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perfect fifth : ウィキペディア英語版
perfect fifth

In music theory, a perfect fifth is the musical interval corresponding to a pair of pitches with a frequency ratio of 3:2, or very nearly so.
In classical music from Western culture, a fifth is the interval from the first to the last of five consecutive notes in a diatonic scale.〔Don Michael Randel (2003), "Interval", ''Harvard Dictionary of Music'', fourth edition (Cambridge, MA: Harvard University Press): p. 413.〕 The perfect fifth (often abbreviated P5) spans seven semitones, while the diminished fifth spans six and the augmented fifth spans eight semitones. For example, the interval from C to G is a perfect fifth, as the note G lies seven semitones above C.
The perfect fifth may be derived from the harmonic series as the interval between the second and third harmonics. In a diatonic scale, the dominant note is a perfect fifth above the tonic note.
The perfect fifth is more consonant, or stable, than any other interval except the unison and the octave. It occurs above the root of all major and minor chords (triads) and their extensions. Until the late 19th century, it was often referred to by one of its Greek names, ''diapente''. Its inversion is the perfect fourth. The octave of the fifth is the twelfth.
A helpful way to recognize a perfect fifth is to hum the starting of "Twinkle, Twinkle, Little Star"; the pitch of the first "twinkle" is the root note and pitch of the second "twinkle" is a perfect fifth above it.
==Alternative definitions==

The term ''perfect'' identifies the perfect fifth as belonging to the group of ''perfect intervals'' (including the unison, perfect fourth and octave), so called because of their simple pitch relationships and their high degree of consonance.〔Walter Piston and Mark DeVoto (1987), ''Harmony'', 5th ed. (New York: W. W. Norton), p. 15. ISBN 0-393-95480-3. Octaves, perfect intervals, thirds, and sixths are classified as being "consonant intervals", but thirds and sixths are qualified as "imperfect consonances".〕 When an instrument with only twelve notes to an octave (such as the piano) is tuned using Pythagorean tuning, one of the twelve fifths (the wolf fifth) sounds severely dissonant and can hardly be qualified as "perfect", if this term is interpreted as "highly consonant". However, when using correct enharmonic spelling, the wolf fifth in Pythagorean tuning or meantone temperament is actually not a perfect fifth but a diminished sixth (for instance G–E).
Perfect intervals are also defined as those natural intervals whose inversions are also perfect, where natural, as opposed to altered, designates those intervals between a base note and another note in the major diatonic scale starting at that base note (for example, the intervals from C to C, D, E, F, G, A, B, C, with no sharps or flats); this definition leads to the perfect intervals being only the unison, fourth, fifth, and octave, without appealing to degrees of consonance.
The term ''perfect'' has also been used as a synonym of ''just'', to distinguish intervals tuned to ratios of small integers from those that are "tempered" or "imperfect" in various other tuning systems, such as equal temperament. The perfect unison has a pitch ratio 1:1, the perfect octave 2:1, the perfect fourth 4:3, and the perfect fifth 3:2.
Within this definition, other intervals may also be called perfect, for example a perfect third (5:4) or a perfect major sixth (5:3).

抄文引用元・出典: フリー百科事典『 ウィキペディア(Wikipedia)
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