Semitone Calculator - Note-Pair Interval in Semitones, Cents, and Hz

A semitone calculator converts any pair of musical notes into the interval between them, expressed in semitones, cents, and hertz. A semitone is the smallest step in standard Western tuning: twelve semitones fill one octave, and each semitone multiplies a frequency by the equal-tempered ratio of 2^(1/12). The calculator handles upward, downward, and octave-wrap intervals in one calculation.

• • Vocalists measuring range: Find the semitones between two notes a singer can reach, then map the result to cents to plan a transposition that keeps the melody in range.
• • Instrument tuners reading deviation: Convert a tuner app's cents reading into a semitone count and frequency ratio so the player can decide whether to retune or transpose.
• • Music students naming intervals: Build a chromatic interval table by reading the standard interval name that matches each semitone count for every note pair.
• • Sound designers shifting MIDI notes: Translate a semitone shift into a frequency ratio and target frequency so a sampler or synth can apply the same shift.

The semitone is the atomic unit of 12-tone equal temperament, the tuning used by every standard piano, guitar, and MIDI controller. Two semitones make a whole tone, six make a tritone, and twelve return to the same pitch class one octave higher. The same arithmetic shows up in any tool that moves a melody between keys.

Multiplying by 2^(semitones/12) raises or lowers a pitch by the chosen interval, because equal temperament is logarithmic. That is why a chord transposer and a frequency-shifting sampler share the same backend math.

When a user already knows the target hertz rather than the note pair, a separate frequency calculator can convert that frequency to wavelength or period without going through MIDI arithmetic.

The calculator assigns every pitch class a chromatic index from 0 to 11, adds the octave to compute a MIDI note number, and subtracts the source from the target to get the interval. The frequency ratio and the target frequency both follow from a single exponent of 2, and the cents value is the semitone count multiplied by 100.

• sourceNote, sourceOctave: Pitch class and scientific pitch notation octave for the starting note. Middle C is C4.
• targetNote, targetOctave: Pitch class and octave for the destination note. The interval can go up or down.
• targetMidi: MIDI note number of the target. Equal to 12 * (octave + 1) + chromatic index of the pitch class.
• A4: Reference frequency for A4 in hertz. The default is 440 Hz, the international standard concert pitch.

The same exponent appears twice: once for the frequency ratio and once for the target frequency in hertz. The ratio is 2^(semitones/12) regardless of the A4 reference, but the absolute target frequency shifts if A4 is tuned above or below 440 Hz.

Negative semitones come from subtracting a lower MIDI note from a higher one. When the target falls below the source, the cents value goes negative and the frequency ratio drops below 1, which the interval name table flags with a 'down' qualifier.

According to Wikipedia (equal temperament), equal temperament divides the octave into 12 identical semitone steps, so the ratio between consecutive semitones is exactly 2^(1/12).

Four ideas explain every number this semitone calculator produces.

These four ideas cover every output on the result panel. The chromatic index and MIDI note number do the arithmetic, the frequency ratio answers the 'how much do I multiply?' question, and the cents value answers the 'how far off am I?' question that tuners report.

A chord transposer moves a progression by adding a constant semitone count to every root, and a frequency calculator works in the same logarithmic space when it converts a wavelength into a frequency.

Five steps cover every common semitone query, from a single note pair lookup to a full transposition check.

1. 1 Pick the source note: Choose the starting pitch class from the Source note menu. The list covers every chromatic pitch from C to B; Db, Eb, Gb, Ab, and Bb are accepted on input.
2. 2 Set the source octave: Type the scientific pitch notation octave for the source. Middle C is C4, the standard reference for vocal range and piano repertoire.
3. 3 Pick the target note: Choose the destination pitch class. Pick a note higher than the source for a positive interval, lower for a negative interval, or the same pitch class in a higher octave to measure an octave jump.
4. 4 Set the target octave: Type the target octave. The calculator subtracts the source MIDI note from the target MIDI note, so the sign of the result tells you whether the target is above or below the source.
5. 5 Read the result panel: The result panel shows the signed interval in semitones, target frequency in hertz assuming a 440 Hz A4 reference, the multiplicative frequency ratio, the cents value, and the standard interval name.

With source C4 and target G4 the panel shows 7 semitones up, 391.9954 Hz, a frequency ratio of 1.498307, 700 cents, and 'Perfect fifth up'. Switching the target to G5 keeps the interval name but adds 12 semitones, doubles the ratio, and gives a compound twelfth.

If the target is a chord progression rather than a single note, a separate chord transposer applies the same semitone arithmetic to every root in the progression.

Putting semitone, cents, ratio, frequency, and interval name in one calculation saves a chain of single-purpose lookups.

• • Five outputs from one note pair: Semitones, target frequency, frequency ratio, cents, and interval name appear together, so a tuner can match the cents reading to a frequency ratio without a separate calculation.
• • Negative intervals handled automatically: A target below the source returns a negative semitone count and a frequency ratio below 1, so the same input covers both directions without flipping inputs by hand.
• • Octave wrap handled by MIDI arithmetic: Moving from B4 to C5 returns a clean 1-semitone-up result because the MIDI subtraction takes the octave change into account.
• • Interval name with up/down qualifier: Standard music-theory names appear with an up/down qualifier, which makes the result easy to read for singers, students, and players.
• • Frequency ratio ready for samplers and synths: The multiplicative ratio matches what a sampler pitch-shift knob or a synth's pitch-bend input expects, so the calculator doubles as a quick reference for audio plugins.

These benefits stack when the calculator is used as a teaching aid. A teacher can ask a class to predict the interval name from a note pair, then show the same interval as a frequency ratio and a cents value so the numbers line up with the name.

Audio engineers get the same value when checking a tuning session: the cents reading lines up with the frequency ratio, and the interval name gives a label that the rest of the recording session can reference.

The frequency-ratio exponent on this page is a binary logarithm in disguise, and a separate log 2 calculator confirms the same log base 2 step for any positive input.

Three inputs and one reference assumption drive the result, and two limitations tell you when to switch to a different tool.

• • Equal temperament assumes every semitone is exactly 2^(1/12). Just intonation, Pythagorean tuning, and meantone temperament use slightly different ratios for the same named interval, so the cents row will not match those systems exactly.
• • A change in the A4 reference shifts the absolute hertz output but does not change the semitone, ratio, or cents values. A user who works with baroque pitch (A=415 Hz) needs to scale the hertz result rather than rely on the default 440 Hz.

These factors apply to every calculation on this page. The cents row stays correct in equal temperament regardless of the A4 reference, which is why tuner apps report pitch deviation in cents. A user who needs a hertz reading can still trust the ratio and the cents while scaling the hertz output to match the room.

According to Wikipedia (cent, music), the cent is the logarithmic unit that splits a semitone into 100 equal parts, giving 1200 cents per octave.

According to Wikipedia (scientific pitch notation), scientific pitch notation assigns C4 to middle C and A4 to the standard 440 Hz reference pitch, with MIDI note 69 mapped to A4.

The 12-semitone octave is a modulo-12 system, and a separate modulo calculator shows how the same remainder-after-division pattern handles any wrap-around step.