Perfect fifth

In music theory, a perfect fifth is a special musical interval. It is the distance between two notes where one note vibrates exactly 1.5 times faster than the other. This creates a pleasing and natural sound that has been used in music for centuries.

In classical music from Western culture, a perfect fifth is found between the first and fifth notes of any scale. For example, in the scale starting with C, the note G is a perfect fifth above C. This interval is very important because it sounds harmonious and stable.

The perfect fifth is more pleasing to the ear than most other intervals, except for when two notes are the same pitch (a unison) or exactly eight notes apart (an octave). It is a key part of many chords and is used in countless songs and pieces of music. Even in simple melodies like "Twinkle, Twinkle, Little Star", the perfect fifth can be heard between the first and second "twinkle."

Alternative definitions

The term perfect helps us identify the perfect fifth as part of a group called perfect intervals. This group includes the unison, perfect fourth, and octave. These intervals are special because they have simple relationships between notes and sound very harmonious together.

Perfect intervals are also defined by their ability to stay natural when their positions are reversed, called inversions. This means they remain the same type of interval even when flipped. In music, the perfect intervals are the unison, fourth, fifth, and octave. They can also be described using simple ratios of numbers, like 3:2 for the perfect fifth.

Other qualities

Besides the perfect fifth, there are two other types of fifths. The diminished fifth is one small step, called a chromatic semitone, smaller than a perfect fifth. The augmented fifth is one chromatic semitone larger. In terms of the steps between notes, the diminished fifth is the same as a tritone, and the augmented fifth is the same as a minor sixth.

Main article: diminished fifth
Main articles: tritone, minor sixth

Pitch ratio

The pitch ratio of a perfect fifth is 3:2. This means that the upper note vibrates three times for every two vibrations of the lower note. When a violin is tuned with this exact ratio, it sounds smooth and in tune.

Keyboard instruments like the piano usually use an equal-tempered version of the perfect fifth. This allows the piano to play in all keys. The equal-tempered perfect fifth is slightly narrower than the exact 3:2 ratio.

Use in harmony

The perfect fifth is an important part of building chords in music. It helps create major and minor triads, which are common in many songs and pieces. Because instruments naturally produce perfect fifths as overtones, musicians sometimes leave out the fifth note of a chord when playing.

The perfect fifth is also found in more complex chords, like seventh chords, where it can make dissonant intervals sound softer. In modern music, stacking perfect fifths creates quintal harmonies, used by composers like Paul Hindemith and in Stravinsky’s The Rite of Spring.

Bare fifth, open fifth, or empty fifth

A bare fifth, open fifth, or empty fifth is a chord that includes only a perfect fifth without a third note. This type of chord appears at the end of some famous pieces, like those by Pérotin and Guillaume de Machaut, as well as in the Kyrie of Mozart's Requiem and the first movement of Bruckner's Ninth Symphony. These chords are often found in Medieval music, Sacred Harp singing, and many types of rock music.

In genres like hard rock, metal, and punk music, musicians use bare fifths because they sound clear on overdriven or distorted electric guitar. These chords, called power chords, are easier to play quickly. Empty fifths are also used in traditional music, such as in Asian and some Andean music styles. Composers sometimes use these chords to create a unique or mysterious sound.

Use in tuning and tonal systems

The perfect fifth, along with the octave, is a key part of Pythagorean tuning. A slightly smaller perfect fifth is also used in meantone tuning.

The circle of fifths helps us understand how notes relate to each other in music. It shows how many perfect fifths are needed to move from one note to another in the chromatic scale.