Chord sequences that show how major chords (in bold) can be utilized:
1. C F G
2. C Em F G
3. C F Am G
In Roman numerals*:
1. I IV V
2. I iii IV V
3. I IV vi V
* Roman numerals describe chord intervals that can be used the same way in all keys. See a table over major keys including Roman numerals.
Let us continue with major 7 chords that are built by adding the seventh note in the related scale.
Comparing the C Major Scale with the C Major 7 chord:
C Major scale: C β D β E β F β G β A β B
C Major 7 chord: C β E β G β B
There are also Major 6th chords with the sixth note in the scale added to a triad. These are, however, written without the abbreviation βmajβ and sometimes this category is called added 6th. Relevant here is also the less common 6/9, or 6add9 (6th with an added major 9th).
Comparing the C Major Scale with C6 and C6/9:
C Major scale: C β D β E β F β G β A β B
C6 chord: C β E β G β A
C6/9 chord: C β E β G β A β D
Next type to know about is Major ninth (maj9). This chord is built by adding a major third to a major seventh chord; this note is also the second scale degree an octave higher. Maj9 must not be confused with the Dominant 9th.
Comparing the C Major Scale with Cmaj9:
C Major scale: C β D β E β F β G β A β B
C Major 9 chord: C β E β G β B β D
Rather unusual is the Major eleventh (maj11), which more correctly is written maj9(#11) since the eleventh normally is raised a semi-tone. This is because of the dissonance that otherwise occur between the major third and the eleventh.
Comparing the C Major Scale with Cmaj11, or Cmaj9(#11):
C Major scale: C β D β E β F β G β A β B
Cmaj11 (not so common in practice): C β E β G β B β D β F
Cmaj9#11: C β E β G β B β D β F#
Next is the Major thirteenth (maj13), which is built by adding a 13th. This chord includes seven notes, but to make it more practical, some notes (the least important for the chord color, which especially include the eleventh) are normally left out. Maj13 not to be confused with the dominant 13th.
Comparing the C Major Scale with Cmaj13:
C Major scale: C β D β E β F β G β A β B
C Major 13 chord: C β E β G β B β D β A
(the 11th, F in the case of Cmaj13, is normally excluded)
To mention is also maj13#11:
Cmaj13#11: C β E β G β B β D β F# β A
See links above or use the search box for diagrams (some of the less common categories are not presented).
Alternative chord symbols
Besides the major chord symbol that is presented on this site, you may find alternatives, including the following instead of C:
CMaj (relative common symbol there βMajβ is written out as the abbreviation for major)
Cβ³ (the triangle is sometimes used in piano sheets as a symbol for major)
CM (here a capital letter is being used for βmajorβ, which are not recommended due to the possible confusing with a βminorβ symbol)
Cma (uncommon symbol there βmaβ is written out as the abbreviation for major)
CM7 or Cβ³7 are alternative chord names used instead of Cmaj7 (the triangle is sometimes also used in piano sheets as a single symbol for major seventh).
CM9 or Cβ³9 are alternative chord names used instead of Cmaj9, CM11 or Cβ³11 are alternative chord names used instead of Cmaj11 and CM13 or Cβ³13 are alternative chord names used instead of Cmaj13.
CM6 is an alternative chord name sometimes used instead of C6.
Additionally, C13, which is an extended chord, could be written Cmaj9(add13).