: Whats the triad formed root +maj 3rd +maj 2nd called? Extremely dissonant but is there an official name for it. formula: root +maj 3rd +maj 2nd

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The most straightforward interpretation is as a simple triad, without any implied notes. In this case, the formula for the chord would need to be re-interpreted as:

root - major third - diminished third

which is enharmonically the same as the formula in your question. With root C, you'd have

C - E - Gb

I know that in German and Dutch, there is a specific name for this chord: hartvermindert (German), and hardverminderd (Dutch).
As far as I know there is no specific term for it in English.

The most common chord symbol for this chord is C(b5), because it simply is a major triad with a diminished fifth.

Note that more often than not, this chord voicing (interpreted enharmonically) is used as the upper structure of a different chord. E.g., that chord based on the note C could be used as an upper structure of an Am6 chord, of a D9 chord, or of an Ab7(#5) chord:

Am6: (A -) C - E - F#
(R) b3 5 6

D9: (D - A -) C - E - F#
(R - 5) b7 9 3

Ab7(#5): (Ab -) C - E - Gb
(R) 3 #5 b7

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Let's take a concrete example. In C major, your notes are C, E and F#.

You could consider this a part of an F#m7b5 chord. It's missing the A, which defines the minor quality of the chord, but I've seen it notated that way (in the progression Am, F#m7b5, Fmaj7, G).

This depends on the surrounding progression. If the three notes are in isolation, I'd use the add#11 from Dom's answer.

For interest's sake, I located an instance of a very similar chord in a song. It's notated as A(#4), which I suspect is rather unconventional:

It's built on a b7 root, so it's kind of a b7sus4 sort of thing. The notated piano part does not have a third, but the guitar chord diagram does:

%3/.4/.0/0.0/0.0/0.3/[G(#4)]

The notes are G, C#, D, G, B, G, if I read it correctly.

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It's a chord and chord symbol that doesn't come up much in many styles but you could look at it as and add#11 chord with an implied 5th. So in C major it will contain the notes C, E, and F# with the G implied and it would be called Cadd#11.

A much better way to look at this chord is to look at it in set notation. In this instead of using the typical naming scheme we just need it based the distance from root in semitones. So for this we can look at it as the set containig the notes 0, 4, and 6. Not really the prettiest thing especially when explaining to other musicians, but it best reflects the name without getting crazy.