Sixth
A sixth is an interval of six letter names, such as C–A. A major sixth is nine half steps, a minor sixth eight.
From C to A there are six letter names, both ends included: C, D, E, F, G, A. That is a sixth. On the staff one note sits on a line and the other in a space, with two lines skipped between them: far apart, but not yet an octave.
Sixths come in two sizes. From C to A is nine half steps: a major sixth. From E to C is eight: a minor sixth. A sixth is a third turned upside down: C–E is a third, and E up to C is a sixth. Inverting a major third gives a minor sixth, and the other way round.
That is why the first inversion of a triad is called a sixth chord: in E–G–C the bottom and top notes are a sixth apart. An easy way to remember the sixth is “My Bonnie Lies over the Ocean”: on “My Bon-” the melody rises a major sixth.
What it sounds like
A sixth sounds soft, wide and singing – like a third, but opened up. A major sixth is bright, a minor sixth more wistful.
Where it is taught: the studio’s interactive textbook, chapter 15, “Intervals: unison to octave”.