Intervals

An interval is the distance between two notes. Every pair of notes you can play has one, and the interval, not the notes themselves, is what gives a melody or a chord its character.

There are two ways to sound an interval. Play the notes one after the other and you have a melodic interval. That is what a tune is made of. Play them at the same time and you have a harmonic interval. That is the beginning of harmony.

A melodic interval also has a direction. If the second note is higher it is ascending; if it is lower it is descending. D up to A and A down to D are the same distance, just travelled in opposite directions.

Every interval name has two parts, a number and a quality. The number is the easy part: count the letter names from the lower note to the upper note, including both.

Two notes with the same letter and the same pitch are a unison (1). The same letter eight positions later is an octave (8). Sharps and flats do not change the number: D to F and D to F# are both thirds. They differ only in quality, which is the subject of the rest of this chapter.

The two smallest intervals need defining first. The semitone (also called a half step) is the smallest distance in Western music: from any piano key to the very next key, black or white, with nothing in between.

Two semitones make a whole tone. On the piano a whole tone always skips exactly one key. Most white-key neighbours are a whole tone apart, but E to F and B to C are only a semitone apart. Those are the two places with no black key in between.

Every wider interval is built from these two, and an octave holds twelve semitones: one full trip round the twelve notes and back to the same letter. But we will not name intervals by counting keys. From here on each distance gets a name of its own and, above all, a place in the major scale, and that is how you will recognise it.

Inside one octave there are exactly thirteen intervals, from unison to octave, and every one of them has a name. Here is the whole family measured up from C. The column to remember is the degree: where the interval sits in the major scale, written the way every formula in this course writes it. The semitone count is there only as a reference.

Notice the pattern in the words. Unison, 4th, 5th and octave are perfect. 2nds, 3rds, 6ths and 7ths come in pairs, minor just below major. The plain degrees 1 2 3 4 5 6 7 8 are the major scale, and every b is the minor version of one of them. The gap in the middle, between 4 and 5, has a name of its own: the tritone. Play each row as a harmonic interval too, and start attaching a sound to every degree.

Four intervals are called perfect: the unison, the 4th, the 5th and the octave. In the major scale they are degrees 1, 4, 5 and 8. They are the most stable, open-sounding intervals we have, so blended that the two notes almost fuse into one.

Why "perfect" and not "major"? Because these intervals have no major/minor pair. A 5th is either perfect or it is something else (we will meet those exceptions soon). The perfect 5th is so fundamental that tuning systems, the circle of fifths and the whole layout of keys are built on it.

Seconds and thirds are not perfect. Each comes in two sizes. The major version is the one the major scale gives you (2 and 3), and the minor version is one semitone smaller (b2 and b3). The same letters, a different colour.

The third is the one to remember. It decides whether a chord is major or minor. D to F# is a major third, the 3 of D, and gives you a D major sound. D to F is a minor third, the b3, and gives you D minor. Rather than "happy" and "sad", think brighter and darker: both colours turn up in joyful and in mournful music.

Sixths and sevenths follow the same rule as seconds and thirds: the major scale gives the major size (6 and 7), and the minor size sits one semitone lower (b6 and b7). But they are wider, so they sound less like a step and more like a leap.

The two sevenths are worth hearing side by side. The minor 7th is the b7 that turns G B D into the G7 chord you hear before nearly every return to home. The major 7th is the 7 of the scale, the leading tone. It sits just under the octave and leans up toward it. Play G to F# and let the F# slide into G to feel that pull.

Exactly halfway round the octave sits the tritone. It is the interval the major scale skips over: wider than the perfect 4th, narrower than the perfect 5th, so in a formula it appears as #4 or b5. Its name comes from its size, three whole tones (six semitones) stacked up. It is the most restless interval we have. It does not sit still, it points somewhere.

It has two spellings depending on the letters. F to B counts as a 4th (F G A B) but is wider than the perfect 4th, so it is an augmented 4th. B to F counts as a 5th (B C D E F) but is narrower than the perfect 5th, so it is a diminished 5th. Same sound, two names.

Beyond major, minor and perfect there are two more qualities. Augmented means a semitone larger than major or perfect. Diminished means a semitone smaller than minor or perfect. In formulas that is exactly what # and b do: #5 is an augmented 5th, b5 a diminished 5th. They let us keep the letter count while shifting the size.

That last row is the important lesson: C to D# and C to Eb are played on the same keys, yet one is an augmented 2nd and the other a minor 3rd. Notes that sound the same but are spelled differently are enharmonic. Which name you use depends on the letters the music is built from. Later, augmented 5ths (1 3 #5) and diminished 5ths (1 b3 b5) will give us the augmented and diminished chords.

To invert an interval, move the lower note up an octave (or the upper note down) so the two notes swap places. D under F# is a major 3rd; put the D on top and F# to D is a minor 6th. The notes are the same, the interval is not.

Why does this matter? Because a chord keeps its identity when its notes are re-stacked. Whether the E sits above the C (major 3rd) or below it (minor 6th), you are still hearing C and E, the same chord tones. Inversions of whole chords, in a later chapter, are this idea applied to three notes.

Intervals wider than an octave are called compound intervals. They are just a simple interval with an octave added: a 9th is an octave plus a 2nd, an 11th is an octave plus a 4th, a 13th is an octave plus a 6th.

The name tells you the octave is there: D right next to C is a 2nd, but the same D an octave higher is a 9th. Chord symbols use these numbers for extensions, notes added above the seventh, which is why you see C9, C11 and C13 rather than C2, C4 and C6.

Here is where intervals turn into the tool we use for the rest of the course. The major scale is seven notes, and each one is a specific interval above the first note, the tonic. Number those intervals and you get the degree formula.

Every degree of the major scale is either a perfect or a major interval above the tonic, never minor, never diminished. That is exactly why we call it *major*, and why it becomes the ruler: a b3 in a formula means "a minor 3rd where the major scale had a major 3rd", a #4 means "an augmented 4th where it had a perfect 4th". Move the whole set of intervals onto G and you get G major, with F# as the major 7th.

In the next chapter we build this scale note by note, name its degrees, and take it round all twelve keys.