Major seventh chord on C  Play (help·info). I⁷ in C major.^[1]

Dizzy Gillespie's 1956 recording of "Dizzy's Business" ends with a major seventh chord^[2] 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.

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] Other examples include New Radicals' "You Get What You Give".

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

Major seventh chord on F  Play (help·info). IV⁷ in C major.^[1]

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 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]

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 table

Sources