## 5. Intervals

An interval is the distance between two notes, and every scale, chord and melody is built from them.

Source: https://musictheory.center/course/intervals
Level: Beginner · Materials · 6 sections
Before this: Pitch, Notes and the Octave

### Half Steps and Whole Steps

https://musictheory.center/course/intervals#half-steps-and-whole-steps

> Play these two pairs. One of them is the smallest move a piano can make; the other skips a key.

**Plays:** Pair one (E4 F4) · Pair two (C4 D4)

C to D is a whole step; E to F is a half step. On the keyboard, a half step is the next key of either colour.

| Move | Semitones | Example |
| --- | --- | --- |
| Half step | 1 | E4 → F4 |
| Whole step | 2 | C4 → D4 |

**half step**

*also called*: semitone (British and European usage)

**Definition.** A half step is the smallest interval in Western music: the distance from any note to the very next note, with nothing in between.

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.

**Good to know**

- (Fact) Twelve half steps make an [octave](https://musictheory.center/course/pitch-and-notes#the-octave), because the twelve-tone system divides the octave equally.
- (Convention) Guitarists say "one fret" for a half step and "two frets" for a whole step; the sound is identical.

**You already know this**

- The twelve notes of the octave from Chapter 2 — https://musictheory.center/course/pitch-and-notes#the-twelve-notes

**Where this goes**

- The major scale is a fixed pattern of whole and half steps — https://musictheory.center/course/scales

**In real music**

- John Williams — “Jaws (Main Theme)” — the two-note ostinato at the very start is a half step
- Traditional — “Happy Birthday” — the first two different notes, "Hap-py birth-", are a whole step

**Try it on your instrument:** On your instrument, start on any note and play a half step up, then a whole step up. Do it from three different starting notes.

**Check:** Listen. Half step or whole step?

- Half step — You heard a small move, which it is. But a half step is even smaller: compare with E to F, where there is no key between them.
- Whole step **(correct)** — Correct. G to A skips G♯: two half steps, a whole step.

### Number and Quality

https://musictheory.center/course/intervals#number-and-quality

> Play the first two. Both start on the same note and both rise by roughly the same amount — but only one of them sounds bright. Then play the third, which is the staff below note for note: home, the lower of the two upper notes, then the higher one, so the half step between them is the only thing left to hear.

**Plays:** Brighter pair (C4 E4) · Darker pair (C4 Eb4) · Both thirds, as written (C4 Eb4 E4)

C up to E and C up to E flat both count three letter names, so both are thirds. The half-step count is what separates them: four against three.

| Number | Letter names counted | Qualities it can take |
| --- | --- | --- |
| Unison | C | perfect · augmented |
| Second | C–D | diminished · minor · major · augmented |
| Third | C–D–E | diminished · minor · major · augmented |
| Fourth | C–D–E–F | diminished · perfect · augmented |
| Fifth | C–D–E–F–G | diminished · perfect · augmented |
| Sixth | C–D–E–F–G–A | diminished · minor · major · augmented |
| Seventh | C–D–E–F–G–A–B | diminished · minor · major · augmented |
| Octave | C–D–E–F–G–A–B–C | diminished · perfect · augmented |

**interval quality**

**Definition.** 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](https://musictheory.center/course/pitch-and-notes#naming-notes) 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: C4 up to E4 counts C, D, E, so it is a third. Sharps and flats never change that count, which is why C4 up to E♭4 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](https://musictheory.center/course/pitch-and-notes#the-octave) 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](https://musictheory.center/interval/major-third) is four half steps and a [Minor Third](https://musictheory.center/interval/minor-third) is three, and that single half step is the difference between a chord that sounds bright and one that sounds sad.

**Good to know**

- (Convention) Interval numbers count both end notes, so a note to the next one up is a second, never a first. It is a count of letter names, not of half steps — which is why the numbers start at one rather than zero.
- (Convention) The numbers 1, 4, 5 and 8 take "perfect" rather than major or minor. The word is inherited from medieval theory, where those intervals were the only ones allowed to stand alone; it is not a claim that they sound better.
- (Fact) Two intervals can share a number and still differ in size: C4 to E4 is four half steps, C4 to E♭4 is three, and both are thirds.

**You already know this**

- Sharps and flats, and why lowering a note keeps its letter name, from Chapter 2 — https://musictheory.center/course/pitch-and-notes#sharps-flats-and-enharmonics
- The half step, the unit every quality is measured in — https://musictheory.center/course/intervals#half-steps-and-whole-steps

**Where this goes**

- A triad is major or minor because of the quality of the third inside it — https://musictheory.center/course/chords

**In real music**

- Traditional — “Oh, When the Saints” — the opening leap, "Oh when the", rises a major third
- Deep Purple — “Smoke on the Water” — the first two notes of the riff leap a minor third

**Try it on your instrument:** Pick any note on your instrument. Play the note four half steps above it, then the note three half steps above it. Repeat from two more starting notes, and name the bright one each time before you check.

[Name the interval between any two notes you play — the calculator gives its number and its quality](https://musictheory.center/tools/interval-calculator?a=C4&b=E4)

**Check:** Count up from this note by a major sixth — nine half steps. Which note do you land on?

- A **(correct)** — Correct. Counting letter names C–D–E–F–G–A gives six, and C up to A is nine half steps, which makes that sixth major.
- A flat — A flat is the right letter but the wrong size: eight half steps, one short. That is a minor sixth.
- G — G is only seven half steps up, and counting C–D–E–F–G gives five letter names, so it is a fifth, not a sixth.

### The Twelve Intervals

https://musictheory.center/course/intervals#the-twelve-intervals

> Play all three. Each one starts on the same note. Put them in order from smallest to largest using nothing but your ears.

**Plays:** Pair A (C4 G4) · Pair B (C4 Db4) · Pair C (C4 A4)

Twelve half steps from C up to the C above it, spelled exactly as the table below spells them. Stopping on each one in turn gives the twelve intervals.

| Interval | Half steps | From C | Song that starts with it |
| --- | --- | --- | --- |
| [Minor Second](https://musictheory.center/interval/minor-second) | 1 | C4 → D♭4 | Jaws (Main Theme) |
| [Major Second](https://musictheory.center/interval/major-second) | 2 | C4 → D4 | Happy Birthday |
| [Minor Third](https://musictheory.center/interval/minor-third) | 3 | C4 → E♭4 | Smoke on the Water |
| [Major Third](https://musictheory.center/interval/major-third) | 4 | C4 → E4 | Oh, When the Saints |
| [Perfect Fourth](https://musictheory.center/interval/perfect-fourth) | 5 | C4 → F4 | Here Comes the Bride |
| [Tritone](https://musictheory.center/interval/tritone) | 6 | C4 → F♯4 | The Simpsons Theme |
| [Perfect Fifth](https://musictheory.center/interval/perfect-fifth) | 7 | C4 → G4 | Twinkle Twinkle Little Star |
| [Minor Sixth](https://musictheory.center/interval/minor-sixth) | 8 | C4 → A♭4 | Love Story (Theme) |
| [Major Sixth](https://musictheory.center/interval/major-sixth) | 9 | C4 → A4 | My Bonnie Lies Over the Ocean |
| [Minor Seventh](https://musictheory.center/interval/minor-seventh) | 10 | C4 → B♭4 | Somewhere (West Side Story) |
| [Major Seventh](https://musictheory.center/interval/major-seventh) | 11 | C4 → B4 | Take On Me |
| [Octave](https://musictheory.center/interval/octave) | 12 | C4 → C5 | Somewhere Over the Rainbow |

**simple interval**

**Definition.** A simple interval is any interval no wider than an [octave](https://musictheory.center/course/pitch-and-notes#the-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](https://musictheory.center/course/melody#what-makes-a-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](https://musictheory.center/interval/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](https://musictheory.center/interval/major-third) is four half steps up from C, from F, or from B flat.

**Good to know**

- (Fact) Interval size in half steps is absolute, so the same interval sounds the same from every starting note: C4 to E4, F4 to A4 and B♭4 to D5 are all major thirds.
- (Convention) The six-half-step interval is called an augmented fourth when it is spelled C to F♯ and a diminished fifth when it is spelled C to G♭. "Tritone" is the name used when the spelling does not matter.

**You already know this**

- Number and quality, the two halves of every name in the table — https://musictheory.center/course/intervals#number-and-quality
- The octave, where the note names start over, from Chapter 2 — https://musictheory.center/course/pitch-and-notes#the-octave

**Where this goes**

- A practice method for naming all twelve by ear — https://musictheory.center/course/ear-training

**In real music**

- Traditional — “Twinkle Twinkle Little Star” — the leap between the first and second "twinkle" is a perfect fifth
- Wagner — “Here Comes the Bride” — the opening leap, before the melody settles, is a perfect fourth
- Harold Arlen — “Somewhere Over the Rainbow” — the opening "Some-where" leaps a full octave

**Try it on your instrument:** Play a note, then find the note seven half steps above it and play both. Do that from five different starting notes, until the sound arrives before the count does.

[Check any pair from the table: count its half steps and hear it harmonic or melodic](https://musictheory.center/tools/interval-calculator?a=C4&b=G4)

**Check:** Listen to this pair of notes. Which interval is it?

- Perfect fourth **(correct)** — Correct. Five half steps, C up to F. It is open and stable, but it leans upward rather than settling — that lean is the giveaway.
- Perfect fifth — A fifth is two half steps wider, seven in all, and it comes to rest instead of leaning. Play the first two notes of "Twinkle Twinkle Little Star" straight after this one and the difference in weight is obvious.
- Major third — A major third is four half steps and sounds noticeably sweeter and narrower. This interval is wider and more hollow: there is no warmth in it.

### Consonance and Dissonance

https://musictheory.center/course/intervals#consonance-and-dissonance

> Play all three as chords, both notes at once. Two of them make you want to move on; one of them could sit there all day.

**Plays:** Chord one (C4 G4) · Chord two (C4 F#4) · Chord three (C4 Db4)

C and G sounded together: seven half steps, and the most restful interval there is after the octave.

| Category | Intervals | How it behaves |
| --- | --- | --- |
| Perfect consonance | unison · perfect fourth · perfect fifth · octave | Blends so completely it can sound hollow or empty |
| Imperfect consonance | major and minor thirds · major and minor sixths | Stable but coloured; this is what makes chords sound warm |
| Dissonance | major and minor seconds · major and minor sevenths · the tritone | Audibly rubs; in tonal music it wants somewhere to go |

**consonance**

**Definition.** 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.

**Good to know**

- (Fact) The intervals heard as most consonant are the ones whose frequencies stand in the simplest ratios: 2:1 for the [octave](https://musictheory.center/course/pitch-and-notes#the-octave), 3:2 for the perfect fifth, 4:3 for the perfect fourth. The more complex the ratio, the rougher the blend.
- (Tendency — common-practice tonal music, roughly 1600–1900, and the popular music that inherited its habits) A dissonance is followed by a consonance a step or a half step away — the tritone inside a [dominant seventh chord](https://musictheory.center/course/chords#seventh-chords) spreading outward to a sixth, or closing inward to a third.
- (Convention) Where the line between consonance and dissonance falls is a historical agreement, not an acoustic constant: thirds were counted as dissonances in early medieval practice, and the perfect fourth above the bass was treated as a dissonance for centuries after that.

**You already know this**

- The twelve simple intervals and their sizes in half steps — https://musictheory.center/course/intervals#the-twelve-intervals
- Pitch as frequency, from Chapter 2 — the reason some pairs of notes blend — https://musictheory.center/course/pitch-and-notes#high-and-low

**Where this goes**

- A seventh chord builds the dissonance into the chord itself — https://musictheory.center/course/chords

**In real music**

- Danny Elfman — “The Simpsons Theme” — the opening "The Simp-sons" leaps a tritone, and the phrase spends the next bar getting out of it
- John Williams — “Star Wars (Main Title)” — the opening fanfare leaps a perfect fifth, which is why it sounds like an arrival rather than a question
- Jimi Hendrix — “Purple Haze” — the guitar-and-bass figure under the intro is built on a tritone

**Try it on your instrument:** Hold a low note on your instrument and add the note seven half steps above it. Then move that upper note down one half step and hold both again. Swap between the two and notice which one you can walk away from.

**Check:** Listen to these two notes sounded together. Which interval is it?

- Tritone **(correct)** — Correct. Six half steps, C and F♯ — exactly half an octave, which is why it belongs to no key as a home and hangs in the air unresolved.
- Perfect fifth — A fifth is one half step wider and it settles completely. Play C and G after this and the fifth will sound almost empty by comparison; this pair never stops rubbing.
- Octave — An octave blends into what sounds like one thicker note. This pair stays audibly two notes, arguing with each other.

#### Why simple ratios sound smooth

A sounding note is not one frequency but a stack of them: a fundamental plus a series of overtones at whole-number multiples of it. When two notes stand in a simple ratio, many of their overtones coincide exactly, and the pair fuses. When the ratio is complex, overtones land a few hertz apart and beat against each other, which is the roughness we call dissonance.

Equal temperament, the tuning on almost every keyboard, deliberately mistunes those ratios so that all [twelve keys](https://musictheory.center/course/keys-and-key-signatures#what-a-key-is) are equally usable. An equal-tempered perfect fifth is about two cents narrower than a pure 3:2, and an equal-tempered major third is fourteen cents wider than a pure 5:4 — audible to a tuner, and the reason a barbershop quartet or a string section sounds sweeter than a piano on a held chord.

### Inversion

https://musictheory.center/course/intervals#inversion

> Play the first two. The same two note names are in both; only which one is on the bottom has changed. Then play the third, which is the staff below note for note: the two pairs run together, with the note they share struck once in the middle.

**Plays:** Bottom note low (C4 E4) · Bottom note moved up (E4 C5) · The third and the sixth, as written (C4 E4 C5)

C up to E is a third; E up to the next C is a sixth. Three plus six is nine, and the two together fill an octave.

| Interval | Inverts to | Numbers |
| --- | --- | --- |
| [Minor Second](https://musictheory.center/interval/minor-second) (1 half step) | [Major Seventh](https://musictheory.center/interval/major-seventh) (11) | 2 + 7 = 9 |
| [Major Second](https://musictheory.center/interval/major-second) (2) | [Minor Seventh](https://musictheory.center/interval/minor-seventh) (10) | 2 + 7 = 9 |
| [Minor Third](https://musictheory.center/interval/minor-third) (3) | [Major Sixth](https://musictheory.center/interval/major-sixth) (9) | 3 + 6 = 9 |
| [Major Third](https://musictheory.center/interval/major-third) (4) | [Minor Sixth](https://musictheory.center/interval/minor-sixth) (8) | 3 + 6 = 9 |
| [Perfect Fourth](https://musictheory.center/interval/perfect-fourth) (5) | [Perfect Fifth](https://musictheory.center/interval/perfect-fifth) (7) | 4 + 5 = 9 |
| [Tritone](https://musictheory.center/interval/tritone) (6) | [Tritone](https://musictheory.center/interval/tritone) (6) | 4 + 5 = 9 |

**interval inversion**

**Definition.** Interval inversion is what happens when the lower of two notes is moved up an [octave](https://musictheory.center/course/pitch-and-notes#the-octave), or the upper moved down, so that the same pair of [note names](https://musictheory.center/course/pitch-and-notes#naming-notes) is measured the other way round.

The two numbers always add to nine. C4 up to E4 is a third; move that C up an octave and E4 up to C5 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](https://musictheory.center/interval/major-third) inverts to a [Minor Sixth](https://musictheory.center/interval/minor-sixth); a [Perfect Fourth](https://musictheory.center/interval/perfect-fourth) inverts to a [Perfect Fifth](https://musictheory.center/interval/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](https://musictheory.center/course/voice-leading#bass-lines-and-inversions) 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.

**Good to know**

- (Fact) An interval and its inversion always add to nine, because together they span an octave and the note they share is counted at both ends.
- (Fact) The tritone is its own inversion: six half steps and six more half steps make a full octave, so it is the only interval that inverts to the same size.
- (Convention) Quality flips under inversion — major to minor, augmented to diminished, perfect to perfect. That is a consequence of how the names were assigned, not a separate rule to remember.

**You already know this**

- Number and quality, which both change when an interval is turned over — https://musictheory.center/course/intervals#number-and-quality
- Moving a note up an octave keeps its name, from Chapter 2 — https://musictheory.center/course/pitch-and-notes#the-octave

**Where this goes**

- Chord inversion applies the same move to three and four notes at once — https://musictheory.center/course/chords

**In real music**

- Scott Joplin — “The Entertainer” — the opening melodic leap is a minor sixth — a major third stood on its head
- Traditional — “My Bonnie Lies Over the Ocean” — the opening leap is a major sixth, the inversion of the minor third that opens "Smoke on the Water"

**Try it on your instrument:** Play two notes four half steps apart, low note first. Now play the lower of the two an octave higher so the same pair becomes a sixth. Do it from three different starting notes and listen to how the mood changes.

[Enter the third and read off what it becomes when you flip it](https://musictheory.center/tools/interval-calculator?a=C4&b=E4)

**Check:** This is a perfect fourth. Invert it — what interval does it become?

- Perfect fifth **(correct)** — Correct. Four plus five is nine, and perfect stays perfect: move the C up an octave and F to C is a perfect fifth.
- Perfect fourth — The quality does stay perfect — that part is right — but the number cannot stay the same. Only the tritone inverts to its own size; every other interval swaps for the number that makes nine with it.
- Major sixth — Sixths are what thirds invert to: 3 + 6 = 9. A fourth needs a five to reach nine, so it inverts to a fifth.

### Compound Intervals

https://musictheory.center/course/intervals#compound-intervals

> Play these two as chords. The upper note has the same name in both. Only how far away it sits has changed.

**Plays:** Notes close together (C4 D4) · Notes an octave apart (C4 D5)

C and the D an octave above it, sounded together: a major ninth. The same two letter names as a major second, with an octave added and seven added to the number.

| Compound interval | Made of | Half steps |
| --- | --- | --- |
| [Major Ninth](https://musictheory.center/interval/major-ninth) | major second + octave | 14 |
| [Major Tenth](https://musictheory.center/interval/major-tenth) | major third + octave | 16 |
| [Perfect Eleventh](https://musictheory.center/interval/perfect-eleventh) | perfect fourth + octave | 17 |
| [Perfect Twelfth](https://musictheory.center/interval/perfect-twelfth) | perfect fifth + octave | 19 |
| [Major Thirteenth](https://musictheory.center/interval/major-thirteenth) | major sixth + octave | 21 |

**compound interval**

**Definition.** A compound interval is any interval wider than an [octave](https://musictheory.center/course/pitch-and-notes#the-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](https://musictheory.center/interval/major-ninth), a perfect fourth a [Perfect Eleventh](https://musictheory.center/interval/perfect-eleventh).

What changes is not the name but the friction. Two notes a [Major Second](https://musictheory.center/interval/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](https://musictheory.center/course/chords#reading-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.

**Good to know**

- (Fact) A compound interval's number is the simple number plus seven, because the octave spans eight and the shared note is counted at both ends: 2 + 8 − 1 = 9.
- (Convention) Chord symbols name added notes with compound numbers — a ninth, an eleventh, a thirteenth — even when a player voices them inside the octave. The number identifies the note, not the register it has to sit in.
- (Tendency — jazz and contemporary popular harmony) Ninths, elevenths and thirteenths are treated as colour rather than as tension, and are added freely without being resolved.

**You already know this**

- The twelve simple intervals, one of which sits inside every compound interval — https://musictheory.center/course/intervals#the-twelve-intervals
- The octave, the thing being added, from Chapter 2 — https://musictheory.center/course/pitch-and-notes#the-octave

**Where this goes**

- Chord extensions are compound intervals stacked above a seventh chord — https://musictheory.center/course/chords

**In real music**

- Harold Arlen — “Somewhere Over the Rainbow” — the opening "Some-where" leaps a full octave — the jump every compound interval starts from
- Traditional — “Happy Birthday” — the first two different notes, "Hap-py birth-", rise a major second; sing the higher one an octave up and you have a major ninth

**Try it on your instrument:** Play a note and the note a whole step above it together. Then play the same pair with the upper note an octave higher. Listen to how much of the roughness disappears, and repeat from two more starting notes.

[Enter the wide pair and see its simple form named beside it](https://musictheory.center/tools/interval-calculator?a=C4&b=D5)

**Check:** Listen to these two notes sounded together. Which interval is it?

- Major ninth **(correct)** — Correct. The two note names are C and D, a major second apart, but the D is an octave higher: fourteen half steps in all, and the wide spacing is what makes it sound open rather than harsh.
- Major second — The note names are right, and this is a major second with an octave added. A plain major second puts the two notes next to each other and the result audibly grinds; this one does not.
- Major seventh — A major seventh is eleven half steps and lands just below the octave, so the upper note sounds as if it is straining towards the lower one repeated. This upper note is above the octave, not below it.

### Key Takeaways

https://musictheory.center/course/intervals#key-takeaways

- Every interval is a count of half steps, and that count decides how it sounds from any starting note.
- Intervals are named by number, which counts letter names, and by quality, which fixes the exact size.
- There are twelve simple intervals inside the octave, and a familiar song is the fastest way to learn each one.
- Consonant intervals sit still and dissonant intervals want to move, at least in tonal music.
- Inverting an interval turns it over: the two numbers add to nine, and major swaps with minor.
- A compound interval is a simple interval plus an octave, and its number is the simple number plus seven.

### Questions

**What is an interval in music?**

An interval is the distance in pitch between two notes, [measured in half steps](https://musictheory.center/tools/interval-calculator) and named by a number and a quality, such as "major third" or "perfect fifth". Intervals are the units that [scales](https://musictheory.center/course/scales#what-a-scale-is), chords and melodies are all built from.

**How many intervals are there?**

Within one [octave](https://musictheory.center/course/pitch-and-notes#the-octave) there are twelve simple intervals plus the unison, running from the minor second at one half step to the octave at twelve. Anything wider is a compound interval: a ninth is an octave plus a second, an eleventh an octave plus a fourth.

**What is the difference between a major and a minor interval?**

A minor interval is exactly one half step smaller than the major interval with the same number. C up to E is a major third, four half steps; C up to E♭ is a minor third, three. Only seconds, thirds, sixths and sevenths come in major and minor.

**Why does the tritone sound tense?**

The tritone splits the octave exactly in half, six half steps, so it points at no note as a home. In common-practice tonal music it is the most unstable interval, and it usually resolves outward to a sixth or inward to a third in the next chord.

**How do I learn to recognise intervals by ear?**

Attach each interval to the opening of a song you already know: a perfect fifth to "Twinkle Twinkle Little Star", a minor second to the Jaws theme. Then test yourself in short daily sessions. Start with fifths and octaves, add thirds, and leave sevenths until last.

### Other languages

- https://musictheory.center/course/intervals/llms.txt
- https://musictheory.center/fr/cours/intervalles/llms.txt
- https://musictheory.center/es/curso/intervalos/llms.txt