Music Interval Calculator
Calculate frequencies, semitones, cents, frequency ratio, direction, and interval name based on starting and ending notes, octaves, and tuning. Music Interval Calculator helps musicians, composers, producers, educators, and students analyze pitch relationships accurately.
Highlights
- Calculate the distance between any two musical notes.
- View precise frequencies using your chosen A4 tuning reference.
- Measure intervals in semitones and cents.
- Identify interval names and ascending or descending direction.
- Compare frequency ratios and MIDI note numbers.
Table of Contents
How Music Interval Calculator Works?
The Music Interval Calculator represents each chromatic pitch with a pitch-class number and combines it with the selected octave. The pitch classes are assigned as C = 0, C♯/D♭ = 1, D = 2, and so on through B = 11. A MIDI-style note number is then calculated from the pitch class and octave:
Here, is the note number, is the octave, and is the chromatic pitch-class number. A4 is assigned note number 69, so the frequency of either selected note is calculated from the chosen A4 reference frequency:
The signed semitone distance preserves direction:
The absolute semitone distance ignores direction, while the cents result expresses the same equal-temperament distance at finer resolution:
The frequency ratio compares the ending frequency with the starting frequency:
A positive signed value produces an ascending or higher result, a negative value produces a descending or lower result, and zero indicates identical pitch. The interval name is selected from the chromatic semitone distance, using the nearest standard interval designation.
| Semitones | Interval name |
|---|---|
| 0 | Unison |
| 1 | Minor second |
| 2 | Major second |
| 3 | Minor third |
| 4 | Major third |
| 5 | Perfect fourth |
| 6 | Tritone |
| 7 | Perfect fifth |
| 8 | Minor sixth |
| 9 | Major sixth |
| 10 | Minor seventh |
| 11 | Major seventh |
| 12 | Octave |
Practical Use Cases
Musicians and performers: Musicians can compare two notes to identify the interval, direction, and exact semitone distance when checking melodies, harmonies, vocal jumps, or instrumental intonation.
Composers and arrangers: Composers can use the calculator to verify melodic leaps, harmonic spacing, octave displacement, and the frequency relationship between notes while developing arrangements.
Music producers and sound designers: Producers can calculate the pitch relationship between two synthesizer tones, samples, or tuned layers and use the cents result to diagnose small tuning differences.
Music educators: Teachers can demonstrate how pitch names, octave numbers, MIDI note numbers, frequencies, semitones, cents, and interval names describe the same musical relationship.
Music students: Students can enter familiar note pairs and observe how ascending and descending intervals differ, reinforcing ear-training, keyboard theory, and equal-temperament calculations.
Accuracy and Limitations
The calculator uses the twelve-tone equal-temperament formula with the selected A4 reference between 400 and 480 Hz, so its frequency, ratio, semitone, and cents results are mathematically consistent with that tuning model. It treats enharmonic choices such as C♯ and D♭ as the same chromatic pitch class and identifies intervals from chromatic semitone distance rather than spelling-based theory; therefore, it does not distinguish theoretically different names such as an augmented second and a minor third. Octaves are limited to -1 through 9, and the selected notes are restricted to the listed twelve chromatic pitch classes. The interval name is based on the calculator's standard chromatic mapping, while the frequency outputs are rounded for display.
Quick Examples
Example #1: Perfect Fifth
Analyze the interval from middle C to G in standard tuning.
Example #2: Octave Comparison
Measure the frequency relationship between A4 and the A one octave above it.
Example #3: Descending Minor Third
Evaluate a descending interval from E5 to C5 using a slightly lowered tuning reference.
