What is "just intonation"

Just \Just\, a. [F. juste, L. justus, fr. jus right, law, justice; orig., that which is fitting; akin to Skr. yu to join. Cf. Injury, Judge, Jury, Giusto.]

1. Conforming or conformable to rectitude or justice; not doing wrong to any; violating no right or obligation; upright; righteous; honest; true; -- said both of persons and things. ``O just but severe law!''
   --Shak.

   There is not a just man upon earth, that doeth good, and sinneth not.
   --Eccl. vii. 20.

   Just balances, just weights, . . . shall ye have.
   --Lev. xix. 36.

   How should man be just with God?
   --Job ix.

2. We know your grace to be a man. Just and upright.
   --Shak.

   2. Not transgressing the requirement of truth and propriety; conformed to the truth of things, to reason, or to a proper standard; exact; normal; reasonable; regular; due; as, a just statement; a just inference.

   Just of thy word, in every thought sincere.
   --Pope.

   The prince is here at hand: pleaseth your lordship To meet his grace just distance 'tween our armies.
   --Shak.

   He was a comely personage, a little above just stature.
   --Bacon.

   Fire fitted with just materials casts a constant heat.
   --Jer. Taylor.

   When all The war shall stand ranged in its just array.
   --Addison.

   Their names alone would make a just volume.
   --Burton.

3. Rendering or disposed to render to each one his due; equitable; fair; impartial; as, just judge. Men are commonly so just to virtue and goodness as to praise it in others, even when they do not practice it themselves. --Tillotson. Just intonation. (Mus.)

   1. The correct sounding of notes or intervals; true pitch.

   2. The giving all chords and intervals in their purity or their exact mathematical ratio, or without temperament; a process in which the number of notes and intervals required in the various keys is much greater than the twelve to the octave used in systems of temperament.
      --H. W. Poole.

      Syn: Equitable; upright; honest; true; fair; impartial; proper; exact; normal; orderly; regular.

n. 1 (context music English) The correct sounding of notes or intervals; true pitch. 2 (context music English) The giving all chords and intervals in their purity or their exact mathematical ratio, or without temperament; a process in which the number of notes and intervals required in the various keys is much greater than the twelve to the octave used in systems of temperament.

In music, just intonation (sometimes abbreviated as JI) or pure intonation is any musical tuning in which the frequencies of notes are related by ratios of small whole numbers. Any interval tuned in this way is called a pure or just interval. Pure intervals are important in music because they naturally tend to be perceived by humans as " consonant": pleasing or satisfying. Intervals not satisfying this criterion, conversely, tend to be perceived as unpleasant or as creating dissatisfaction or tension. The two notes in any just interval are members of the same harmonic series. Frequency ratios involving large integers such as 1024:729 are not generally said to be justly tuned. "Just intonation is the tuning system of the later ancient Greek modes as codified by Ptolemy; it was the aesthetic ideal of the Renaissance theorists; and it is the tuning practice of a great many musical cultures worldwide, both ancient and modern."

Just intonation can be contrasted and compared with equal temperament, which dominates Western instruments of fixed pitch (e.g., piano or organ) and default MIDI tuning on electronic keyboards. In equal temperament, all intervals are defined as multiples of the same basic interval, or more precisely, the intervals are ratios which are integer powers of the smallest step ratio, so two notes separated by the same number of steps always have exactly the same frequency ratio. However, except for doubling of frequencies (one or more octaves), no other intervals are exact ratios of small integers. Each just interval differs a different amount from its analogous, equally tempered interval.

Justly tuned intervals can be written as either ratios, with a colon (for example, 3:2), or as fractions, with a solidus (3 ⁄ 2). For example, two tones, one at 300 hertz (cycles per second), and the other at 200 hertz are both multiples of 100 Hz and as such members of the harmonic series built on 100 Hz. Thus 3/2, known as a perfect fifth, may be defined as the musical interval (the ratio) between the second and third harmonics of any fundamental pitch.