Way back when, in my days of college and keg beer, I had a band. And we had a song called "Both Sides." It was a gnarly and dissonant thing, played for maximum ouch. For my part, I played a snarling F#♭5 'power chord' in the verses:

--x--
--x--
--x--
--4-- F#
--3-- C
--2-- F#

It's not actually a chord, since a chord requires three notes (with certain constraints about the distance between them). It's a 'power chord' (root, fifth, octave).

And in the choruses I came up with a cluster of notes that I thought was beautifully screechy and whiny. I played it high up on the neck and moved it around, but the shape is:

--4-- G#
--3-- D
--1-- G#
--2-- E
--x--
--x--

Here's the song. The chorus starts about 28 seconds in.

Mmmm. A-tonal.

The top three strings there are doing the same ♭5 thing as the verse chord (G#, D, G#). And then there's that E which sounds awkward against all the rest, as intended.

So, I was bored today and decided to find out once and for all, if that little mess has an official chord name. It does!

This site gives it two names: the daunting "D/E Suspended 2nd Flat 5th" (yessss) or .... it's a boring old stupid lame E7.

What?

The notes in that thing are E, G#, D, G#. But a standard E7 is E, B, D, G#:

--0--  E
--0--  B
--1--  G#
--0--  D
--2--  B
--0--  E

So how can it be an E7 if there's no B? Isn't the fifth an import note? A standard major/minor triad is root + third + fifth. In this case, E + G# + B = E major. An E7 happens when you add a D to an E major (E + G# + B + D = E7). So I wouldn't have thought that leaving out the fifth was possible. But, according to this site, it's perfectly legal:

Usually one of the most unessential notes of any chord is the fifth. In these chords the fifth is essentially “inert”. It does not contribute to the sense of major or minor, nor does it add any interest (tension, dissonance or sense of forward movement) to the sound. Therefore it can typically be omitted quite safely without affecting the stability or tonality of the chord.

As an example, while a Cmaj7 would normally have the notes C, E, G and B, it is common to leave the G out, keeping only the C, E, and B. This is also true for dominant and minor type chords.

And not only is it legal, it's quite common for choirs and piano.

Always learning.