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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. The two notes in any just interval are members of the same harmonic series. Frequency ratios involving large integers such as 1024:927 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."〔Gilmore, Bob (2006). "Introduction", ''"Maximum Clarity" and Other Writings On Music'', p.xiv. ISBN 978-0-252-03098-7.〕 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. ==Examples== An A-major scale, followed by three major triads, and then a progression of fifths in just intonation. An A-major scale, followed by three major triads, and then a progression of fifths in equal temperament. By listening to the above file, and then listening to this one, one might be able to hear a slight buzzing in this file. A pair of major thirds, followed by a pair of full major chords. The first in each pair is in equal temperament; the second is in just intonation. Piano sound. A pair of major chords. The first is in equal temperament; the second is in just intonation. The pair of chords is repeated with a transition from equal temperament to just temperament between the two chords. In the equal temperament chords a roughness or beating can be heard at about 4 Hz and about 0.8 Hz. In the just intonation triad, this roughness is absent. The square waveform makes the difference between equal and just temperaments more obvious. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「just intonation」の詳細全文を読む スポンサード リンク
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