Emaj7#5 is E, G#, B# and D# — with the fifth raised a semitone.
It sounds weightless, with no pull in it. Unlike an aug7 there is no flat seventh dragging it anywhere, so it colours a tonic rather than replacing it with a dominant.
Tonic — the lydian augmented sound.
Also written EM7#5, EΔ7#5, E+M7 or Emaj7(#5).

How you get to it. The turn that lands on Emaj7#5 is to — the ii and the V of E — and shares its third and seventh with , so the hand barely moves between them.
Hear it land:→→
Every note of Emaj7#5 is in E lydian augmented.
Each of those is a page: the scale across the neck, and the chords it harmonises into — which is where Emaj7#5 sits in it. Every scale.
Change one note of Emaj7#5 and you have (the sharp fifth becomes the fifth), (the sharp fifth becomes the flat fifth), (drop the major seventh), (the major seventh becomes the flat seventh) or (the sharp fifth becomes the fifth).
Emaj7#5 is a major chord — root, major third, fifth. Major chords on every root.
The common shapes and the derived voicings come from different places, and both are explained in how this site is built.
Shows each chord the way this style would voice it, and marks which of its alternatives belong to the idiom.