Interval Quality

In Intervals you counted letter names to find an interval's number. C up to E is a third: C, D, E. C up to E-flat is a third too, because it uses the same three letters. Same number, but the two do not sound the same.

The difference is the exact size. E-flat sits one half step below E, so C to E-flat is a little narrower than C to E. Musicians name each size with a word called the quality. C to E is a major third, written M3, and C to E-flat is a minor third, written m3.

At a keyboard, play C and E together, then C and E-flat together. Listen for the change. Many listeners hear C and E as brighter, and C and E-flat as a little darker.

Number and quality measure two different things. The number counts letters, so it follows the staff: a third always joins line to line or space to space, whatever accidentals sit on its notes. The quality reads the half-step count against that number: across three letters, four half steps make a major third and three a minor third. The five qualities, perfect, major, minor, augmented, and diminished, are written P, M, m, A, and d, so a major third is M3.

Notation needs both readings. C to E-flat and C to D-sharp are played with the same two keys, yet C to E-flat is a third and C to D-sharp a second, because their letters span three names and two. The full name tells a reader how the interval sounds and how it is spelled.

Intervals come in two families. Unisons, fourths, fifths, and octaves are one family, and their normal size is called perfect. Seconds, thirds, sixths, and sevenths are the other family, and each of them comes in two common sizes, major and minor.

So you will hear about a perfect fifth or a perfect octave, but never a major fifth. You will hear about a major third or a minor third, but never a perfect third. The number tells you which family's words to use.

If you play violin, you already know the sound of a perfect fifth. The open strings, G, D, A, and E, are tuned a perfect fifth apart, and a viola's open strings, C, G, D, and A, are too. Pluck two neighboring strings, like D and A, one after the other, and listen.

The word perfect has a long history. Since antiquity, theorists have set the octave, fifth, and fourth apart because their string lengths, and as later shown their frequencies, stand in ratios of small whole numbers: 2:1, 3:2, and 4:3, with the unison at 1:1. Early written polyphony moved in these intervals. Medieval writers ranked them in different ways, some calling only the unison and octave perfect, and the modern name covers all four.

Theory still sorts consonance along these lines. The unison, fifth, and octave are perfect consonances; thirds and sixths, major or minor, are imperfect consonances; seconds, sevenths, and the tritone, the six-half-step interval of the last part, are dissonances. The fourth is the odd case: tonal harmony treats it as a dissonance when its lower note is the bass and as a consonance between upper voices.

You learned in Half & Whole Steps that a half step is the move from one key to the key right beside it. To tell a major third from a minor third, count those moves from the bottom note up to the top note. Do not count the key you start on.

C up to E takes four moves, so it is a major third. C up to E-flat takes three, so it is a minor third. Seconds work the same way. A minor second is one half step, and a major second is two, which is a whole step.

At a keyboard, put a finger on C and walk up to E, counting each key you land on. Then walk from C to E-flat. Four for major, three for minor.

For each number, every quality has a fixed half-step count. The unison, fourth, fifth, and octave take perfect as their reference size, and the other numbers take major. Minor is one half step under major, diminished one under minor or perfect, and augmented one over major or perfect.

The same counts handle inversion. An interval and its inversion fill an octave between them, so their half steps add up to 12 and their numbers to 9. A major third, 4 half steps, turns over into a minor sixth, 8; a perfect fifth, 7, into a perfect fourth, 5. Major and minor trade places, augmented and diminished trade places, and perfect stays perfect.

Here is a shortcut. Build a major scale on the bottom note of an interval. Every note in that scale makes a major or perfect interval with the bottom note: a major second, major third, perfect fourth, perfect fifth, major sixth, major seventh, and perfect octave.

In C major, C up to E is a major third and C up to A is a major sixth, because E and A are in the scale. If the top note keeps its letter but sits one half step below the scale note, the major interval turns minor. C up to A-flat is a minor sixth, because A-flat is the A of C major moved down a half step.

Play C, then each note of the C major scale above it, and name each pair: major second, major third, perfect fourth, and on up to the octave.

The shortcut works because a major scale lays out the reference sizes: measured up from its tonic, its notes form the major and perfect intervals and nothing else. The check depends only on the major scale of the bottom note, not on the key of the piece, which is why this class follows The Major Scale.

The words major and minor are Latin for larger and smaller. They name the two sizes of second, third, sixth, and seventh, and the same words name keys by the third above the tonic: a major key has a major third there, and a minor key a minor third, the change the next class starts from.

Two more quality words cover intervals stretched or squeezed past the usual sizes. Make a major or perfect interval one half step wider, keeping the same letters, and it becomes augmented. Make a minor or perfect interval one half step narrower, and it becomes diminished.

One size has a name of its own: the tritone, six half steps wide. Among the white keys it sits from F up to B. That is an augmented fourth, the perfect fourth F to B-flat made a half step wider. Turned around, B up to F, it is a diminished fifth.

At a keyboard, play F and B together. That tense sound is the tritone. Now move the B down to B-flat for a perfect fourth, and hear it smooth out.

Inside a major scale, the only augmented and diminished intervals are the tritones between its fourth and seventh notes, F to B and B to F in C major. Every other one needs a note raised or lowered from the scale, and in equal temperament it shares keys with an interval you already know: an augmented second uses the same keys as a minor third, and a diminished fourth the same keys as a major third. The spelling hints at direction, since a raised note usually leads upward and a lowered one downward.

The tritone splits the octave into two equal halves, six half steps each, so inverting it gives six half steps again: an augmented fourth turned over is a diminished fifth. Inside the dominant seventh chord, the tritone's two notes pull toward the tonic chord, a role the chord classes take up.