Seventh
A seventh is an interval of seven letter names, such as G–F or C–B. A minor seventh is ten half steps, a major seventh eleven.
From G to F there are seven letter names, both ends included: G, A, B, C, D, E, F. That is a seventh, one letter short of an octave. On the staff its notes stand far apart, both on lines or both in spaces, with two lines skipped between them.
Sevenths come in two sizes. From G to F is ten half steps: a minor seventh. From C to B is eleven: a major seventh, just a half step short of the octave. A seventh is a second turned upside down: G up to F is a seventh, F up to G a second.
The seventh gives the dominant seventh chord its name. Add a fourth note, F, to the dominant G–B–D, and from the bottom G to F is a seventh – hence the 7 in G7. That F wants to fall to E, and the chord comes home to the tonic. The first leap of “Somewhere” from West Side Story is a minor seventh up.
What it sounds like
A seventh sounds tense and unfinished, as if waiting for the top note to fall. A minor seventh is the softer of the two; a major seventh is sharp, almost an octave that “missed”.
Where it is taught: the studio’s interactive textbook, chapter 11, “Triad inversions and the dominant seventh” and chapter 15, “Intervals: unison to octave”.