Intervals

A half step is the smallest interval in Western music: the distance from any note to the very next note, with nothing in between. (also called semitone, British and European usage)

A whole step is two half steps. Between E and F, and between B and C, there is no black key, so those pairs are half steps; every other pair of white keys is a whole step apart.

Every larger interval is a count of half steps. That count is what makes an interval sound the way it does, wherever you start.

Interval quality is the word in front of an interval's number — major, minor, perfect, augmented or diminished — and it fixes the exact size in half steps of an interval whose number has already said how many letter names it spans.

The number comes first, and it is pure counting. Call the lower note one and count letter names up to the higher one, including both ends: C4Play up to E4Play counts C, D, E, so it is a third. Sharps and flats never change that count, which is why C4Play up to E♭4Play is also a third.

Quality then settles the size. Seconds, thirds, sixths and sevenths come in major and minor, and minor is always one half step smaller than major. Unisons, fourths, fifths and octaves take perfect instead, and have no major or minor form at all. Squeeze any of them a further half step and it is diminished; stretch it and it is augmented.

The pair of words is the whole name. A Major Third is four half steps and a Minor Third is three, and that single half step is the difference between a chord that sounds bright and one that sounds sad.

A simple interval is any interval no wider than an octave, and there are twelve of them above a given note — one for each half step from one to twelve, with the unison, a distance of no half steps at all, as the thirteenth case this table leaves out.

That is the whole vocabulary. Every melody you have ever heard is made of these twelve moves in some order, up or down, and every chord is two or three of them stacked. Learning them is not learning twelve rules; it is learning twelve sounds.

The fastest way in is the last column of the table. A song you already know gives you the interval for free: sing the first two notes of "Twinkle Twinkle Little Star" and you have just produced a Perfect Fifth without counting anything.

Counting half steps is the slow check you fall back on when the sound is not yet automatic, and it never lies. The count is fixed: a Major Third is four half steps up from C, from F, or from B flat.

Consonance is the quality of an interval that sounds settled: two notes that blend, need nothing after them, and could be held indefinitely without discomfort.

Dissonance is the opposite quality. The two notes are close enough in frequency to interfere audibly with each other, and the result is an edge, a beating or a grind that the ear reads as unfinished.

Tradition sorts the intervals into three groups rather than two, as the table shows. Perfect consonances blend so thoroughly that they can sound bare; imperfect consonances — the thirds and sixths — are stable but full of colour, which is why nearly every chord in popular music is built from them; everything else is dissonance.

Dissonance is not a mistake, and consonance is not a compliment. A piece made only of consonance has no forward motion at all: the tension of a dissonance and its release is a large part of what makes music feel like it is going somewhere.

Interval inversion is what happens when the lower of two notes is moved up an octave, or the upper moved down, so that the same pair of note names is measured the other way round.

The two numbers always add to nine. C4Play up to E4Play is a third; move that C up an octave and E4Play up to C5Play is a sixth, and three plus six is nine. The arithmetic works because the pair now spans an octave — an eighth — and the note they share is counted twice, once at the top of one interval and once at the bottom of the other.

The quality flips with it. Major becomes minor and minor becomes major, augmented becomes diminished and diminished becomes augmented, and perfect stays perfect. A Major Third inverts to a Minor Sixth; a Perfect Fourth inverts to a Perfect Fifth.

This is worth more than the arithmetic suggests. It halves what you have to learn by ear, because the wide intervals are the narrow ones turned over; it explains why a bass line falling a fifth and rising a fourth sound like the same move; and it is the same idea you will meet again when a chord is rearranged so a different note sits at the bottom.

A compound interval is any interval wider than an octave: a simple interval with an octave added on top of it.

Naming one is addition. Take the number of the simple interval inside it and add seven — a second becomes a ninth, a third a tenth, a fourth an eleventh, a fifth a twelfth, a sixth a thirteenth. Seven rather than eight, because the octave is an eighth and the note the two intervals share is counted twice. The quality carries over untouched: a major second becomes a Major Ninth, a perfect fourth a Perfect Eleventh.

What changes is not the name but the friction. Two notes a Major Second apart are close enough to grind; spread them an octave and the same two notes open out into the mild, bright sound that a great deal of modern harmony lives on. Same note names, a completely different effect.

That is why chord symbols bother with the big numbers at all. Writing a chord as a ninth rather than an added second is a way of saying which note to add and roughly where it belongs — above the seventh, in the open air, rather than jammed against the root.