Music Intervals Explained: How to Count, Name and Hear Every Interval from the Half Step to the Octave

Play C, then the E above it. Now play them together. Whichever way you play them, the distance between the two notes is the same, and musicians have a name for it: a major 3rd. That distance is an interval, and once you can name intervals you stop reading music one note at a time. You see a leap, you know its size, and your hand is already shaped for it.

Below: two counts that name any interval from the unison to the octave, the five qualities, the trick for turning an interval upside down, and a tune you already know for most intervals. Every step has a free Tissimo worksheet.

What an interval is

An interval is the distance between two notes. When the notes sound one after the other, as in a tune, it is a melodic interval. When they sound together, as in a chord, it is a harmonic interval. The name does not change: C–E is a major 3rd either way.

The same major 3rd, C up to E, played melodically (one note, then the other) and harmonically (both together).

Every interval name has two parts. The number (2nd, 3rd, 4th and so on) says how many letters the interval spans. The quality (major, minor, perfect, augmented or diminished) says its exact size in half steps. You find them with two separate counts, and it pays to do them in that order.

Two counts, always in this order: letters first for the number, then half steps for the quality.

Count the letters: the number

To find the number, count every letter name from the bottom note to the top note, and count both ends. C up to D: C is 1, D is 2, so it is a 2nd. C up to E: C, D, E, three letters, so it is a 3rd, even though you only play two notes. The letter you skip still gets counted. This is how Intervals: Steps & Skips starts, and Open Music Theory gives the same rule: count the letter names "including both pitches in your count."

Count the bottom note as 1: C–D is a 2nd, C–E a 3rd, C–F a 4th and C–G a 5th.

Why start at 1 and not 0? Because the smallest interval, two voices on the very same note, is called a unison (or "prime"): one letter, so its number is 1. It also means an octave, C up to the next C, is an 8th: C D E F G A B C, eight letters.

On the staff you can often read the number from the shape before you count. Odd numbers (3rds, 5ths, 7ths) go line to line or space to space. Even numbers (2nds, 4ths, 6ths, octaves) go line to space or space to line. Check both directions: E–G is line to line, F–A is space to space, and both are 3rds. The worksheets Intervals: the 4th and Intervals: the 5th show these shapes: a 4th leaves "daylight" between the notes, and a 5th skips a whole line or space.

Odd numbers sit line to line or space to space; even numbers go from a line to a space or from a space to a line, whichever you start on.

One more rule saves a lot of confusion: sharps and flats never change the number. C–E, C♯–E and C–E♭ are all 3rds, because each one uses the letters C, D, E. The accidental changes the size, not the letter count. Name the Intervals: the distance (Exercise 04) drills this first count with 25 intervals in treble and bass clef.

Three 3rds. The letters (C, D, E) fix the number; the sharp or flat only changes how many half steps the 3rd spans.

Count the half steps: the quality

The number tells you which family an interval belongs to. To name it exactly you need a finer ruler: the half step (also called a semitone). A half step is the move from any key to its very nearest neighbor, black or white (Half Steps & Whole Steps; the layout of the keys is on The Piano Keyboard). Most neighbors are a white key and a black key, but E–F and B–C are white keys with no black key between them. Those two pairs are exactly where major and minor come from.

Count the keys you land on, not the key you start on. C up to E lands on C♯, D, D♯, E: four half steps. E up to G lands on F, F♯, G: three. Both are 3rds, but the first is one half step wider. The wider one is called major, the narrower one minor.

C up to E is four half steps (a major 3rd); E up to G is three (a minor 3rd), because E–F has no black key between them.

The same thing happens with 2nds. C–D has a black key hiding between, so it spans two half steps: a major 2nd, also called a whole step. E–F spans one: a minor 2nd, the smallest step between two different keys. Major & Minor 2nds and 3rds (Handout 05) shows these four pairs on the keyboard, and Whole Step or Half Step? (Exercise 52) is a quick warm-up for counting keys rather than white keys. Its hint is worth memorizing: two black keys are never a half step apart.

Major and minor 2nds and 3rds. Same number, one half step apart.

Here is the whole ruler, measured up from C. Learn the half-step counts and you can name any interval on the keyboard:

• Unison (P1): 0 half steps, C–C
• Minor 2nd (m2): 1, C–D♭
• Major 2nd (M2): 2, C–D
• Minor 3rd (m3): 3, C–E♭
• Major 3rd (M3): 4, C–E
• Perfect 4th (P4): 5, C–F
• Tritone: 6, C–F♯ (augmented 4th) or C–G♭ (diminished 5th)
• Perfect 5th (P5): 7, C–G
• Minor 6th (m6): 8, C–A♭
• Major 6th (M6): 9, C–A
• Minor 7th (m7): 10, C–B♭
• Major 7th (M7): 11, C–B
• Octave (P8): 12, C–C

Every interval from C, with its half steps. The Intervals reference chart has the same set on one printable page.

Notice something in that list: measured up from C, every white-key interval is major or perfect (C–D, C–E, C–F, C–G, C–A, C–B, C–C). The same holds from the home note of every major key, because it is how the major scale is built: from the home note up to each note of its own major scale, you only get major and perfect intervals. So a quick check for any interval is to ask, "Is the top note in the major scale of the bottom note?" If it is, the interval is major or perfect; if it is a half step lower, it is minor (or diminished, for 4ths, 5ths and octaves); a half step higher, augmented. The scale itself is on The Major Scale.

You can feel the sizes in your hand. A 2nd is two neighboring fingers, a 5th fills a five-finger position, and the octave, as The 6th, the 7th & the Octave (Handout 65) puts it, is "the full handspan — thumb and pinky as far as they go."

Small intervals sit under neighboring fingers; wide ones open the hand. Photo: pxhere, CC0, via Wikimedia Commons.

Perfect, major, minor, augmented, diminished

The numbers come in two families that never mix. Unisons, 4ths, 5ths and octaves are perfect. 2nds, 3rds, 6ths and 7ths are major or minor. Augmented and diminished can stretch or squeeze either family. Open Music Theory puts it plainly: "There is no generic interval that can be both major/minor and perfect." So there is no such thing as a "major 5th" or a "perfect 3rd."

Why "perfect"? The name is old. These intervals were traditionally considered perfectly consonant, the smoothest sounds in music, as Wikipedia's article on intervals puts it. It is a label from history, not a rule you can work out from the notes.

Augmented means one half step wider than major or perfect. Diminished means one half step narrower than minor or perfect.

The quality ladder. Major and minor intervals have four rungs; perfect ones have three. Each step to the right adds one half step.

Watch how a sharp or flat on the top note moves an interval up and down the ladder while the letters, and so the number, stay put. C–E♭ is a minor 3rd, C–E a major 3rd and C–E♯ an augmented 3rd. C–G♭ is a diminished 5th, C–G a perfect 5th and C–G♯ an augmented 5th. Yes, E♯ is the same key as F: when the letters say 3rd, the interval is a 3rd, even on the keys of a 4th.

One number, three sizes. Under each pair: its name and its half steps.

Sometimes a spelling needs a double sharp or double flat to stay on the right letter. Double Sharps and Double Flats shows why G♯ harmonic minor raises its 7th note to F double sharp instead of calling it G. If sharps and flats themselves are still new, start with The Sharp and The Flat. Name the Intervals: the full toolkit (Exercise 06) then mixes all five qualities in 20 intervals.

Same keys, different names

C–F♯ and C–G♭ are played on exactly the same two keys, six half steps apart, but they are different intervals. C–F♯ uses four letters (C, D, E, F), so it is a 4th: an augmented 4th. C–G♭ uses five (C, D, E, F, G), so it is a 5th: a diminished 5th. Wikipedia's article on intervals uses this very pair as its example. The same goes for C–D♯ (two letters, three half steps: an augmented 2nd) and C–E♭ (three letters, three half steps: a minor 3rd).

Same keys, different names. Read the letters for the number, then count half steps for the quality.

So when you write an interval, work in the order Write the Intervals (Exercise 41) gives. Letters first: count up from the bottom note to find the line or space. Then size: count the half steps and add a sharp or flat if the size is not right yet. Its hint says it best: "Keep the letter you found — never switch to the next letter to fix the size." Accidentals on the Staff (Exercise 25) is good practice for reading those sharps and flats correctly.

The six-half-step interval has its own nickname, the tritone, because it spans three whole steps. It splits the octave exactly in half. You meet it constantly in real music: B–F is the tritone inside the B diminished triad and the G7 chord, and it is why those chords sound like they want to move (The Diminished Triad). You may also hear it called "the devil in music." That phrase has been attached to the interval since at least the early 18th century, but Wikipedia's article on the tritone calls the stories of singers being punished by the Church for it "likely fanciful."

Consonance and dissonance

Play C–G together, then C–D. The first sounds settled; the second rubs. Smooth combinations are called consonant, tense ones dissonant. The common classroom grouping:

• Perfect consonances: unisons, octaves and 5ths
• Imperfect consonances: 3rds and 6ths
• Dissonances: 2nds, 7ths and the tritone

Treat that as a guide, not a law. The composer Paul Hindemith stressed that the two concepts "have never been completely explained, and for a thousand years the definitions have varied." The difference is better thought of as a scale from smooth to tense than as a switch, and it depends on style and period.

A rough map, not a rulebook. Where each interval sits also depends on its context and the style of the music.

The perfect 4th is the famous case of "it depends." Some textbook lists count it as a perfect consonance (Wikipedia's consonance article gives one), and between two upper voices it sounds as open as a 5th. But against the bass, in classical counterpoint, it is treated as a dissonance: Open Music Theory lists the harmonic perfect consonances as "all perfect intervals except the perfect fourth," and by 1473 the theorist Johannes Tinctoris described the 4th as dissonant except between the upper parts, according to Wikipedia's article on intervals. You can hear why in a suspended chord. In Csus4 (C–F–G), the 4th above the bass, F, sounds like it is waiting, and it settles when it falls a half step to E.

Tension that moves. In Csus4 the 4th (F) falls to the 3rd (E); in B° the tritone B–F closes in to C–E (B rises, F falls). Both resolutions are on Suspended Chords and The Diminished Triad.

Why do some intervals sound smoother? One of the oldest answers is about simple ratios: in pure tuning, the octave's two frequencies are in the ratio 2:1, the 5th 3:2 and the 4th 4:3. The engraving below, from Robert Fludd's book on the "temple of music," draws those same intervals as arcs over a one-string instrument, the monochord.

The monochord in Robert Fludd's De Templo Musicae (Frankfurt printing, 1624). The arcs are labeled with the old Greek names: diapason (octave), diapente (5th) and diatessaron (4th). Image: public domain, Sächsische Landesbibliothek Dresden, via Deutsche Fotothek and Wikimedia Commons.

Pianos are not tuned to those pure ratios: they use equal temperament, in which the 5th is about two cents (a fiftieth of a half step) narrower than a pure 3:2. Modern research adds more. A 2010 study of more than 250 listeners found that liking consonant chords went along with liking "harmonic" sounds, and that people who had played an instrument for longer liked harmonic sounds more. A 2016 study in Nature found that the Tsimane', a native Amazonian society with little exposure to Western music, rated consonant and dissonant chords as equally pleasant, even though they disliked rough sounds. Culture, in other words, shapes what sounds sweet.

Tuning forks of different frequencies. Every interval is a relationship between two frequencies. Photo: K. Venkataramana, CC0, via Wikimedia Commons.

Hearing Intervals (Handout 375) gives a plain-language version you can use at the piano. Play each pair together and sort it into one of four families: open (P4, P5, P8), sweet (3rds and 6ths), clashing (2nds and 7ths) and restless (the tritone). Chords are built by stacking these intervals, mostly 3rds; Triads & Their Inversions is the next step.

Flip it: inversions and compound intervals

To invert an interval, move the bottom note up an octave so it lands on top. C–E (a major 3rd) becomes E–C (a minor 6th). Four rules tell you the new name without counting:

1. The numbers add up to 9: 2nd and 7th, 3rd and 6th, 4th and 5th, unison and octave.
2. Major becomes minor and minor becomes major.
3. Perfect stays perfect.
4. Augmented becomes diminished and back.

Check with half steps: the pair always adds up to 12.

Why 9 and not 8? Open Music Theory explains that the two intervals together fill an octave, but one note gets counted twice: E counts as the top of the 3rd and the bottom of the 6th. The tritone is the odd one out: an augmented 4th flips into a diminished 5th, six half steps both ways.

Four inversions, as on Inverting intervals & compound intervals (Handout 228). The numbers always add to 9 and the half steps to 12.

The rules are a shortcut for big intervals: a minor 6th is awkward to count, but "a major 3rd, flipped" is easy, as Handout 228 suggests.

Four quick checks for any inversion.

Intervals wider than an octave are compound intervals: an octave plus a simple interval. Subtract 7 from the number to find the simple interval inside, and keep the quality. C up to the E an octave higher is a 10th: 10 − 7 = 3, a major 3rd plus an octave, so a major 10th.

Compound intervals over C. Subtract 7 from the number; the quality stays the same.

Practice both ideas on Invert the Intervals (Exercise 44), which has you flip eight intervals on the staff and twelve more in your head.

Hear them: a tune for every interval

Counting on paper is half the job; the other half is hearing. The fastest ruler for your ear is a tune you already know: play the two notes, then sing the start of the tune from the first note, and see whether it lands on the second. Every hook below was checked against a printed score, and the excerpts in the figures come straight from those scores.

• Minor 2nd: up, Für Elise, the D♯ back up to E; down, Für Elise's first two notes, E to D♯.
• Major 2nd: up, "Twinkle, Twinkle" from the second "-kle" to "lit-" (G to A); down, from "won-der" to "what" (E to D).
• Minor 3rd: up, Mozart's Sonata in C, K. 545, its second leap (E to G), or Für Elise's B up to D; down, Für Elise from C to A.
• Major 3rd: up, K. 545's first leap (C to E); down, "Swing low" (A to F in the 1872 printing).
• Perfect 4th: up, Wagner's Bridal Chorus ("Here Comes the Bride"), its first two notes, "Treu-lich" or "Faith-ful" in the 1897 vocal score (F to B♭), or Eine kleine Nachtmusik's D up to G; down, Eine kleine Nachtmusik's opening, G to D.
• Tritone: B to F inside a G7 chord; no public-domain tune here, so play it from the chord.
• Perfect 5th: up, "Twinkle, Twinkle" from the first "-kle" to the second "twin-" (C to G); down, the Minuet in G's first two notes (D to G).
• Minor 6th: up, The Entertainer's main tune, E to C; down, the same tune, C back to E.
• Major 6th: no verified public-domain tune, so compare it with the minor 6th above: one half step wider (C up to A).
• Minor 7th: G up to F inside a G7 chord, a whole step under the octave (Handout 375's trick).
• Major 7th: C up to B, a half step under the octave.
• Octave: up, "Take me out to the ball game," on "Take me" (D to D).

Hooks from three pieces you may already play. Für Elise and the Minuet in G are both in our guide to 12 classical piano pieces to learn in order, and the full study sheets are Inside Für Elise and Inside the Minuet in G.

The first bar of The Entertainer's main tune leaps between E and the C above it, up and down: a minor 6th each way.

More hooks: Joplin's The Entertainer, Mozart's K. 545 and Eine kleine Nachtmusik. The piano pieces have study sheets too: Inside The Entertainer and Inside Mozart's Sonata in C, K. 545.

The songs below come from old printings, so their keys may differ from the version you sing; the leap is the same on any starting note.

Three songs, in the keys of the old printings: Swing Low (Jubilee Songs, 1872), the Bridal Chorus from Lohengrin (Schirmer vocal score, 1897) and Take Me Out to the Ball Game (1908 sheet music).

What about a falling interval with no tune? Handout 375's answer is to turn it around: sing the second note first, so it climbs, and use its rising tune. Its routine is "one song a day": pick one interval, play its two notes, sing the tune going up and coming down. After a week, have someone play intervals while you face away, then test yourself with Ear Training: Intervals (Exercise 65), which has a teacher's script and audio for practicing alone.

A 10-minute interval routine

Work through the exercises in this order over a few weeks, one sheet at a time, and give each practice day ten minutes:

1. Two minutes: half steps on the keyboard with a row of Whole Step or Half Step?.
2. Three minutes: name intervals on today's sheet. Start with the distance (Exercise 04), then major or minor (Exercise 05), then the full toolkit (Exercise 06).
3. Two minutes: write or flip. Once Exercise 06 feels easy, add Write the Intervals, then Invert the Intervals.
4. Two minutes: one hook from the list above, up and down, at the piano.
5. One minute: three items of Ear Training: Intervals, with your back to the keyboard.

Say every answer as two counts out loud: "C to E, three letters, four half steps, major 3rd." It feels slow at first, then becomes automatic.

Free worksheets for this article

• Intervals: Steps & Skips — count the letters; 2nds and 3rds on the staff and keyboard
• Major & Minor 2nds and 3rds — count half steps to tell major from minor
• Intervals: the 4th and Intervals: the 5th — the first leaps, their shapes and a song for each
• The 6th, the 7th & the Octave — the three wide intervals, felt in the hand
• Intervals reference chart — every interval from C on one page, plus inversions and compound intervals
• Inverting intervals & compound intervals — the four inversion rules and "subtract 7"
• Hearing Intervals — a song or trick for every interval, up and down, with audio
• Half Steps & Whole Steps and The Piano Keyboard — the keys you count on
• Name the Intervals: the distance, major or minor and the full toolkit — Exercises 04, 05 and 06
• Write the Intervals and Invert the Intervals — Exercises 41 and 44
• Whole Step or Half Step? and Ear Training: Intervals — Exercises 52 and 65
• The Chromatic Scale — all twelve half steps in a row

Put it together

Every interval you will meet comes down to two counts: letters for the number, half steps for the quality. Unisons, 4ths, 5ths and octaves are perfect; 2nds, 3rds, 6ths and 7ths are major or minor; one half step more or less makes them augmented or diminished. Flip an interval and the numbers add to 9. And when your eyes say "a 4th" but your ears are not sure, sing the Bridal Chorus.

If you would like someone to check your counting, or to quiz your ear in real time, a Tissimo piano teacher can do it in a live lesson, using these same worksheets.

Sources

• Intervals and dyads — Open Music Theory
• Interval (music) — Wikipedia
• Consonance and dissonance — Wikipedia
• Tritone — Wikipedia
• Perfect fifth — Wikipedia
• Individual differences reveal the basis of consonance — Current Biology (2010)
• Indifference to dissonance in native Amazonians reveals cultural variation in music perception — Nature
• Jubilee Songs as Sung by the Jubilee Singers of Fisk University (1872) — Internet Archive
• Lohengrin, vocal score (G. Schirmer) — Internet Archive
• Take Me Out to the Ball Game — Wikipedia