# Music Interval Calculator

URL: https://speedycalculator.com/calculators/other/music-interval/
Last updated: 2026-10-30

> The music interval calculator names the interval between two notes – such as a major third, perfect fifth or diminished fourth – using the letter names so augmented and diminished intervals are recognised, or between two pitches by semitones, with tones, cents, frequency ratios and the inversion.

## Inputs

- Interval between
- Note 1
- Octave of note 1
- Note 2
- Octave of note 2

## Results

- Interval
- Short name
- Semitones
- Tones (whole steps)
- Cents
- Equal-tempered frequency ratio
- Just-intonation ratio
- Inversion
- Sounds the same as
- Note 1 frequency (A4 = 440 Hz)
- Note 2 frequency
- Interval on a keyboard

## Formula

```
Interval number = letter steps + 1 (C→E = 3rd)
Quality from semitones: P/M (reference) · m = M − 1 · A = P or M + 1 · d = P − 1 or m − 1
Cents = 100 × semitones · equal-tempered ratio = 2^(semitones ÷ 12)
```

## Explanation

An interval is the distance between two notes. It has two parts: a number, found by counting letter names (C up to E is C–D–E, a third), and a quality, found from the exact number of semitones (a third with 4 semitones is major, with 3 semitones minor). Perfect intervals – unisons, fourths, fifths and octaves – can be perfect, augmented or diminished; seconds, thirds, sixths and sevenths can be major, minor, augmented or diminished.

Because the number comes from the letters, two intervals can sound the same yet be named differently. F♯ up to B♭ spans four semitones like a major third, but its letters F–G–A–B make it a fourth – a diminished fourth. Such spellings matter in harmony and in reading music, which is why the calculator offers a “note names” mode. In “pitches” mode only the semitone count is used, as you would hear the interval.

You also get the size in tones and cents, the equal-tempered and just-intonation frequency ratios, the frequencies of both notes and the inversion of the interval (the interval that completes the octave).

### How to use the Music Interval Calculator

- **Interval between**
- **Note 1**
- **Octave of note 1**
- **Note 2**
- **Octave of note 2**

Everything is calculated in your browser, so results appear instantly and nothing you type is sent to a server.

### How it works

In note-name modes the calculator counts the letter steps between the notes (plus octaves) and compares the semitone count with the major or perfect interval of that number to find the quality. In pitch mode the interval is named from the semitone count alone.

### Worked example

F♯ to B♭: the letters F, G, A, B make a fourth. A perfect fourth from F♯ would be B (5 semitones), but B♭ is only 4 semitones above F♯, one less than perfect, so the interval is a **diminished fourth (d4)**. It sounds like a major third: 400 cents, ratio 2^(4/12) = 1.2599. Its inversion is an augmented fifth (8 semitones).

### Intervals within an octave

SemitonesShortIntervalJust ratio0P1Perfect unison1:11m2Minor second16:152M2Major second9:83m3Minor third6:54M3Major third5:45P4Perfect fourth4:36A4 / d5Tritone45:327P5Perfect fifth3:28m6Minor sixth8:59M6Major sixth5:310m7Minor seventh9:5 or 16:911M7Major seventh15:812P8Perfect octave2:1

## Worked example

Inputs — Interval between: Note names – note 2 above note 1 (within an octave); Note 1: F♯; Note 2: B♭.

Results — **Interval = Diminished fourth**; Short name = d4; Semitones = 4; Tones (whole steps) = 2; Cents = 400; Equal-tempered frequency ratio = 1.25992.

## Key terms

- **Interval number**: The count of letter names from the lower to the upper note, both included.
- **Interval quality**: Perfect, major, minor, augmented or diminished.
- **Compound interval**: An interval wider than an octave.
- **Inversion**: The interval obtained by moving the lower note up an octave; the two sum to 9 (number) and 12 (semitones).
- **Cent**: 1/100 of a semitone.

## FAQ

**What interval is C to E?**
A major third – three letter names (C, D, E) and four semitones.

**What interval is F to C?**
A perfect fifth (F, G, A, B, C = five letters, seven semitones).

**What interval is A♯ to C?**
A diminished third: three letters (A, B, C) but only two semitones.

**What interval is F♯ to B♭?**
A diminished fourth – it sounds like a major third (4 semitones) but spans four letter names.

**How many semitones are in a perfect fifth?**
Seven; the just ratio is 3:2 and the equal-tempered ratio 1.4983.

**What is the inversion of a major third?**
A minor sixth – the two add up to an octave (4 + 8 = 12 semitones), and major turns into minor.

**What is a compound interval?**
An interval larger than an octave, e.g. a major tenth = an octave plus a major third (16 semitones).


## Sources

- [musictheory.net – Lessons (notes, intervals, chords, keys)](https://www.musictheory.net/lessons)
- [Open Music Theory (open textbook)](https://viva.pressbooks.pub/openmusictheory/)
- [Wikipedia – Interval (music)](https://en.wikipedia.org/wiki/Interval_(music))