Just Intonation

-The term just intonation has two different definitions. The first is ancient and strictly mathematical. It states that just intonation is a method of tuning intervals and scales based exclusively on rational numbers. The second is modern and strictly acoustic. It states that just intonation is a method of tuning based on the intervals of the harmonic series.

-In the notation of just-intonation (pure) tuning, pitches are given as fractions, which are actually ratios between the named pitch and a constant fundamental. For example, if C is the reference pitch (if we're in the "key of C"), then C is denoted as 1/1.
Any C in the scale can then be denoted as 1/1. Or, the C an octave above a particular C can be denoted as 2/1, since a 2-to-1 ratio between frequencies is an octave.