# Fifth

Diatonic intervals
Prime
second
third
fourth
fifth
sixth
seventh
octave
none
decime
undezime
duodecime
tredezime
semitone / whole tone
Special intervals
Microinterval
Comma
Diësis
Limma
Apotome
Ditone Tritone
Wolf
fifth
Natural septime
units
Cent
Millioctave
Octave
Savart

The fifth or fifth (from Latin quinta : "the fifth", ancient Greek diapente διά (dia) πέντε (pente) "every fifth or all five") is an interval in music that spans five notes of a diatonic , heptatonic scale .

Example : scale section from f 'to c' '- fifth f' c '' in a row - fifth f 'c' 'at the same time.

As a “pure” fifth, the fifth consists of seven, and in its variants also six or eight semitone steps. The fifth is the complementary interval to the fourth .

In the narrower sense, the fifth is also understood to mean the fifth degree of the respective scale; the more precise term quintone is sometimes used for this.

## variants

Note example: fifth intervals

The fifth can appear in three variants:

• The perfect fifth (a), which has a frequency ratio of 3: 2 in the pure tuning and thus represents the most consonant interval after the octave , is the most common. It is used very frequently in all types of music, e.g. B. as a drone or mixed tone , and is important both in the musical mood and in music theory (see circle of fifths ). The fifth, similar to the fourth , is also often used as a signal interval. The falling fifth is also the most important element of the cadence .
• The diminished fifth (b), like its inversion interval, the augmented fourth or tritone , is a dissonant interval. It occurs as a characteristic interval in the dominant seventh chord .
• The excessive fifth (c) occurs mainly as the frame interval of the excessive triad (e.g. c - e - g sharp). It can be confused enharmonically with the minor sixth .

The fifth also forms the frame interval for the major (d) and minor triads.

interval Semitones example Reversal interval
(a) perfect fifth 7 (3 whole tones + 1 semitone) C - G , D - A
"How beautifully the morning star shines for us"
pure fourth
(b) diminished fifth 6 (2 whole tones + 2 semitones) H - F , D - As excessive fourth (tritone)
(c) excessive fifth 8 (4 whole tones) F - C sharp , C - G sharp diminished fourth

In connection with the partial tones , e.g. B. in organ registers , the 3rd, but also the 6th partial tone are designated as a fifth, the latter alternatively also as a super-fifth. This fifth (3rd partial tone) has a frequency ratio of 3: 2 to the next lower octave.

### Double meaning of the expression "perfect fifth"

The term "perfect fifth" is used on the one hand to mean "neither diminished nor excessive", on the other hand also for the frequency ratio of exactly 3: 2, as it belongs to pure tuning , i.e. as a contrast to "tempered" (out of tune) fifths (see following section).

## Mood

The exact frequency ratio of the pure, ie neither diminished nor excessive fifth is decided by the respective musical tuning system .

Surname Frequency ratio Cent value
Fifth in pure tuning ${\ displaystyle {\ frac {3} {2}}}$ 701.96 cents
5th in the equal mood ${\ displaystyle \ left ({\ sqrt [{12}] {2}} \ right) ^ {7}}$ 700 cents
Fifth in the 1 / 4 -Komma-meantone ${\ displaystyle {\ frac {\ sqrt [{4}] {80}} {2}}}$ 696.58 cents

## Empty fifth

An empty fifth is a dual sound like CG. "Empty" refers to the missing third step - in the example E or Eb - which would make the sound a major or minor triad . Empty fifths are used in tuning e.g. B. to hear the violins of an orchestra.

In rock music, such a genderless sound is called a “power chord”.