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Home›Music theory

Intervals

An interval is the distance between two notes. Count half steps on the keyboard, name thirds, fourths, fifths and octaves, hear why some intervals sound stable, and train your ear and voice with melodies everyone knows.

Progress

About this course

An interval is the distance between two notes, and the course starts with the smallest ones. Twelve half steps make an octave, and only two pairs of white keys, E to F and B to C, are a half step apart. C up to E is a third, not a second, because you count both notes: C is one, D is two, E is three. A major third is four half steps and a minor third is three, and that single half step changes the mood of a chord.

The eight units go from counting to hearing. After half steps and whole steps and counting intervals, you learn major and minor thirds and perfect fourths and fifths. A perfect fifth is seven half steps, and flipping it upside down gives a perfect fourth of five. Octaves come next: middle C vibrates about 261.63 times a second and the C above it about 523.25, almost exactly twice as fast. Consonance and dissonance notes that the perfect fifth has a frequency ratio of 3:2, though on a piano it is tuned about 2 cents narrower. Intervals in famous openings points out that "My Bonnie Lies Over the Ocean" opens with a jump of nine half steps, a major sixth. The last unit is ear training and singing, where studies of music practice find that short sessions spread over several days work better than the same practice crammed into one.

Several of the tunes have long histories. "Twinkle, Twinkle, Little Star" is sung to the 18th-century French melody "Ah! vous dirai-je, maman", which Mozart used for a famous set of piano variations. The words of "Amazing Grace" were published by John Newton in 1779, and Brahms' Lullaby in 1868.

Before you start

Knowing the note letters and their places on the staff helps when you count the distance between two notes. Review Reading notes if those are unfamiliar. The first unit explains half steps on the keyboard before you compare larger intervals by sight and sound.

When you finish

You can count both endpoints to name an interval, distinguish major and minor thirds, and identify perfect fourths, fifths and octaves. You can explain how an octave changes frequency, use familiar song openings to remember a leap, and practise both naming a heard interval and singing one from a given note.

  1. 1Half steps and whole stepsTwelve half steps make an octave, and only two pairs of white keys, E to F and B to C, are a half step apart.
  2. 2Counting intervalsC up to E is a third, not a second, because you count both notes: C is one, D is two, E is three.
  3. 3Major and minor thirdsA major third is four half steps and a minor third is three, and that single half step changes the mood of a chord.
  4. 4Perfect fourths and fifthsA perfect fifth is seven half steps, and flipping it upside down gives a perfect fourth of five half steps.
  5. 5OctavesMiddle C vibrates about 261.63 times a second and the C above it about 523.25 times, almost exactly twice as fast.
  6. 6Consonance and dissonanceThe perfect fifth has a frequency ratio of 3:2, and on a piano it is tuned about 2 cents narrower than that.
  7. 7Intervals in famous openings"My Bonnie Lies Over the Ocean" opens with a jump of nine half steps, a major sixth, on "My Bon-".
  8. 8Ear training and singing intervalsStudies of music practice find that short sessions spread over several days work better than the same practice crammed into one long session.

Related courses

  • Reading notes
    Learn to read pitches on the staff: treble clef, bass clef, ledger lines, the grand staff, sharps and flats, and the different names musicians use for the same notes. Every unit has a staff quiz or a keyboard you can play.
  • Rhythm and meter
    How music is measured in time: the beat and tempo, note values and rests, dots and ties, simple meters like 3/4 and 4/4, compound meters like 6/8, and syncopation, triplets and pickups. Every unit has the rhythm lab with a tap-along test that scores each tap in milliseconds, and most units add a metronome for any time signature and note blocks you stack into bars.
  • Scales and keys
    Build any major scale from one pattern of whole and half steps, name every scale degree, read a key signature at a glance, find your way around the circle of fifths, and tell a minor key from its relative major.
  • Chords
    Stack thirds to build triads, hear the difference between major, minor, diminished and augmented, name every chord in a key with Roman numerals, read inversions and seventh chords, and follow the progressions and cadences that end a musical phrase.
Sources for this course (12)
  • Open Music Theory (Viva Pressbooks)
  • chapters "Half and Whole Steps" (viva.pressbooks.pub/openmusictheory/chapter/half-and-whole-steps/)
  • "The Keyboard and the Grand Staff" generic intervals (viva.pressbooks.pub/openmusictheory/chapter/the-keyboard-and-grand-staff/)
  • "Intervals" incl. qualities, white-key method, inversion, compound intervals, consonance and dissonance tables, semitone chart (viva.pressbooks.pub/openmusictheory/chapter/intervals/)
  • Wikipedia "Major scale" W-W-H-W-W-W-H and ratios 3/2, 5/4 (en.wikipedia.org/wiki/Major_scale)
  • "Pythagorean tuning" 2:1, 3:2, about 702 cents and the disputed Pythagoras attribution (en.wikipedia.org/wiki/Pythagorean_tuning)
  • "Consonance and dissonance" (en.wikipedia.org/wiki/Consonance_and_dissonance)
  • "Interval recognition" (en.wikipedia.org/wiki/Interval_recognition)
  • "Amazing Grace" 1779 text and 1835 tune New Britain (en.wikipedia.org/wiki/Amazing_Grace)
  • "Brahms' Lullaby" 1868 (en.wikipedia.org/wiki/Brahms%27_Lullaby)
  • Miami Dade College Music Lab interval sheet (mdc.edu/kendall/academic-departments/performing-arts-and-industries/documents/MHL_Interval_Sheet.pdf) and The Salvation Army USA interval reference chart (music.saconnects.org/wp-content/uploads/App.-6.1-Interval-Reference-Chart.pdf) for reference songs. Only public-domain or traditional melodies are quoted. Cents computed with 1200 x log2(ratio)
  • frequencies with f = 440 x 2^((m - 69) / 12).

Checked: 2026-10-17