Interval Calculator

Key Takeaways

• An interval is the distance between two pitches, named by size (2nd, 3rd, 5th) and quality (major, minor, perfect, augmented, diminished).
• Count semitones first, name second: 7 semitones is a perfect fifth — the fastest reliable identification method.
• Perfect intervals (unison, 4th, 5th, octave) are never major or minor — only augmented or diminished.
• The tritone (6 semitones) splits the octave exactly in half — the most unstable interval in tonal music.
• Intervals are the atoms of harmony: stack them to build chords (chord identifier) and scales (scale finder).

What Is an Interval Calculator?

An interval calculator measures the musical distance between two notes and names it. Select C and G and it reports a perfect fifth spanning 7 semitones. The name carries two facts: the size (fifth = five letter-names apart) and the quality (perfect = the stable, pure version).

Intervals underpin everything else: chords stack intervals, scales sequence them, melodies move through them. Chord names confuse beginners; intervals are the simpler layer underneath. Learn these and chords start making sense.

How This Calculator Works

The widget above names intervals by semitone counting with wraparound — the theorist's method minus the spelling nuance. The exact procedure:

1. Pick two notes: each pitch maps to its chromatic position (C = 0, C♯ = 1, D = 2 … B = 11).
2. Subtract and wrap: semitones = (second − first + 12) mod 12, so a downward pair still yields a positive ascending distance.
3. Look up the name: the count maps to a fixed table — 4 → major 3rd, 6 → "Tritone / Augmented 4th", 7 → perfect 5th, 12 → octave.
4. Display: the interval name plus its semitone count, e.g. "Minor 3rd (3 semitones)."

Two simplifications matter. The widget names by semitone count alone, so C to D♯ reads as "minor 3rd" (3 semitones) though the spelling makes it an augmented 2nd — the enharmonic section below explains when that distinction counts. And the same note in both fields reads as "Octave (12 semitones)": with no register input, the tool cannot separate a unison from an octave, so it reports the octave.

Interval Formula and Worked Example

The core computation, with note positions numbered C = 0 through B = 11:

semitones = (note₂ − note₁ + 12) mod 12

Worked example — C up to A:

1. Positions: C = 0, A = 9.
2. Semitones: (9 − 0 + 12) mod 12 = 9.
3. Table lookup: 9 semitones = major 6th.
4. Sanity check: C–D–E–F–G–A spans six letter names, and C major contains A natural — major 6th confirmed.

Descending example — G down to E: the widget measures ascending distance, so G (7) to E (4) gives (4 − 7 + 12) mod 12 = 9 semitones — a major 6th upward. Flip it: E up to G is the minor 3rd you hear going down.

The rule behind the flip: a descending interval is the inversion of the ascending result — the two sizes sum to 9 (6th ↔ 3rd) and the quality inverts (major ↔ minor, perfect stays perfect). G down to E is therefore a minor 3rd, the inversion of the major 6th the calculator reports upward.

How to Use This Calculator

1. Select the first note: the lower (or starting) pitch of the pair.
2. Select the second note: the upper (or target) pitch.
3. Read the result: the interval name and semitone count appear instantly (e.g. "Perfect 5th (7 semitones)").
4. Experiment: change one note at a time to feel how each semitone alters the quality — minor one step below major.

Reading Your Result: The Complete Interval Table

The just ratio is each interval's size in just intonation — the tuning built from whole-number frequency ratios. Equal temperament, this calculator's system, trims most intervals slightly to make every key usable: the perfect 5th narrows from a pure 3:2 (about 702 cents) to exactly 700 cents, and the major 3rd widens from 5:4 to 400 cents. The names stay the same; only the exact pitch shifts by a few cents.

Recognize intervals by ear with famous openings: each melody below starts with the listed interval.

What Each Interval Does in a Key

Intervals have jobs, not just names — each one pushes harmony in a specific direction. The perfect 5th is the stability anchor: C–G sounds finished because its 3:2 frequency ratio is the simplest after the octave. The minor 7th above the tonic spells dominant color — add B♭ to a C major triad and the chord suddenly wants to resolve to F.

The tritone does the heavy lifting. In C major, F–B (scale degrees 4 and 7) spans 6 semitones of pure tension, and it resolves by half steps in opposite directions: F falls to E, B rises to C. That squeeze is the engine inside every dominant-7th chord and the reason V7–I cadences sound inevitable.

Songwriter's shortcut: when a melody note forms a tritone against the bass, you are standing on the dominant — resolve it.

Melodic vs Harmonic: Same Distance, Different Job

A melodic interval sounds its notes in sequence; a harmonic interval sounds them together — and the ear judges them by different rules. Played together, intervals are judged by consonance: thirds and sixths blend, seconds grind. Played in sequence, direction and singability rule instead.

The practical consequence: a melody full of leaps wider than a perfect 5th is hard to sing, while harmony stacks 7ths and 9ths without strain. Write melodies in steps and small leaps; let the chords carry the wide intervals.

Count Intervals on Guitar Frets in Seconds

Every fret is one semitone, so the fretboard is a built-in interval ruler. Pick any string, count frets upward from the starting note, and read the interval off the count.

Worked example on the low E string: open E to the 7th fret is 7 semitones — a perfect 5th (the note is B). The 12th fret is 12 semitones — the octave (E again). The 5th fret gives 5 semitones — a perfect 4th (A). Three landmarks — 5th, 7th, and 12th frets — name the three most-used intervals with no math.

Compound Intervals: 9ths, 11ths, and 13ths

A compound interval is a simple interval plus an octave: a 9th is a 2nd up an octave, an 11th a 4th, a 13th a 6th. The widget reports the simple form (within one octave): subtract 7 from any compound number to find what it displays. A 9th (14 semitones) reads as a major 2nd (2 semitones).

Jazz chord symbols use compound names deliberately — C13 tells the player the 13th sits above the 7th in the voicing, information the simple "6th" would lose. Think compound for naming; the calculator's simple interval is enough for measuring.

Enharmonic Intervals: Same Sound, Different Name

Enharmonic intervals sound identical but are spelled — and named — differently. C to D♯ and C to E♭ are both 3 semitones, but the first is an augmented 2nd and the second a minor 3rd. The widget reports "minor 3rd" for both: it counts semitones, not spelling.

For sound, the distinction never matters — 3 semitones is 3 semitones. For notation and theory exams, it does: the correct name follows the letter distance (C to D is a 2nd of some kind; C to E is a 3rd). Use the calculator for sound; apply the letter-count rule when spelling counts.

Name any interval exactly with two counts. Step 1: count letter names to fix the size — C up to E spans C–D–E, so the interval is some kind of 3rd. Step 2: count semitones to fix the quality — for a 3rd, 4 semitones is major, 3 is minor, 2 is diminished. Apply both counts and the spelling-correct name falls out:

The last two rows are the same sound with two correct names — which one applies depends on the spelling in front of you. That is the whole enharmonic rule: semitones give the distance, letters give the name.

The Quality Pattern: Major, Minor, Perfect in 30 Seconds

Interval quality follows one pattern. Seconds, thirds, sixths, and sevenths come in major/minor pairs — the major version is one semitone wider. Unisons, fourths, fifths, and octaves are perfect: no major/minor form, only augmented (wider) or diminished (narrower).

Memory hook: perfect intervals sound hollow and stable (P4, P5, P8) — the pillars of the scale. Everything else carries major/minor color. Widen any perfect or major interval by a semitone for augmented; narrow any perfect or minor interval for diminished.

From Intervals to Chords and Scales

Every chord is a stack of intervals, and every scale is a sequence of them. A major triad is a major 3rd plus a minor 3rd (4 + 3 semitones); a major scale is the interval pattern whole–whole–half–whole–whole–whole–half. Name intervals instantly and chord formulas become arithmetic instead of memorization.

Workflow: measure an unfamiliar chord's intervals here, then enter the full note set into the chord identifier for the complete name — or check a melody's notes against candidate scales in the scale finder.

Limitations

• Spelling-blind: the widget names by semitone count, so enharmonic intervals (augmented 2nd vs minor 3rd) get one shared name.
• No unison: the same note in both fields reads as "Octave (12 semitones)". With no octave/register input, the tool cannot tell a unison from an octave, so it reports the octave.
• One octave range: compound intervals (9ths and beyond) are reported in their simple form — subtract 7 yourself for the compound name.
• Ascending measurement: distances are measured upward with wraparound; descending melodic intervals need mental flipping.
• 12-tone equal temperament: just-intonation and microtonal intervals are rounded to the nearest semitone.

Interval Calculator vs Alternatives

Interval names follow 12-tone equal temperament convention. Enharmonic equivalents (e.g. augmented 2nd vs minor 3rd) share semitone counts and are reported under their most common name.

Frequently Asked Questions