Interval
Distance in pitch between two notes.
What it means
An interval is the distance between two notes. If they sound one after another, one speaks of a melodic interval; if they sound at the same time, of a harmonic one. Two indications belong to its determination: the number of scale degrees involved and the exact size in semitones.
In the notation
The number of degrees is counted including both notes: from C to E there are three degrees, that is, a third. This way of counting explains why the prime, as the “first” interval, designates the distance zero. In the notation the number of degrees can be read off directly — line to the next line is always a third, line to the line after next a fifth.
The exact size follows from the accidentals. Prime, fourth, fifth, and octave are called perfect; second, third, sixth, and seventh are called major or minor. If a perfect or major interval is widened by a semitone, it is called augmented; if a perfect or minor one is narrowed, it is called diminished.
Musical use
Intervals are the stuff from which melodies and chords are built, and their description is independent of the key — precisely this makes them a basic concept. With inversion the rule of nine holds: the numbers of an interval and its inversion add up to nine, major becomes minor, augmented becomes diminished, perfect remains perfect.
Bear in mind that the spelling is not arbitrary: an augmented fourth and a diminished fifth sound the same on tempered instruments but lead on differently — the former strives outward, the latter contracts.
Intervals are named by the number of degrees they comprise and by their quality as perfect, major, minor, augmented, or diminished. One distinguishes melodic intervals, in which the notes sound one after another, from harmonic ones, in which they sound simultaneously. Intervals larger than the octave are called compound.
Performance practice
Read intervals as a picture instead of an arithmetic problem: recognize the number of degrees in the notation at a glance and then check the accidentals. Sing intervals regularly, upward and downward — that is the most effective part of any ear training. And grasp leaps as an interval, not as two single notes; this is faster and more secure.