has a unique set of harmonics..
The Harmonic Series is a naturally occurring series of notes present in every voice, vibrating string, electrical hum, and elsewhere. The common 12-Tone Equal Tempered system found on almost all pianos, guitars, and other instruments in this country is a man-made system that distorts the pure intervals of Nature for the sake of “convenience.”
It is possible to divide the octave into other equal divisions using more (or less) than 12 steps. 19-tone equal temperament yields major thirds almost 7 cents below the Just major third, and minor thirds that are .2 cents sharp. Both intervals are thus much closer to Just than their 12-Equal counterparts, which are 14 cents sharp and 16 cents flat respectively. Guitarist Neil Haverstick of Denver has done some nice work with 19-tone. Dividing the octave into 31-equal intervals also has interesting results, including 7th harmonics within 1.1 cents of the Just 7th (a note not even approximated in 12-ET). These and other equal-tempered systems each have their own characteristic sound and are well worth pursuing on their own, or to work towards a better understanding of the Harmonic Series.
How can I experience Pure intervals?
Guitars can be open-tuned to harmonically pure intervals or re-fretted. Pianos can also be re-tuned, and fingerings can be altered on wind instruments. In fact, almost any instrument can be altered to play in Just Intonation.