Intervals
An interval is the distance in pitch between two notes. Intervals are named by two properties: size (a number from 1 to 8 and beyond, counted by letter names inclusive) and quality (perfect, major, minor, augmented, or diminished). The size is determined by counting the letter names spanned, including both endpoints: C to G spans five letters (C D E F G), so it is some kind of fifth.
Quality refines the size. Unisons, fourths, fifths, and octaves take the qualities perfect, augmented, or diminished. Seconds, thirds, sixths, and sevenths take major, minor, augmented, or diminished. A major interval narrowed by a half step becomes minor; narrowed again, diminished. A perfect or major interval widened by a half step becomes augmented. Key diatonic intervals: perfect fourth = 5 half steps, perfect fifth = 7, major third = 4, minor third = 3, major sixth = 9, minor sixth = 8, major seventh = 11, minor seventh = 10.
Intervals can be harmonic (both notes sounding together) or melodic (notes in succession). Inverting an interval means moving the lower note up an octave (or the upper note down): the size numbers of an interval and its inversion always add to 9, and qualities invert as follows — perfect stays perfect, major becomes minor, minor becomes major, augmented becomes diminished, and diminished becomes augmented. Intervals larger than an octave are called compound intervals (a ninth = an octave plus a second, and so on).
