Just Intonation

Just Intonation is a specific state of tuning, for a musical interval, in which the fundamental frequencies of the notes are in, or close to, an harmonic ratio. 

Just Intonation is a term that has very specific acoustical meaning, when applied to tuning practice. When not used in this specific, acoustical sense, it becomes a semantic term, and is open to all kinds of irresolvable philosophical debate.

In practice, a Justly Intoned interval will be an interval tuned to its optimum state of acoustical consonance. 

Just intonation is also a term sometimes used to describe a scale that is tuned so that each note forms a Just Interval (a Justly Intoned interval) with the lowest note of the scale. This can give the erroneous impression that there exists a scale in which all the intervals are Justly Intoned. Remember that intervals exist between any two notes of the scale, not just between a given note and the lowest note. No scale can exist, using normal acoustic musical instruments, in which all the intervals are Justly Intoned.

Just Intonation is a term that only properly applies to musical intervals where the individual notes have tone-structures that are harmonic or approximately harmonic. Explanation: The tone of a musical instrument or voice is invariably a complex and changing recipe of simpler sound-components. Just as chemicals are composed of molecules, so musical tones are composed of partials. A musical tone whose structure is harmonic or approximately harmonic, has partials whose musical pitches are arranged approximately in a specific series of musical intervals of decreasing size. 

Approximately speaking therefore, when an interval is tuned with Just Intonation, the pitches of its two notes will be separated by an interval found in the harmonic series of partials, in the tone recipe of the lower note.

Just Intonation and harmonic ratios

Just as molecules can be "split" into atoms, so partials can often be "split" into pure tones. If each partial were just a single pure tone, then the partials could be arranged in a perfect harmonic series. In practice, the tone of a guitar string or piano string, for example, invariably contains many partials that contain two or more pure tones.

Furthermore, real strings like guitar strings or piano strings, have their partials arranged inharmonically. These strings have tones whose recipes are affected by inharmonicity, which is caused by stiffness in the string. This means, the higher up the harmonic series a partial falls, the more it will be sharpened or raised above its proper harmonic position, by inharmonicity.    

It is often said that in Just Intonation, the notes of an interval are in an harmonic ratio. In fact only an interval whose notes have tone recipes consisting of a true harmonic series of pure tones can be said to have such a ratio. In practice, the statement is usually an approximation. The real ratio will be determined by the condition of optimum acoustical consonance, and this is determined by a great many different factors.