1.
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 notes in a diatonic scale. The perfect fifth spans seven semitones, while the diminished fifth spans six, for example, the interval from C to G is a perfect fifth, as the note G lies seven semitones above C. Play The perfect fifth may be derived from the series as the interval between the second and third harmonics. In a diatonic scale, the dominant note is a fifth above the tonic note. The perfect fifth is more consonant, or stable, than any other interval except the unison and it occurs above the root of all major and minor chords and their extensions. Until the late 19th century, it was referred to by one of its Greek names. Its inversion is the perfect fourth, the octave of the fifth is the twelfth. The term perfect identifies the perfect fifth as belonging to the group of perfect intervals, so called because of their simple pitch relationships and their high degree of consonance. However, when using correct enharmonic spelling, the fifth in Pythagorean tuning or meantone temperament is actually not a perfect fifth. The perfect unison has a pitch ratio 1,1, the perfect octave 2,1, the perfect fourth 4,3, within this definition, other intervals may also be called perfect, for example a perfect third or a perfect major sixth. In terms of semitones, these are equivalent to the tritone, the justly tuned pitch ratio of a perfect fifth is 3,2, meaning that the upper note makes three vibrations in the same amount of time that the lower note makes two. The just perfect fifth can be heard when a violin is tuned, if adjacent strings are adjusted to the ratio of 3,2, the result is a smooth and consonant sound. Keyboard instruments such as the piano normally use a version of the perfect fifth. In 12-tone equal temperament, the frequencies of the perfect fifth are in the ratio 7 or approximately 1.498307. An equally tempered fifth, defined as 700 cents, is about two cents narrower than a just perfect fifth, which is approximately 701.955 cents. Kepler explored musical tuning in terms of ratios, and defined a lower imperfect fifth as a 40,27 pitch ratio. His lower perfect fifth ratio of 1.4815 is much more imperfect than the equal temperament tuning of 1.498, the perfect fifth is a basic element in the construction of major and minor triads, and their extensions