Semitone Calculator
Choose two notes or enter two frequencies and this calculator returns the number of semitones between them, the musical interval name, the frequency ratio, the deviation in cents, and the MIDI note numbers. Switch between note-to-note mode, frequency-to-frequency mode, and transposition mode. The A4 reference pitch is adjustable from the standard 440 Hz to any concert pitch you need.
Formula
Worked example
From A4 (440 Hz) to E5 (659.255 Hz): n = 12 x log2(659.255 / 440) = 12 x log2(1.4983) = 12 x 0.5833 = 7.0 semitones, which is a Perfect 5th. In cents: 7 x 100 = 700 c. The frequency ratio is 2^(7/12) = 1.498307.
What is a semitone?
A semitone is the smallest interval in standard Western music. In 12-tone equal temperament (12-TET), the octave is divided into exactly 12 equal semitones. Each adjacent key on a piano keyboard, whether black or white, is one semitone apart. Because the octave represents a 2:1 frequency ratio, each semitone corresponds to a frequency ratio of 2^(1/12), approximately 1.0595. This means moving up one semitone multiplies the frequency by about 1.0595, and moving up twelve semitones exactly doubles it. Semitones are the building blocks of all Western scales, chords, and harmonic relationships.
How to use this calculator
Select a mode from the dropdown. In note-to-note mode, pick two notes from the selectors and the calculator returns the semitone distance, cents, interval name, frequency ratio, frequencies, and MIDI numbers for both notes. In frequency-to-frequency mode, enter two frequencies in Hz and the same outputs are computed from those raw values, which is useful for audio engineering, tuning work, or any situation where you have measured frequencies rather than named notes. In transposition mode, choose a starting note and a semitone shift (positive to go up, negative to go down) and the calculator gives you the target frequency, its nearest note name, and the MIDI number. The A4 reference pitch defaults to 440 Hz and can be adjusted for baroque tuning (415 Hz), Verdi tuning (432 Hz), or high-pitch orchestral tuning (442-443 Hz).
Cents and why they matter for tuning
A cent is one hundredth of a semitone, so there are 1,200 cents in an octave. Cents provide a much finer resolution than semitones for describing small pitch differences that are musically significant but below the threshold of a full semitone. A deviation of 10-15 cents is audible to most trained musicians, and deviations above 20-25 cents sound noticeably out of tune. The frequency-to-frequency mode shows the cent deviation between any two pitches, making this calculator useful for checking whether a recording or instrument is sharp or flat relative to a reference, for specifying pitch-shift amounts in a DAW, or for comparing just-intonation ratios to their 12-TET equivalents.
MIDI note numbers and frequency conversion
MIDI (Musical Instrument Digital Interface) assigns each note a number from 0 to 127. A4 is MIDI note 69, C4 (middle C) is MIDI note 60. The formula linking MIDI number m to frequency is f = A4 x 2^((m - 69) / 12), where A4 is the reference pitch. This calculator displays MIDI numbers for both the start and target notes, making it straightforward to cross-reference results with synthesisers, sequencers, and any software that works in MIDI. The reverse calculation - finding the nearest MIDI note for any arbitrary frequency - is also shown, with the cent deviation from perfect tune displayed for each.
Standard musical intervals in 12-TET
| Semitones | Interval name | Frequency ratio | Cents |
|---|---|---|---|
| 0 | Unison | 1.000000 | 0 |
| 1 | Minor 2nd | 1.059463 | 100 |
| 2 | Major 2nd | 1.122462 | 200 |
| 3 | Minor 3rd | 1.189207 | 300 |
| 4 | Major 3rd | 1.259921 | 400 |
| 5 | Perfect 4th | 1.334840 | 500 |
| 6 | Tritone | 1.414214 | 600 |
| 7 | Perfect 5th | 1.498307 | 700 |
| 8 | Minor 6th | 1.587401 | 800 |
| 9 | Major 6th | 1.681793 | 900 |
| 10 | Minor 7th | 1.781797 | 1000 |
| 11 | Major 7th | 1.887749 | 1100 |
| 12 | Perfect Octave | 2.000000 | 1200 |
Semitone counts, interval names, and frequency ratios for the 12 chromatic steps within one octave in 12-tone equal temperament.
Frequently asked questions
How many semitones are in an octave?
There are exactly 12 semitones in one octave in standard 12-tone equal temperament. Moving up 12 semitones doubles the frequency. For example, A4 is 440 Hz and A5 is 880 Hz, a ratio of exactly 2:1 and a distance of 12 semitones.
What is the difference between a semitone and a cent?
A semitone is the smallest standard interval in Western music. A cent is one hundredth of a semitone, or one twelve-hundredth of an octave. Cents are used when precision finer than a semitone is needed, such as measuring how flat or sharp an instrument is, comparing just-intonation ratios to equal temperament, or specifying pitch-shift amounts in audio software.
What is the formula for converting frequency to semitones?
The formula is n = 12 x log2(f2 / f1), where f1 and f2 are the two frequencies in hertz and n is the number of semitones. For cents, multiply by 100 instead: cents = 1200 x log2(f2 / f1). The reverse formula - finding f2 from a semitone count - is f2 = f1 x 2^(n/12).
Why would I change the A4 reference from 440 Hz?
Standard concert pitch sets A4 at 440 Hz, but this has not always been the norm. Baroque ensembles often tune to A4 = 415 Hz (one semitone below modern pitch). Some orchestras, particularly in continental Europe, tune to A4 = 442 or 443 Hz for a brighter sound. The numerology-influenced 432 Hz tuning is also widely discussed. Changing the reference shifts all calculated frequencies proportionally, so you can match any tuning system your ensemble or project uses.
What is a perfect fifth and how many semitones is it?
A perfect fifth is 7 semitones. It is one of the most consonant intervals, with a frequency ratio very close to 3:2 (1.498307 in 12-TET vs. exactly 1.5 in just intonation). The difference between the equal-tempered and just fifth is about 2 cents, which is below the threshold of detectability for most listeners. It forms the basis of the circle of fifths and is used in power chords, drone tuning, and countless harmonic structures.
What is MIDI note 69?
MIDI note 69 corresponds to A4, the A above middle C, which vibrates at 440 Hz in standard tuning. MIDI note 60 is middle C (C4). The numbering runs from 0 (C-1, about 8.18 Hz) to 127 (G9, about 12,544 Hz). Every semitone is one MIDI number.
How do I use this calculator for a capo?
Use transposition mode. Set the starting note to the open string pitch (for example E2 on a guitar) and set the semitones to shift equal to the capo fret number. The result is the effective pitch of the string with the capo in place. A capo on fret 2 shifts every string up by 2 semitones, so E2 becomes F#2 at approximately 92.50 Hz.