E major 13th chord

Emaj13 chord for piano with keyboard diagram.
Explanation: The E major thirteenth is a six-note chord (the 11th, A in the case of Emaj13, is normally excluded). For practical reasons the chord is normally played with omitted notes and/or inverted. It is often abbreviated as Emaj13 (not to be confused with E13).
Omissions: Emaj13(no5): E - G# - D# - F# - C#, Emaj13(no9): E - G# - B - D# - C#.
Theory: The E major thirteenth chord is constructed by extending the major eleventh chord with a major thirteenth note.

Emaj13

Emaj13 piano chord diagram
Notes: E - G# - B - D# - F# - C#

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Emaj13 inversions and voicings

Emaj13/D# chord diagram
Notes: D# - G# - B - C# - E
One of many possible inversions (Emaj13/D# with the 9th and the 11th omitted)

Emaj13 chord voicing diagram
Notes: E - D# - G# - C#
Two-hand voicing

E chord categories

E Em E7 Em7 Emaj7 EmM7 E6 Em6 E6/9 E5 E9 Em9 Emaj9 E11 Em11 Emaj11 E13 Em13 Emaj13 Eadd E7-5 E7+5 Esus Edim Edim7 Em7b5 Eaug Eaug7