What Is a Semitone? Half Steps, Cents and the 12 Steps in an Octave
· 7 min read
A semitone is the distance between two notes that sit next to each other: C to C sharp, E to F, one fret up on a guitar, one key to the right on a piano counting the black keys. In the United States the same step is called a half step; two of them make a tone, or whole step. Twelve semitones make an octave, and every interval, chord and key change in Western music is some number of them stacked up.
If the backing track is on your computer, hear CountIn count it in on beat one. Listening is free and needs no account.
The semitone in numbers
On a piano tuned the usual way, equal temperament, every semitone is the same size. Going up one semitone multiplies the frequency by the twelfth root of two, which is 1.05946, a rise of a little under 6 per cent. Twelve of those multiplications double the frequency, which is what an octave is.
Tuning theorists measure intervals in cents, a unit Alexander Ellis introduced in 1885 in his English edition of Helmholtz's On the Sensations of Tone. There are 1,200 cents in an octave, so a semitone is exactly 100 cents, and the number is handy because the ear can hear a difference of about 5 cents on a sustained note, and almost nobody hears 2.
| Note | Semitones from A4 | Frequency (Hz) |
|---|---|---|
| C4 | -9 | 261.63 |
| C#4/Db4 | -8 | 277.18 |
| D4 | -7 | 293.66 |
| D#4/Eb4 | -6 | 311.13 |
| E4 | -5 | 329.63 |
| F4 | -4 | 349.23 |
| F#4/Gb4 | -3 | 369.99 |
| G4 | -2 | 392.00 |
| G#4/Ab4 | -1 | 415.30 |
| A4 | 0 | 440.00 |
| A#4/Bb4 | +1 | 466.16 |
| B4 | +2 | 493.88 |
| C5 | +3 | 523.25 |
The table starts from A4 at 440 Hz, the reference pitch agreed at a conference in London in 1939 and written into ISO 16 in 1975. Notice that the semitone is not a fixed number of hertz. From A4 to Bb4 it is 26 Hz, from A3 to Bb3 it is 13 Hz, and from A5 to Bb5 it is 52 Hz. It is always the same ratio, never the same difference, which is why a song moved up one semitone sounds moved by the same amount in the bass and in the vocal.
Why there are 12 in an octave
The 12-note division is old and it is not the only one. Chinese theorist Zhu Zaiyu published the exact figures for twelve equal semitones in 1584, and the Flemish mathematician Simon Stevin worked them out independently a year or two later. Before that, and for a long time after in practice, semitones came in different sizes. In Pythagorean tuning the step from E to F (the limma, ratio 256:243) is about 90 cents and the step from C to C sharp (the apotome) is about 114 cents. In just intonation the diatonic semitone is 16:15, about 112 cents. Keyboards settled on equal 100-cent semitones in the nineteenth century because it was the only way to play in all 12 keys on one instrument without retuning.
The 12 steps are still not all the same kind of step on paper. Theory books distinguish:
- a diatonic semitone, between two notes with different letter names, like E to F or B to C, the two natural semitones in every major scale;
- a chromatic semitone, between two notes with the same letter name, like C to C sharp or Bb to B.
On a piano they are the same distance. In a vocal line or a string part they are written differently, and in the days of unequal tuning they were tuned differently too.
Intervals counted in semitones
Every interval has a name and a semitone count. Musicians learn them from the opening notes of songs, which is why the last column exists.
| Semitones | Interval | Example | Tune that opens with it |
|---|---|---|---|
| 1 | Minor second | C to Db | Jaws theme |
| 2 | Major second | C to D | Happy Birthday, first two notes |
| 3 | Minor third | C to Eb | Greensleeves |
| 4 | Major third | C to E | Oh When the Saints |
| 5 | Perfect fourth | C to F | Here Comes the Bride |
| 6 | Tritone | C to F# | The Simpsons theme |
| 7 | Perfect fifth | C to G | Twinkle Twinkle |
| 8 | Minor sixth | C to Ab | The Entertainer, after the pickup |
| 9 | Major sixth | C to A | My Bonnie Lies over the Ocean |
| 10 | Minor seventh | C to Bb | Somewhere, from West Side Story |
| 11 | Major seventh | C to B | Take On Me, chorus |
| 12 | Octave | C to C | Somewhere over the Rainbow |
A major scale is the pattern tone, tone, semitone, tone, tone, tone, semitone: 2, 2, 1, 2, 2, 2, 1, which adds up to 12. The two semitones fall between the third and fourth degrees and between the seventh and the octave, E to F and B to C in C major. A minor scale moves them: 2, 1, 2, 2, 1, 2, 2.
Semitones on the instruments
On a piano the 88 keys span 87 semitones, from A0 at 27.5 Hz to C8 at 4,186 Hz. On a guitar every fret is one semitone, so the twelfth fret is the octave, and standard tuning puts the strings 5, 5, 5, 4 and 5 semitones apart: E to A, A to D, D to G, G to B, B to E. A capo on the second fret raises every open string by two semitones, which is why a G chord shape with a capo there sounds as A. Wind players deal with the same thing in reverse: a B flat trumpet or clarinet sounds two semitones lower than written, an alto saxophone in E flat sounds nine lower, and a French horn in F sounds seven lower.
What a semitone means when you change the key of a song
When a singer asks for a song "down a step", they usually mean a whole tone, two semitones. "Down a half step" is one semitone. The key names follow the count: a song in G moved down two semitones is in F, moved up three it is in B flat. A transposition chart lists every key for every shift, and a capo chart does the same for guitar shapes.
| Shift | Semitones | What it does to a song in G |
|---|---|---|
| Half step down | -1 | F#/Gb |
| Whole step down | -2 | F |
| Minor third down | -3 | E |
| Half step up | +1 | Ab |
| Whole step up | +2 | A |
| Fourth up | +5 | C |
Small shifts are the useful ones. One or two semitones put a chorus back inside a singer's comfortable range and leave the record sounding like the record. Three or four are still natural on most mixes, though a low bass or a kick drum starts to sound a touch different. Past five the processing becomes audible on a dense mix, which is why most tools that change the key of an audio file, including the song key changer here, stop at 7 semitones in either direction. Those tools move pitch alone and keep the tempo and the length: a 3:42 song shifted two semitones is still 3:42 at the same BPM. If you are moving a backing track for a singer, change the key of a song to fit your singer walks through how far to go and in which direction.
Frequently asked questions
How many semitones are in an octave?
Twelve. An octave doubles the frequency, and in equal temperament each of the 12 semitones multiplies it by 1.05946, the twelfth root of two.
Is a semitone the same as a half step?
Yes. Semitone is the British and classical term, half step the American one. A tone or whole step is two semitones.
How many cents are in a semitone?
100 cents in equal temperament, out of 1,200 in the octave. In older tunings a semitone could be anywhere from about 90 to about 114 cents.
How many semitones are between C and G?
Seven: C to C#, D, D#, E, F, F#, G. That interval is the perfect fifth.
How much does a semitone change the frequency?
By about 5.9 per cent. A4 is 440 Hz and A#4 is 466.16 Hz, a difference of 26 Hz, but the same semitone an octave lower is a difference of 13 Hz, because a semitone is a ratio, not a number of hertz.
Is one fret on a guitar one semitone?
Yes. Each fret raises the string by one semitone, the twelfth fret is the octave, and a capo at fret n raises every open string by n semitones.
How many semitones can you move a song before it sounds wrong?
One or two are invisible on most recordings. Three or four are natural on vocals and guitars. Five to seven are audible on dense mixes and fine on sparse ones. Most online key changers, including the key changer on this site, go up to 7 semitones either way and keep the tempo untouched.
Sources
- Hermann von Helmholtz, On the Sensations of Tone, English edition by Alexander J. Ellis, 1885 (cents).
- ISO 16:1975, Acoustics, Standard tuning frequency (A4 = 440 Hz).
- Zhu Zaiyu, Lülü jingyi, 1584 (equal temperament figures).
- Wikipedia: Semitone, Equal temperament, Cent (music).
If the backing track is on your computer, hear CountIn count it in on beat one. Listening is free and needs no account.
← Back to Blog · Click track · Free BPM finder · Tap tempo · Key changer