To play the Ebaug chord, place the middle finger on the 3rd fret of the C-string, ring finger on the 3rd fret of the E-string, and index finger on the 2nd fret of the bottom A-string. Let the other string ring open.
The Ebaug chord (also known as a D#aug chord) contains the notes Eb-G-B.
To build an Ebaug chord, take the augmented triad formula (1-3-#5) and apply it to the Eb major scale (Eb, F, G, Ab, Bb, C, D).
Identify the first, third, and fifth scale degrees in an Eb major scale which are Eb-G-Bb.
Because the fifth scale degree is a "#5" (said "sharp five") raise the Bb note a half step to B making the chord augmented with the notes Eb-G-B.
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