Semitone Calculator

Semitone Calculator

Introduction

A semitone is the smallest step between two notes in Western music. On a piano, it is the move from one key to the very next key, black or white. Twelve semitones make one octave.

This Semitone Calculator works with those steps in three ways:

Note Interval Finder: Pick two notes, like C4 and G4, and see how many semitones apart they are and what the interval is called.
Transpose / Add Semitones: Start on a note, move it up or down by any number of semitones, and get the new note.
Frequency Calculator: Change semitones into hertz, or find how many semitones sit between two frequencies.

Each answer comes with the interval name, the cents value, the frequency ratio, and a step-by-step solution so you can see the math. You can click the piano keys, play the notes to hear them, and switch between sharp and flat spellings.

All the math uses 12-tone equal temperament, the tuning used by most modern instruments. That means 12 semitones per octave and 100 cents per semitone. Music students, singers, songwriters, guitar and piano players, and producers who need to transpose a part or check tuning can all use it.

How to use our Semitone Calculator

Pick a mode, type in your notes or frequencies, and the tool shows the semitone distance, interval name, cents, frequency ratio, and pitch in Hz.

Mode tabs: Choose "Note Interval Finder" to compare two notes, "Transpose / Add Semitones" to move a note up or down, or "Frequency Calculator" to work with Hz.

Input Style: Pick "Text Input" to type a note like C4, or "Dropdown + Octave" to choose the note name and octave from menus.

From Note: Enter your starting note, such as C4, F#3, or Bb4. The range is C0 to B8.

To Note: Enter the second note you want to measure to. The calculator counts the semitones between the two notes.

Swap Notes: Click this to flip the From and To notes and change the direction of the interval.

Piano keyboard: Click "Select From Note" or "Select To Note", then click a key to set that note. Use the arrow buttons to move the keyboard up or down an octave.

Play Interval: Click to hear both notes played one after the other.

Start Note (Transpose mode): Enter the note you want to move, like C4.

Semitone Shift: Type how many semitones to move, from −24 to +24. Plus moves the pitch up, minus moves it down.

Quick Presets: Tap a button like +7 or −5 to fill in a common shift fast.

Calculation Direction: In Frequency mode, pick "Semitone → Frequency" to find a new pitch, or "Frequency → Semitone" to compare two frequencies.

Base Frequency: Enter your starting pitch, such as 440, and choose Hz or kHz.

Show Result In: Pick Hz or kHz for the answer. Both units are shown anyway.

Frequency 1 and Frequency 2: Enter two pitches between 1 Hz and 20,000 Hz to see how many semitones and cents apart they are.

Show as Flat / Sharp: Click to switch note spelling, like C# or Db. The pitch stays the same.

Calculate: Click to update the results, steps, gauge, and chart. Click Reset to go back to the default values.

What Is a Semitone?

A semitone is the smallest step in Western music. On a piano, it is the distance from one key to the very next key, black or white. C to C# is one semitone. E to F is also one semitone, even though both keys are white. Semitones are also called half steps.

Two semitones make a whole tone (a whole step), like C to D. Twelve semitones make one octave, like C4 to C5. When you go up an octave, the note sounds like the same letter, just higher.

Semitones and Frequency

Every note has a frequency, measured in hertz (Hz). Higher frequency means a higher pitch. Modern tuning uses equal temperament, which splits the octave into 12 equal semitones. Moving up one semitone multiplies the frequency by about 1.0595. Moving up 12 semitones doubles it.

Here is the formula:

New frequency = old frequency × 2^(n/12), where n is the number of semitones.
A4 is tuned to 440 Hz. Seven semitones up is E5 at about 659.26 Hz.
Going down uses a negative number, like −5 semitones.

Cents

Cents are a smaller way to measure pitch. One semitone equals 100 cents, so one octave equals 1200 cents. Tuners use cents to show how sharp or flat a note is. Most people can hear a change of about 5 to 10 cents.

Common Intervals

The gap between two notes is called an interval. Counting semitones tells you which interval it is:

0: Unison
1: Minor 2nd
2: Major 2nd
3: Minor 3rd
4: Major 3rd
5: Perfect 4th
6: Tritone
7: Perfect 5th
8: Minor 6th
9: Major 6th
10: Minor 7th
11: Major 7th
12: Octave

Intervals with simple frequency ratios, like the perfect 5th and the octave, sound smooth and stable. Musicians call these consonant. Intervals like the minor 2nd and the tritone sound tense or clashing. Those are dissonant.

Sharps, Flats, and Enharmonics

A sharp (#) raises a note by one semitone. A flat (b) lowers it by one semitone. That means C# and Db are the same pitch with two different names. Notes like this are called enharmonic equivalents. The key you choose in a song decides which spelling looks correct on the page, but the sound does not change.

Why Semitones Matter

Semitones are the building blocks of scales, chords, and melodies. A major scale follows the pattern 2-2-1-2-2-2-1 in semitones. Singers move songs up or down a few semitones to fit their voice. This is called transposing. Producers use semitones to pitch-shift samples, tune guitars, set capo positions, and match tracks in a DAW.

Formulas used

MIDI note number from octave and pitch class

m = (\text{octave} + 1) \times 12 + \text{pitch class}

Frequency of a MIDI note (A4 = 440 Hz)

f = 440 \times 2^{(m - 69)/12}

Semitone distance between two notes

n = m_2 - m_1

Cents from semitones

\text{cents} = n \times 100

Frequency ratio from semitones

r = 2^{n/12}

Transposed frequency from a base frequency

f = f_{base} \times 2^{n/12}

Semitones between two frequencies

n = 12 \times \log_2\!\left(\frac{f_2}{f_1}\right)

Cents between two frequencies

\text{cents} = 1200 \times \log_2\!\left(\frac{f_2}{f_1}\right)

Frequently asked questions

Is a half step the same as a semitone?

Yes. They are two names for the same thing. "Half step" is common in the United States, and "semitone" is common in the United Kingdom and in most books about music theory. Both mean the smallest step between two notes, like C to C#.

Why is there no black key between B and C or between E and F?

Because B to C and E to F are already one semitone apart. A black key would have nothing to fill. The white keys follow the major scale pattern from C, which has two natural half steps in it: between the 3rd and 4th notes (E to F) and between the 7th and 8th notes (B to C).

Why is a perfect fifth called a fifth if it is 7 semitones?

Interval names count letter names, not semitones. From C to G you count C, D, E, F, G, which is five letters, so it is a fifth. But if you count keys on a piano, C to G is 7 semitones. Letter counting gives the name; semitone counting gives the exact size.

How many Hz is one semitone?

There is no fixed number. A semitone is a multiply, not an add. You multiply the frequency by about 1.0595.

110 Hz up one semitone = 116.5 Hz (about 6.5 Hz change)
440 Hz up one semitone = 466.2 Hz (about 26 Hz change)
880 Hz up one semitone = 932.3 Hz (about 52 Hz change)

High notes move more hertz per semitone than low notes.

Is one guitar fret one semitone?

Yes. Each fret moves the pitch by exactly one semitone. Twelve frets up is one octave, which is why the 12th fret plays the same note name as the open string, just higher. A capo works the same way: a capo on fret 3 raises every string 3 semitones.

How many semitones apart are guitar strings in standard tuning?

Standard tuning is E A D G B E from low to high. The gaps are:

E to A: 5 semitones
A to D: 5 semitones
D to G: 5 semitones
G to B: 4 semitones
B to E: 5 semitones

The low E and high E are 24 semitones apart, which is two octaves.

How many semitones do you transpose for a Bb instrument like trumpet or clarinet?

Two semitones. When a Bb instrument plays a written C, the sound you hear is Bb, which is 2 semitones lower. So to write music for a Bb player from concert pitch, move the notes up 2 semitones. For an Eb instrument like alto sax, the shift is 9 semitones up.

How do you transpose a song from C major to G major?

Move every note up 7 semitones, or down 5 semitones. Both land on G. Keep the same distance between all the notes so the melody still sounds right. Chords move too: C becomes G, F becomes C, and G becomes D.

How many semitones separate a major key from its relative minor?

Three semitones down. C major and A minor share the same notes, and A is 3 semitones below C. You can also count 9 semitones up to reach the same note in the next octave. This works for every key: G major pairs with E minor, F major pairs with D minor.

Why does the tritone sound so tense?

A tritone is 6 semitones, exactly half an octave. Its frequency ratio is about 1.414 to 1, which is not a simple fraction. The sound waves do not line up neatly, so the ear hears a rough, unsettled sound. Composers use it to build tension before resolving to a smoother interval like a fifth or a third.

Why is A4 tuned to 440 Hz?

It is a worldwide agreement, not a rule of nature. 440 Hz was set as the standard concert pitch in 1939 and confirmed by the ISO in 1955. Before that, orchestras used pitches from about 415 Hz to 455 Hz. Some orchestras today still tune to 442 or 443 Hz for a brighter sound.

What is the difference between equal temperament and just intonation?

Equal temperament splits the octave into 12 identical semitones, so every key sounds the same. Just intonation uses simple whole-number ratios like 3:2 for a fifth, which sounds purer but only in one key.

In equal temperament the fifth is about 2 cents narrow and the major third is about 14 cents sharp compared to pure ratios. Most people never notice, and it lets a piano play in all 12 keys.

How many semitones should you move a song to fit your voice?

Most singers shift a song by 1 to 5 semitones. Find the highest and lowest notes in the song, then compare them to your comfortable range. Move the song down by the number of semitones that brings the highest note into reach, then check that the lowest note is still singable.

Does pitch shifting by semitones change the speed of a track?

It depends on the method. Old tape and simple samplers change both together: shift up 12 semitones and the audio plays twice as fast. Modern software can shift pitch and keep the tempo, or change tempo and keep the pitch. Large shifts of more than about 5 semitones often sound unnatural.

What is a MIDI note number?

It is a number that stands for one key. Each step of 1 equals one semitone. C4 is 60, C#4 is 61, and A4 is 69. Because the steps are even, you can find the distance between two notes by subtracting the numbers. Going up 12 in MIDI is always one octave.

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