Intervals

An interval is the distance between two pitches. The generic sizes, from smallest to largest, are: unison, second, third, fourth, fifth, sixth, seventh, and octave. To determine the generic size of an interval, count from the bottom note to the top note by alternating lines and spaces. The bottom note is always counted as one. For example, to determine the interval C to A, count C as one, D as two, E as three, F as four, G as five, and A as six. C to A then, is a sixth. Because the lines and spaces refer to pitches in the musical alphabet, you can also count through the alphabet to achieve the same answer: C, D, E, F, G, A.

There are five different qualities of intervals, from smallest to largest: diminished, minor, major, perfect, and augmented. Intervals occur naturally in major and minor scales and their quality can be determined by their size and position in a particular scale. In major and natural minor scales, unisons, 4ths, 5ths, and octaves are perfect intervals; 2nds, 3rds, 6ths, and 7ths are either major or minor depending on the scale.

The quality of an interval is determined by its spelling. Decreasing the size of a major interval by one half step results in a minor interval. Increasing the size of a perfect or major interval results in an augmented interval. Decreasing the size of a perfect or minor interval results in a diminished interval.

C to A is a major 6th. By lowering the A to Ab, the interval becomes a minor 6th. The A can be lowered again to Abb, resulting in a diminished 6th. Notice that enharmonically this sounds the same as a perfect fifth — yet it is spelled as a sixth. How intervals are spelled is crucial to correctly identifying their quality. Remember that the generic size is always determined by the letter names.

Intervals can be identified through different processes and techniques. The following is one standard method.

1. Determine the generic size of the interval. The bottom pitch is A, the top pitch is Cb. Counting through the alphabet, and ignoring the accidental on the top note, we learn that this is a 3rd — A, B, C (1, 2, 3).
2. Determine the quality of the interval. Use a major scale to see if the top note fits the scale. In A major, C would be sharp (C#). Since our top note is Cb — two half-steps below C# — the interval is a diminished 3rd.

The bottom pitch of the second interval is Bb and the top pitch is F. Counting through the alphabet gives five letter names — B, C, D, E, F — so this is a 5th. In Bb major, F is natural, meaning this 5th is perfect. Placing a flat on F would produce a diminished 5th; placing a sharp on F would produce an augmented 5th.

To invert an interval, move the bottom pitch up an octave or move the top note down an octave, then identify the new interval. For example, F to A, a major 3rd, inverts to a minor 6th — A to F. The chart below details which intervals invert to one another: unison/octave, m2/M7, M2/m7, m3/M6, M3/m6, P4/P5, +4/°5.

To determine the interval below a given note, follow one of two methods.

1. Inversion: If E is the given note and we need a M3 below, first determine what a m6 above E would be (M3 inverts to m6). Counting up six letters gives C natural — a minor sixth above E. Inverting that m6 brings C natural down one octave, producing a M3 below E.
2. Direct: Count down the generic size from E to C — three letter names. To confirm the quality, use the scale of the lower note, C. Since E natural belongs to the C major scale, this is a M3.

Intervals an octave or smaller are called simple intervals. Intervals larger than an octave are called compound intervals. By transposing the top note of the interval up an octave, it becomes a compound interval: 2nds become 9ths, 3rds become 10ths, 4ths become 11ths, and so on.

Compound intervals have the same harmonic implication as their simple interval counterparts. This means that 10ths are functionally equivalent to 3rds, and 9ths are functionally equivalent to 2nds.