interval
E augmented fourth
ElowerA♯upperA46 half steps
A perfect fourth widened by a half step. Same sound as the diminished fifth, different letter, different behaviour.
On the keyboard
What is true of it
E up a augmented fourth is A♯: 6 half steps, and 4 letters counting both ends.
Turn it upside down — put the E on top — and it becomes a diminished fifth. The two numbers always add to nine, and the two sizes to twelve.
It is a dissonance.
Six half steps can be written two ways: E to A♯ is a fourth, E to B♭ is a fifth. They sound the same and behave differently.
Every interval on E
E → Fminor second · dissonanceE → F♯major second · dissonanceE → Gminor third · imperfect consonanceE → G♯major third · imperfect consonanceE → Aperfect fourth · perfect consonanceE → B♭diminished fifth · dissonanceE → Bperfect fifth · perfect consonanceE → Cminor sixth · imperfect consonanceE → C♯major sixth · imperfect consonanceE → Dminor seventh · dissonanceE → D♯major seventh · dissonance