The Easy Method to Work Out Intervals on Piano

To work out intervals on piano, learn fifths and fourths from the Circle of Fifths and thirds from triads, then build the rest from them: a major seventh is the octave minus one semitone, a minor seventh is the octave minus two, a major sixth is the fifth plus two, a minor sixth is the fifth plus one, and the tritone is the fourth plus one or the fifth minus one.

Video lesson by Jason Zac · Beginner · 19 min

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This music theory lesson from Jason Zac at Nathaniel School of Music gives you a simple framework for working out any interval on the piano. Instead of memorising every interval separately, you learn a few anchor intervals well and then find all the others by adding or subtracting semitones. It suits beginners and anyone who wants to build chords faster. All you need is a notebook, a pen and a keyboard.

Start with a root

An interval always has a root, or reference point. The examples here use C, but the method works from any note.

Step 1: Fifths and fourths from the Circle of Fifths

Fifths and fourths are the most important intervals, because almost all chords, scales, melodies and progressions are built from them.

• Perfect fifths: go clockwise round the circle: C to G, G to D, D to A, A to E, E to B, B to F#, F# to C# (Db), Db to Ab, Ab to Eb, Eb to Bb, Bb to F and F back to C.
• Perfect fourths: go counterclockwise: C to F, F to Bb, Bb to Eb, Eb to Ab and so on.

Piano trick: Bb to F is the only perfect fifth that goes black key to white key, and B to F# is the only one that goes white to black. Every other perfect fifth is white to white or black to black.

Step 2: Major and minor thirds

Thirds are the next essential interval, and they simply need to be learnt until they feel natural. Three ways to find them:

• The third degree of a major scale is a major third; the third degree of a minor scale is a minor third.
• Count semitones: four semitones above any note is a major third (C to E); three semitones is a minor third (C to Eb).
• Use triads: the middle note of a major chord is the major third, and the middle note of a minor chord is the minor third.

Step 3: Build everything else from these

Sevenths

A major seventh is the octave minus one semitone (C to B). A minor seventh, the seventh used in a dominant seventh chord, is the octave minus two semitones (C to Bb). This lets you build seventh chords instantly:

• Major triad + major seventh = major seventh chord
• Major triad + minor (flat) seventh = dominant seventh chord
• Minor triad + major seventh = minor-major seventh chord
• Minor triad + minor seventh = minor seventh chord

It works in inversions too. On E G C, or the second inversion G C E, just think of C major and add Bb wherever it is closest under a free finger. In root position the Bb can go below the C or above the triad.

Sixths

A major sixth is the fifth plus two semitones (C to A). Add it to a minor triad and you get a minor sixth chord. A minor sixth is the fifth plus one semitone (C to Ab). The same key can be named an augmented fifth (C to G#): call it augmented when it replaces the perfect fifth, and a minor sixth when there is no major sixth in the sound. A major sixth is also a diminished seventh: flatten B once to get Bb, then again to get Bbb, which sounds as A. It really functions as a diminished seventh over a diminished triad.

The tritone

The tritone is the fourth plus one semitone (augmented fourth, C to F#) or the fifth minus one (diminished fifth, C to Gb). The Lydian scale's sharp four replaces the perfect fourth, the Locrian's flat five replaces the fifth, and the whole tone scale (1, 2, 3, #4, #5, b7) has neither.

Seconds

A major second is the root plus two semitones (C to D), or a major third minus two. A minor second is the very next semitone (C to Db).

Extended intervals: 9, 11 and 13

The 9 is the 2 an octave higher, the 11 is the 4 and the 13 is the 6, usually heard alongside a seventh. Hold C7 (C E G Bb) in the left hand and add D for the 9, Db for the flat 9 or D# for the sharp 9. Without the flat seventh these notes can sound wrong or harsh; with it they make sense.

How to practise

Write the formulas in your notebook, then use each interval straight away inside a chord rather than memorising it in isolation. Practise from different roots round the Circle of Fifths.

Questions about this lesson

What is the easiest way to remember a major seventh on piano?

Go to the octave of the root and come down one semitone. From C, the octave C minus one semitone gives B.

Is a minor sixth the same as an augmented fifth?

They are the same key on the piano but named differently by context. It is called an augmented fifth when it replaces the perfect fifth, and a minor sixth when there is no major sixth in the sound.

How do I find the tritone from any note?

Take the perfect fourth and go up one semitone, or take the perfect fifth and go down one. From C that is F# (augmented fourth) or Gb (diminished fifth).

What is the difference between a 2 and a 9?

A 9 is the same note as a 2 but played an octave higher and heard with a seventh, such as D over a C7 chord.

Practise it

• Two NotesA guided field guide to intervals: consonance, inversions, scales, modes and the Circle of Fifths.
• Circle of FifthsExplore the Circle of Fifths through keys, scales, chords and intervals.
• All free music apps40 practice tools for harmony, rhythm, ear training and more.

Related lessons

• Ear Training: The Sounds of Intervals (How to Identify Them Fast)To identify an interval by ear, ask whether it sounds resolved (perfect fifth, major third, minor third), dissonant (minor second, diminished fifth, major seventh) or like it wants to move somewhere (major second, perfect fourth, minor seventh), with the sixths sounding mysterious and versatile.
• Build Cinematic Piano Chord Progressions Using Intervals and the Circle of FifthsYou can create cinematic piano progressions by moving major or minor triads by a fixed interval: perfect fifths and fourths around the Circle of Fifths give strong cadences, while repeated minor thirds (diminished seventh roots) or major thirds (augmented triad roots) give mysterious, movie-like chord changes.
• How to Use the Circle of Fifths for Pro Chord WritingTo write non-diatonic progressions with the circle of fifths, move between neighbouring major chords such as C, F, Bb and Eb, or C, G and D, because each neighbour shares a common note and the change sounds smooth even outside one key.
• Laufey's From the Start: An Intervallic Breakdown of Its Richer ChordsIn Laufey's From the Start (key of Db major), each melody note can be heard three ways: as a scale degree of the root Db, as an interval from neighbouring notes, and as a chord tone, so the same F is the 3rd of Db, the 9th of Ebm9 and the 13th of Ab13.