Major seventh chord

Dizzy Gillespie's 1956 recording of "Dizzy's Business" ends with a major seventh chord^[1] with root on G.  Play (help·info)

In music, a major seventh chord is any nondominant seventh chord where the "third" note is a major third above the root.

Major seventh chord on C  Play (help·info). I⁷ in C major.^[2]

Most typically, major seventh chord refers to where the "seventh" note is a major seventh above the root (a fifth above the third note)  play (help·info). This is more precisely known as the major/major seventh chord, and it can be written as maj7, M7, ^Δ, ⑦ etc. It can be represented by the integer notation {0, 4, 7, 11}. In the case where the seventh note is a minor seventh above the root, it is called a dominant seventh chord (although this is also a kind of major seventh chord).

Examples of tonic major seventh chords include the Charlie's Angels theme song, LaBelle's "Lady Marmalade", Chic's "Le Freak", the Eagles' "One Of These Nights", Bread's "Make It With You", America's "Tin Man", Blood Sweat & Tears' "You've Made Me So Very Happy", third and main part of Paul McCartney and Wings' "Band On The Run", Carly Simon's "The Right Thing To Do", and, most famously, Chicago's "Colour My World".^[3]

Moving in the seventies to replace the prominence of the dominant seventh as a stable tonic more common in the first fifteen years of the rock era, the major seventh was common in all styles, "pervading soul, country rock, soft rock, MOR (middle-of-the-road styles), jazz rock, funk, and disco."^[3] "In soul and disco, a tonic minor seventh harmony often alternated with a dominant seventh or dominant ninth chord on $\hat 4$ ['Lady Marmalade' & 'Le Freak']...In other styles, major seventh and minor seventh chords generally mix (usually with eleventh chords...) to create a diatonic composite in either major or minor mode....The most famous major seventh chord in the history of music, [is] the one that opens...'Colour My World', even though the song departs from the usual pattern described above by 'colouring' the harmonic succession with several chromatic chords. Still, seven of that song's fourteen chords, including the tonic, are major sevenths or ninths, demonstrating the primacy of that chord type."^[3]

Melodic origin of IV⁷.^[4]  Play (help·info)

According to Forte, the major seventh chord is exemplified by IV⁷, which originates melodically.^[4]

The just major seventh chord is tuned in the ratios 8:10:12:15, as a just major chord is tuned 4:5:6 and a just major seventh is tuned 15:8.  Play (help·info)

major/major seventh chord

Component intervals from root

major seventh

perfect fifth

major third

root

Major seventh chord on F  Play (help·info). IV⁷ in C major.^[2]

Major/major seventh chord table

Chord	Root	Major Third	Perfect Fifth	Major Seventh
Cmaj7	C	E	G	B
C♯maj7	C♯	E♯ (F)	G♯	B♯ (C)
D♭maj7	D♭	F	A♭	C
Dmaj7	D	F♯	A	C♯
D♯maj7	D♯	F (G)	A♯	C (D)
E♭maj7	E♭	G	B♭	D
Emaj7	E	G♯	B	D♯
Fmaj7	F	A	C	E
F♯maj7	F♯	A♯	C♯	E♯ (F)
G♭maj7	G♭	B♭	D♭	F
Gmaj7	G	B	D	F♯
G♯maj7	G♯	B♯ (C)	D♯	F (G)
A♭maj7	A♭	C	E♭	G
Amaj7	A	C♯	E	G♯
A♯maj7	A♯	C (D)	E♯ (F)	G (A)
B♭maj7	B♭	D	F	A
Bmaj7	B	D♯	F♯	A♯

Sources

1. ^ Walter Everett (Autumn, 2004). "A Royal Scam: The Abstruse and Ironic Bop-Rock Harmony of Steely Dan", p.205, Music Theory Spectrum, Vol. 26, No. 2, pp. 201-235.
2. ^ ^{a b} Benward & Saker (2003). Music: In Theory and Practice, Vol. I, p.229. Seventh Edition. ISBN 978-0-07-294262-0.
3. ^ ^{a b c} Stephenson, Ken (2002). What to Listen for in Rock: A Stylistic Analysis, p.83. ISBN 9780300092394.
4. ^ ^{a b} Forte, Allen (1979). Tonal Harmony in Concept & Practice, p.150. ISBN 0-03-020756-8.