Interval Calculator

Key Takeaways

• An interval is the distance between two pitches, named by its size (2nd, 3rd, 5th…) and quality (major, minor, perfect, augmented, diminished).
• Count semitones first, name second: 7 semitones is always a perfect fifth — the fastest reliable identification method.
• Perfect intervals (unison, 4th, 5th, octave) can't be 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 any two pitches — say, C and G — and it reports the interval: a perfect fifth spanning 7 semitones. The name tells you both the size (fifth = five letter-names apart) and the quality (perfect = the stable, "pure" version).

Intervals are the foundation everything else is built from: chords are stacks of intervals, scales are sequences of them, and melodies are intervals in motion. If chord names confuse you, 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 same method theorists use, minus the spelling nuance. The exact procedure:

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

One simplification to know: the widget names by semitone count alone, so C to D♯ reads as "minor 3rd" (3 semitones) even though the spelling technically makes it an augmented 2nd — see the enharmonic section below.

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 the major scale of C 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 = major 6th upward — equivalently, E to G is the minor 3rd you hear going down.

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

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 above reports the simple form (within one octave), so subtract 7 from any compound number to find what it will display: 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. For naming, think compound; for measuring, the calculator's simple interval is all you need.

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 technically an augmented 2nd and the second a minor 3rd. The widget reports "minor 3rd" for both, because it counts semitones rather than reading spelling.

Does it matter? For sound, no — 3 semitones is 3 semitones. For theory homework and notation, yes: 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, and apply the letter-count rule when spelling matters.

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 — they have no major/minor form, only augmented (wider) or diminished (narrower).

Memory hook: "perfect" intervals are the ones that 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 and it becomes augmented; narrow any perfect or minor interval and it becomes 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. Once you can name intervals instantly, chord formulas stop being memorization and become arithmetic.

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.
• 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