Your chord actually fits perfectly in G# harmonic minor, but since your question really remembers me when I was learning theory for the first time, I'd like to tell you some facts that may have helped me.
There is more than major and minor scales:
There are tons of scales and there is no best scale.
Actually, a scale is just a set of notes, not necesarilly following any rules .
I've already told you about harmonic minor scales, but I hardly suggest you to google more of them, and just as a warning message let me tell you that since modes are just translations of the major scale, the harmony structure "keeps" the same, so it's not like you are going to find any new chords there.
There is no phenomenon on not be major: the fact that this chord doesn't fit into any major scale is not a phenomenon.
Major scale was born as a imitation of the accents that nature adds when a fixed frequency sound sounds (if you are interested in this approach you can read Arnold Schoenberg's book called "Theory of Harmony"), but there is no logical reason to think that we are attached to the major scale just because it is more natural than other sets of notes.
Feel free to use every single combination of notes.
music.stackexchange.com/users/52594/Esteban Gutiérrez
In this context, it may just be an intended Eb chord, the player hit the open E string by mistake and thought 'that sounds nice!'
Chords don't HAVE to come from one scale.
A common one that doesn't is the 'Hendrix' chord, a dom7 shape with the minor 3rd on top.
(Theorists like to call it a #9, your ears will tell you it's a b10.)
However, when a chord is in general use, and has an accepted name, the jazzers generally WILL have discovered (or invented) a scale that fits it.
They like a chord symbol to imply a scale.
Don't worry over esoteric 'slash chords' though.
They might just indicate a pedal note.
C, Db/C, D/C,
Eb/C etc. is a common trick, and you can leave the bass note out of any 'chord=scale' analysis.
music.stackexchange.com/users/17003/Laurence Payne
Without context it's not so easy to identify the chord.
I'd think that it's an Eb chord in root postion with an E as a non-chord tone; the type of non-chord tone depends on the context.
Of course, it could be an E-diminished chord with Eb as a non-chord tone.
music.stackexchange.com/users/23838/ttw
There is more than just major and minor scales, Look up Dorian, Lydian, PentatonicMixolydian.
They are called "Modes" and they vary from the usual Tonic Solfa configuration.
Keep a clear head, remember folk were making music centuries before they decided to put them into categories.
music.stackexchange.com/users/19803/ohdearme
You can alter notes in a chord made from a scale.
A classic example are the Dom 7-th altered chords.
Consider G9 =
{G, B, D, F, A}.
You can create a G#9, Gb9, G7(b5#9) etc.
The #9 is used in blues, jazz, and rock quite a bit and is {G, B, D, F, A#}.
As almost everyone else has stated context helps.
In the case of the Dom 7th chords the alterations create more "tension" and more half steps to neighboring chords in a progression.
This can be done with any chord.
Sometimes we alter chords and they sound good alone.
Mostly these alterations help with movement in a progression.
The ordering of the chords also helps identify it.
Based on you notes you've provided it could be an Eb Maj add b9
(The E is the b9 to the Eb, more strictly the #1
but it's enharmonic to b9).
It could also be an E dim with a Maj 7th added (but I cannot imagine why).
Again, context.
What are the other chords?
music.stackexchange.com/users/50691/ggcg
Understand that the note after the slash is a bass note, and the bass may have its own thing going on, working toward its own resolution, so that its combination with the notes above it may be incidental.
Especially in modern popular music, a certain set of notes may not necessarily be functioning together as a chord.
Always look at what's happening before and after the notes in question, where they are coming from and where they are going.
Think of a musical composition as a story, with multiple ideas moving from point to point; any given chord is an incomplete snapshot, so don't read too much into it.
music.stackexchange.com/users/10083/ScottM
I thought that to create a chord I am supposed to use one scale. And then I saw this chord, called Eb/E that is made of Eb E G Bb notes. They seem not to fit to either major or minor scale (I cannot find a scale that contains all these notes).  Could someone explain to me that phenomenon, please?
Chord that does not fit into any scale
music.stackexchange.com
<chords><chord-theory>
music.stackexchange.com/questions/74211
music.stackexchange.com/users/52459/Ronx
 Especially in modern popular music, a certain set of notes may not necessarily be functioning together as a chord. Always look at what's happening before and after the notes in question, where they are coming from and where they are going. Think of a musical composition as a story, with multiple ideas moving from point to point; any given chord is an incomplete snapshot, so don't read too much into it. In modern popular music, a certain set of notes may not necessarily be functioning together as a chord
In modern popular music, a certain set of notes may not necessarily be functioning together as a chord. Always look at what's happening before and after the notes in question, where they are coming from. Think of a musical composition as a story, with multiple ideas moving from point to point. Any given chord is an incomplete snapshot, so don't read too much into it.