The term "interval" refers to the distance between two notes or pitches. The lettering system for naming notes also designates the size of any given interval. For instance, if you write out the pitches in a C Major scale (C, D, E, F, G, A, B, C) and then write out numbers to correspond with each note in the scale (1, 2, 3, 4, 5, 6, 7, 8, respectively), these numbers tell you how far any note in the scale is from the root, C. So D is a "second" (from C), E a "third," F a "fourth," and so on. You can figure out the size of any interval by counting up or down the note letters. So E to F is a second, A up to E (A, B, C, D, E) is a fifth, A down to E (A, G, F, E) is a fourth, and so on.
Every interval also has a quality descriptor because we use accidentals to represent different pitches even though the letter of the note stays the same. The most common descriptors are: major, minor, perfect, diminished, and augmented. Major refers to the larger of two similar intervals while minor is the smaller of the two (major second versus minor second), perfect is used for the highly consonant fourth and fifth intervals, diminished intervals are one half-step lower than a minor or perfect interval, and augmented intervals are one half-step higher than a major or perfect interval. There are two additional descriptors: doubly diminished and doubly augmented (one extra half-step beyond the normal version), but these intervals are far less common, and we will not use them in the following lessons.