Music Interval Calculator
Use this music interval calculator calculator to understand your numbers quickly and make clearer decisions with confidence.
Mode
What Is a Music Interval Calculator?
A music interval calculator is a music theory tool that determines the relationship between two musical notes — specifically, the number of semitones (half steps) separating them, the interval name (Minor 3rd, Perfect 5th, Major 7th, etc.), the frequency ratio, and the distance in cents. Whether you are a student learning to identify intervals by ear, a composer building chord progressions, or a producer tuning synthesizers, an interval calculator gives you precise, instant information about the mathematical structure of music.
The music interval calculator above offers 4 specialized modes: Find Interval (identify the interval between any two notes with piano visualization), Build Interval (get the result note from a root plus any interval), Frequency Analysis (calculate cents and semitones from two Hz values), and Scale & Chord Builder (generate 14 scales and 14 chord types with a live piano keyboard view).
Piano Visualization
Every result includes a two-octave piano keyboard with highlighted notes, so you can instantly see the physical distance between any two notes on the keyboard.
14 Scales, 14 Chords
The Scale & Chord Builder covers Major, all 7 modes (Dorian, Phrygian, Lydian, Mixolydian, Locrian), Natural/Harmonic/Melodic Minor, pentatonic, blues, whole tone, and all common chord types.
Frequency Precision
Uses the equal temperament formula f(n) = f₀ × 2^(n/12) for exact Hz values, plus just intonation ratios for comparison. The frequency analysis mode accepts any Hz input, including microtonal values.
Complete music interval reference: piano keyboard, frequency formula, and 13 interval table. See all 13 intervals →
The Key Formulas: Semitones, Cents, and Frequency
Music intervals are defined by three related measurements — semitones (discrete steps on a standard keyboard), cents (fine-grained pitch measurement), and frequency ratios (the ratio of vibrations per second between two notes). Here are the essential formulas:
① Semitone Count
MIDI numbering: Middle C (C4) = 60, A4 = 69. Each semitone = 1 MIDI unit. C4 to G4 = |67−60| = 7 semitones = Perfect 5th. C4 to the B below (B3) = |59−60| = 1 semitone = Minor 2nd descending.
② Equal Temperament Frequency
Where: f₀ = reference frequency (A4 = 440 Hz), n = semitones from reference. Example: How many Hz is C5 (3 semitones above A4)? f = 440 × 2^(3/12) = 440 × 1.1892 = 523.25 Hz. Each octave exactly doubles frequency.
③ Cents Calculation
A cent is 1/100th of a semitone. One octave = 1200 cents. One semitone = 100 cents (in equal temperament). Cents allow precise comparison of microtonal differences — useful in guitar intonation, synthesizer tuning, and ear training where pitches are between standard semitones.
④ Interval Quality Color Code
The 13 Standard Music Intervals
Western music theory recognizes 13 intervals spanning one octave (0–12 semitones). Each has a unique name, abbreviation, harmonic quality, and frequency ratio in just intonation. Equal temperament adjusts these ratios to allow consistent tuning in all 12 keys.
| St | Abbr | Interval Name | Quality | Just Ratio | ET Cents | Example (C root) |
|---|---|---|---|---|---|---|
| 0 | P1 | Perfect Unison | Perfect | 1:1 | 0¢ | C → C Most consonant; same pitch |
| 1 | m2 | Minor 2nd | Minor | 16:15 | 100¢ | C → C#/Db Dissonant; semitone step |
| 2 | M2 | Major 2nd | Major | 9:8 | 200¢ | C → D Whole step; sounds like a scale step |
| 3 | m3 | Minor 3rd | Minor | 6:5 | 300¢ | C → D#/Eb Melancholic; minor chord foundation |
| 4 | M3 | Major 3rd | Major | 5:4 | 400¢ | C → E Bright; major chord foundation |
| 5 | P4 | Perfect 4th | Perfect | 4:3 | 500¢ | C → F Open, stable; "Here Comes the Bride" |
| 6 | TT | Tritone | Tritone | √2:1 | 600¢ | C → F#/Gb Maximally dissonant; "The Simpsons" |
| 7 | P5 | Perfect 5th | Perfect | 3:2 | 700¢ | C → G Most consonant after octave; power chord |
| 8 | m6 | Minor 6th | Minor | 8:5 | 800¢ | C → G#/Ab Softer, introspective |
| 9 | M6 | Major 6th | Major | 5:3 | 900¢ | C → A Warm, relaxed consonance |
| 10 | m7 | Minor 7th | Minor | 16:9 | 1000¢ | C → A#/Bb Tension; dominant 7th chord |
| 11 | M7 | Major 7th | Major | 15:8 | 1100¢ | C → B Dreamy tension; maj7 chord |
| 12 | P8 | Perfect Octave | Perfect | 2:1 | 1200¢ | C → C (higher) Full consonance; frequency doubles |
How Intervals Build Scales
A scale is a sequence of notes defined by a specific pattern of intervals. The most common scale in Western music, the Major scale, uses the pattern W–W–H–W–W–W–H (where W = whole step = 2 semitones, H = half step = 1 semitone). Starting from C: C(0) → D(2) → E(4) → F(5) → G(7) → A(9) → B(11) → C(12).
| Scale | Semitone Steps | Pattern | Character |
|---|---|---|---|
| Major (Ionian) | 0-2-4-5-7-9-11 | W-W-H-W-W-W-H | Bright, happy, foundational |
| Natural Minor | 0-2-3-5-7-8-10 | W-H-W-W-H-W-W | Dark, melancholic, emotionally complex |
| Harmonic Minor | 0-2-3-5-7-8-11 | W-H-W-W-H-A-H | Exotic, dramatic, Middle-Eastern feel |
| Dorian | 0-2-3-5-7-9-10 | W-H-W-W-W-H-W | Cool, jazzy, minor with a bright 6th |
| Phrygian | 0-1-3-5-7-8-10 | H-W-W-W-H-W-W | Spanish/flamenco, dark-exotic |
| Lydian | 0-2-4-6-7-9-11 | W-W-W-H-W-W-H | Dreamy, floating, ethereal (raised 4th) |
| Mixolydian | 0-2-4-5-7-9-10 | W-W-H-W-W-H-W | Bluesy, rock, major with flat 7th |
| Pentatonic Major | 0-2-4-7-9 | W-W-WH-W-WH | Universal, no dissonance, easy to improvise |
| Blues | 0-3-5-6-7-10 | WH-W-H-H-WH-W | Soulful, expressive, signature of blues/rock |
How Intervals Build Chords
Chords are simultaneous combinations of notes defined by specific interval relationships from the root. A C Major triad = C + E + G = Root (P1) + Major 3rd (M3, 4 st) + Perfect 5th (P5, 7 st). The difference between major and minor is a single semitone: (M3 = 4 st) versus (m3 = 3 st) for the middle note.
| Chord | Abbr | Semitone Steps | Example in C | Sound |
|---|---|---|---|---|
| Major | maj | 0-4-7 | C-E-G | Bright, happy, stable |
| Minor | m | 0-3-7 | C-Eb-G | Darker, melancholic, stable |
| Diminished | dim | 0-3-6 | C-Eb-Gb | Tense, unstable, dissonant |
| Augmented | aug | 0-4-8 | C-E-G# | Dreamy, ambiguous tension |
| Dominant 7th | 7 | 0-4-7-10 | C-E-G-Bb | Bluesy tension, wants to resolve |
| Major 7th | maj7 | 0-4-7-11 | C-E-G-B | Rich, jazzy, sophisticated |
| Minor 7th | m7 | 0-3-7-10 | C-Eb-G-Bb | Smooth, jazzy, soulful |
| Sus4 | sus4 | 0-5-7 | C-F-G | Suspended tension, open |
| Power (5th) | 5 | 0-7 | C-G | Heavy, ambiguous (no 3rd) |
Equal Temperament vs. Just Intonation
Modern Western instruments use equal temperament (ET) — a tuning system where each of the 12 semitones is exactly equal at a ratio of 2^(1/12) ≈ 1.05946. This makes all keys sound identical and enables free modulation between keys. However, ET slightly mistuned from the pure mathematical ratios found in just intonation (JI) — based on small integer ratios like 3:2 (Perfect 5th) or 5:4 (Major 3rd).
| Interval | ET Hz (from A4=440) | Just Ratio | Just Hz | Difference |
|---|---|---|---|---|
| Perfect 5th (E5) | 659.26 Hz | 3:2 | 660.00 Hz | +1.96 cents |
| Major 3rd (C#5) | 554.37 Hz | 5:4 | 550.00 Hz | −13.69 cents |
| Perfect 4th (D5) | 587.33 Hz | 4:3 | 586.67 Hz | −1.96 cents |
| Minor 3rd (C5) | 523.25 Hz | 6:5 | 528.00 Hz | +15.64 cents |
Note: All from A4 = 440 Hz reference. The Major 3rd is the furthest from pure at −13.69 cents — this is why a cappella singers and string players naturally drift sharp on major thirds compared to piano.
Frequently Asked Questions
🎵How many semitones are in a Perfect 5th?
A Perfect 5th spans exactly 7 semitones (half steps). On a piano, C to G is a Perfect 5th: C→C#→D→D#→E→F→F#→G = 7 steps. In frequency terms, a Perfect 5th has a ratio of exactly 3:2 in just intonation (1.5×), or 2^(7/12) ≈ 1.4983 in equal temperament. A Perfect 5th is the second most consonant interval after the octave and forms the foundation of power chords in rock and roll.
🎵What is the difference between semitones and cents?
A semitone is the smallest standard interval in Western music — one step on a piano keyboard. A cent is 1/100th of a semitone, making it 1/1200th of an octave. Cents are used when comparing tuning systems (equal temperament vs. just intonation) or when working with microtonal music. Guitarists use cents when checking intonation: if your 12th-fret harmonic is a few cents off from the fretted note, your intonation needs adjustment. The cents formula is Cents = 1200 × log₂(f₂/f₁).
🎵What is the tritone and why is it dissonant?
The tritone (abbreviation TT) is exactly 6 semitones — exactly half an octave. Its frequency ratio in equal temperament is 2^(6/12) = √2 ≈ 1.4142. It cannot be expressed as a simple integer ratio, making it maximally dissonant and harmonically unstable. Historically called "diabolus in musica" (the devil in music) in medieval Europe, it was avoided in polyphonic composition. Today it's central to blues and jazz — the "blues note" — and appears in famous themes like "The Simpsons" and "Purple Haze" by Jimi Hendrix.
🎵How do I find what scale a set of notes belongs to?
Use the Scale & Chord Builder mode in the calculator above to generate all 14 scale types for any root and compare notes. Manual method: list your notes in ascending order, calculate semitone gaps between consecutive notes (e.g., C D E F G A B C = 2,2,1,2,2,2,1 = W-W-H-W-W-W-H), then compare that pattern to the standard scale patterns. Major pattern is W-W-H-W-W-W-H. Natural Minor is W-H-W-W-H-W-W. If no standard pattern matches, it may be a mode or an exotic scale.
🎵What is A4 = 440 Hz and why is it used as the reference?
A4 (the A above middle C) is the international standard tuning reference, set at 440 Hz by the International Organization for Standardization (ISO) in 1955. This means when you press A4 on a correctly-tuned piano, the string vibrates 440 times per second. All other notes are calculated relative to this reference using the equal temperament formula f(n) = 440 × 2^(n/12), where n is semitones above or below A4. Some orchestras and historically-informed ensembles use A = 415 Hz (one semitone lower), and some modern orchestras tune to A = 442 Hz for a brighter sound.
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