Music Interval Calculator
Select two notes and their octaves to instantly identify the musical interval between them. The calculator names the interval (such as Perfect Fifth or Major Third), counts the semitones, calculates the equal-temperament frequency ratio, converts to cents, and shows the compound name for intervals spanning more than one octave. Switch between pitch-based mode (enharmonic names only) and note-based mode (full diatonic quality including Augmented and Diminished intervals) using the mode selector.
What is a musical interval?
A musical interval is the distance in pitch between two notes. Intervals are measured in semitones (also called half-steps), each of which is one fret on a guitar, one key on a piano in the equal-temperament system used by virtually all Western music today. The interval is named by its quality (Perfect, Major, Minor, Augmented, Diminished) and its diatonic number (the count of letter-name steps between the two notes, from 1 for a unison up to 8 for an octave and beyond for compound intervals). Understanding intervals is foundational to chord construction, harmony, counterpoint, and ear training.
Pitch-based vs note-based interval identification
This calculator offers two modes. In pitch-based mode, intervals are identified purely by the number of semitones between the two pitches, giving a single enharmonic name such as "Tritone" for 6 semitones regardless of spelling. In note-based mode, the letter names you choose matter: F to B is an Augmented Fourth (6 semitones), while F to Cb is a Diminished Fifth (also 6 semitones on the piano) - these sound identical but function differently in music theory. Note-based mode is the standard used in classical harmony, counterpoint, and most music theory education.
Compound intervals and how to name them
Intervals larger than an octave (more than 12 semitones) are called compound intervals. A compound interval is named by adding 7 to the simple interval number: a ninth is a second spread across two octaves, a tenth is a third, an eleventh is a fourth, and so on. Composers and arrangers use compound interval names constantly in orchestration and chord voicing. This calculator shows both the compound name (e.g., Major Ninth) and the equivalent simple name (Major Second) for any interval exceeding 12 semitones.
Frequency ratios and cents explained
In equal temperament, every semitone is tuned so that 12 semitones exactly double the frequency (a ratio of 2:1). Each semitone therefore has a ratio of 2^(1/12), approximately 1.0595. The frequency ratio between two notes is 2^(n/12), where n is the semitone count. The cent is a logarithmic unit equal to 1/100th of a semitone, giving 1200 cents per octave. Cents are used to measure the tiny tuning differences between equal temperament and just intonation: for example, a just perfect fifth (3:2 ratio) is 701.955 cents, while an equal-temperament fifth is exactly 700 cents, a difference of less than 2 cents - imperceptible to most listeners.
Consonance and dissonance
Historically, intervals have been classified into three consonance categories. Perfect consonances (unison, perfect fourth, perfect fifth, octave) sound highly stable and do not seem to want to move. Imperfect consonances (major and minor thirds and sixths) are stable and pleasant but have a richer, more colorful quality. Dissonances (seconds, sevenths, and the tritone) create tension and instability, and in tonal music they typically resolve to a consonant interval. This classification underpins voice-leading rules, chord resolution, and the entire logic of tonal harmony from the Baroque era through the present day.
Standard musical intervals (equal temperament)
| Semitones | Interval name | Just ratio | Consonance |
|---|---|---|---|
| 0 | Perfect Unison | 1:1 | Perfect consonance |
| 1 | Minor Second | 16:15 | Sharp dissonance |
| 2 | Major Second | 9:8 | Mild dissonance |
| 3 | Minor Third | 6:5 | Imperfect consonance |
| 4 | Major Third | 5:4 | Imperfect consonance |
| 5 | Perfect Fourth | 4:3 | Perfect consonance |
| 6 | Tritone (Aug 4th / Dim 5th) | 45:32 | Dissonance |
| 7 | Perfect Fifth | 3:2 | Perfect consonance |
| 8 | Minor Sixth | 8:5 | Imperfect consonance |
| 9 | Major Sixth | 5:3 | Imperfect consonance |
| 10 | Minor Seventh | 16:9 | Mild dissonance |
| 11 | Major Seventh | 15:8 | Sharp dissonance |
| 12 | Perfect Octave | 2:1 | Perfect consonance |
All twelve intervals within one octave with their semitone count, common name, just-intonation ratio, and consonance classification.
Frequently asked questions
How do I count semitones between two notes?
Count every key (black and white) on a piano from your lower note up to your upper note, not counting the starting note itself. Each key is one semitone. For example, from C to E you pass C#/Db, D, D#/Eb, and reach E - that is 4 semitones, a Major Third. Alternatively, assign C=0, C#=1, D=2, ... B=11, add 12 for each octave higher, and subtract the lower note value from the higher.
What is the difference between an Augmented Fourth and a Diminished Fifth?
Both contain exactly 6 semitones (the tritone), so they sound identical on a modern keyboard. The difference is purely theoretical: an Augmented Fourth spans four letter-name steps (e.g., F to B), while a Diminished Fifth spans five steps (e.g., F to Gb). This distinction matters in classical harmony because the two intervals resolve differently, have different functions in chords, and are spelled differently in written music. Switch this calculator to note-based mode to see both names.
What is a compound interval?
A compound interval is any interval larger than an octave (more than 12 semitones). It is named by taking the simple interval number and adding 7: a ninth = second + octave, a tenth = third + octave, an eleventh = fourth + octave, a twelfth = fifth + octave, a thirteenth = sixth + octave, etc. In chord naming, a "major 9th chord" contains a major ninth above the root, which is a major second spread across two octaves.
Why does the frequency ratio use 2^(n/12)?
Equal temperament divides the octave into 12 mathematically equal steps so that every semitone has the same frequency ratio. Since 12 equal steps must multiply together to give exactly 2:1 (an octave), each step must be the 12th root of 2, or 2^(1/12). For n semitones the ratio is therefore 2^(n/12). This approximates the pure integer ratios of just intonation well enough that most listeners cannot detect the tiny deviations.
What is the tritone and why is it special?
The tritone (6 semitones) divides the octave exactly in half, which makes it unique: it is its own inversion, equally distant from the root and the octave. Because it sits equidistant between two keys (for example, C and F# are both a tritone from each other in the other direction), it does not clearly belong to any one tonal center. Medieval theorists called it diabolus in musica (the devil in music) for its instability. In modern harmony it is central to the dominant seventh chord and is one of the most recognizable harmonic colors in jazz and blues.
How do I identify an interval by ear?
The most reliable method is to associate each interval with a well-known melody that starts with that interval. Common references include: Minor Second - "Jaws" theme; Major Second - "Happy Birthday" (first two notes); Minor Third - "Smoke on the Water"; Major Third - "When the Saints Go Marching In"; Perfect Fourth - "Here Comes the Bride"; Tritone - "The Simpsons" theme; Perfect Fifth - "Star Wars" main theme; Major Sixth - "My Bonnie Lies Over the Ocean"; Minor Seventh - "Somewhere" from West Side Story; Octave - "Somewhere Over the Rainbow".