Music Interval Converter
Convert between semitones, frequency ratios, and cents for music intervals.
Includes standard interval names and tuning references.
Type in any field — the others update instantly.
Music intervals describe the distance between two pitches. They can be expressed as semitones, cents, or frequency ratios.
Core conversion formulas:
- Cents from semitones: cents = semitones x 100
- Frequency ratio from semitones: ratio = 2^(semitones / 12)
- Semitones from frequency ratio: semitones = 12 x log2(ratio)
- Cents from frequency ratio: cents = 1200 x log2(ratio)
What each unit means:
- Semitone: The smallest interval in standard Western music (e.g., C to C#). One fret on a guitar, one key on a piano (including black keys).
- Cent: One hundredth of a semitone. There are 1,200 cents in an octave. Cents are used for fine tuning comparisons and measuring how far a note is from a standard pitch.
- Frequency ratio: The mathematical ratio between two frequencies. An octave is 2:1, a perfect fifth is approximately 3:2.
Standard equal temperament intervals:
| Interval Name | Semitones | Cents | Frequency Ratio |
|---|---|---|---|
| Unison | 0 | 0 | 1.000 |
| Minor 2nd | 1 | 100 | 1.059 |
| Major 2nd | 2 | 200 | 1.122 |
| Minor 3rd | 3 | 300 | 1.189 |
| Major 3rd | 4 | 400 | 1.260 |
| Perfect 4th | 5 | 500 | 1.335 |
| Tritone | 6 | 600 | 1.414 |
| Perfect 5th | 7 | 700 | 1.498 |
| Minor 6th | 8 | 800 | 1.587 |
| Major 6th | 9 | 900 | 1.682 |
| Minor 7th | 10 | 1000 | 1.782 |
| Major 7th | 11 | 1100 | 1.888 |
| Octave | 12 | 1200 | 2.000 |
Just intonation vs equal temperament: In equal temperament (used on pianos), each semitone has the exact ratio of 2^(1/12) = 1.05946. In just intonation, intervals use simple ratios: the perfect fifth is exactly 3/2 = 1.5000 (compared to 1.4983 in equal temperament). The difference between just and equal temperament intervals is typically 2-14 cents.
Practical applications:
- Guitar tuners display pitch deviation in cents. A reading of +5 cents means the note is 5 cents sharp.
- When tuning instruments together, differences of less than 5 cents are generally not noticeable to most listeners.
- Differences of 10-15 cents are clearly audible and make music sound “out of tune.”