Subdominant

Tonic and subdominant in C  Play . C major and F major chords.

Subdominant (IV) in IV-V-I progression, in C  Play 

Major seventh chord on F. Play  IV7
M,^[1] or subdominant seventh in C major.

In music, the subdominant is the technical name for the fourth tonal degree of the diatonic scale. It is so called because it is the same distance "below" the tonic as the dominant is above the tonic - in other words, the tonic is the dominant of the subdominant.^[2] It also happens to be the note immediately "below" the dominant.^[3] It is sung as fa in solfege. In the C major scale (white keys on a piano, starting on C), the subdominant is the note F; and the subdominant chord uses the notes F, A, and C. In music theory, Roman numerals are used to symbolize the subdominant chord as 'IV' if it is within the major mode (because it is a major triad, for example F-A-C in C major) or 'iv' if it is within the minor mode (because it is a minor triad, for example F-A♭-C in C minor).

In very much conventionally tonal music, harmonic analysis will reveal a broad prevalence of the primary (often triadic) harmonies: tonic, dominant, and subdominant (i.e., I and its chief auxiliaries a 5th removed), and especially the first two of these.

— Berry (1976)^[4]

Because ii₆, ii6
5, and neapolitan sixth chords contain the fourth scale degree in the bass, they are also considered subdominant harmonies because they substitute for the same harmonic purpose as chords built on the fourth scale degree.

Subdominant (IV) in I-IV-I progression, in C  Play 

A cadential subdominant chord followed by a tonic chord (the chord of the key of the piece) produces the so-called "plagal" (or "Amen") cadence.

"Subdominant" also refers to a relationship of musical keys. For example, relative to the key of C major, the key of F major is the subdominant. Music which modulates (changes key) often modulates into the subdominant when the leading tone is lowered by a half step to the subtonic (B to B♭ in the key of C). Modulation into the subdominant key often creates a sense of musical relaxation; as opposed to modulation into dominant (fifth note of the scale), which increases tension.

In sonata form, the subdominant key plays a subordinate though still crucial role: typically, in the recapitulation, there is a section written in the subdominant key, occurring at the point corresponding to the location in the exposition where the music modulated into the dominant key. The use of the subdominant in this location often serves as a way of keeping the rest of recapitulation in the tonic.

The circle of fifths drawn within the chromatic circle as a star dodecagram.^[5] In C, the tonic would be on the top with subdominant and dominant at the bottom both equidistant to the tonic.

As with other chords which may or tend to precede the dominant the subdominant diatonic function acts as a dominant preparation or predominant. In theories after Hugo Riemann it is considered to balance the dominant around the tonic (being as far below the tonic as the dominant is above).

Sources

1. Benward & Saker (2003). Music: In Theory and Practice, Vol. I, p.229. Seventh Edition. ISBN 978-0-07-294262-0.
2. Jonas, Oswald (1982). Introduction to the Theory of Heinrich Schenker (1934: Das Wesen des musikalischen Kunstwerks: Eine Einführung in Die Lehre Heinrich Schenkers), p.22. Trans. John Rothgeb. ISBN 0-582-28227-6. "subdominant [literally, lower dominant]" emphasis original.
3. "Subdominant", Dictionary.com.
4. Berry, Wallace (1976/1987). Structural Functions in Music, p.62. ISBN 0-486-25384-8.
5. McCartin, Brian J. (1998). "Prelude to Musical Geometry". The College Mathematics Journal 29, no. 5 (November): 354–70. (abstract) (JSTOR), p. 364.