Cents & Transpose Calculator

Convert between cents and frequency ratios, and transpose a reference frequency by a number of semitones or cents. Includes a reference table comparing equal temperament and just intonation cent values, useful for describing tuning offsets.

Last updated: 2026-09-10

12-Tone Equal Temperament Intervals in Cents (with Just Intonation Comparison)

Equal-tempered values are derived from the definition that one semitone equals 100 cents and one octave equals 1200 cents. For the perfect fifth, perfect fourth, major third and minor third, the table also shows the long-known just intonation ratios for comparison (e.g. a just perfect fifth is a 3:2 ratio).

Interval	Semitones	Equal Temperament (cents)	Just Intonation (cents)
Unison	0	0	0.00
Minor 2nd	1	100	—
Major 2nd	2	200	—
Minor 3rd	3	300	315.64
Major 3rd	4	400	386.31
Perfect 4th	5	500	498.04
Tritone	6	600	—
Perfect 5th	7	700	701.96
Minor 6th	8	800	—
Major 6th	9	900	—
Minor 7th	10	1,000	—
Major 7th	11	1,100	—
Octave	12	1,200	1,200.00

What Is Cents & Transpose Calculation?

A cent is a logarithmic unit for measuring the size of a musical interval, defined so that one semitone in 12-tone equal temperament equals 100 cents and one full octave (a 2:1 frequency ratio) equals 1200 cents. A plain Hz difference cannot be compared meaningfully across registers, because the same musical interval spans far more Hz at high pitches than at low pitches. Cents solve that problem by giving every interval a fixed numeric size regardless of register, which is why transposition, tuning-system comparison, and tuning-offset description are all done in cents.

This tool provides two related calculations: converting between cents and frequency ratios, and transposing a reference frequency by a chosen number of semitones or cents. The transpose calculation assumes 12-tone equal temperament — the modern standard tuning that divides the octave into 12 mathematically equal semitones of exactly 100 cents each — so you can instantly find the frequency that results from any semitone or cent shift. If you need a different tuning system, such as just intonation, you can enter its exact decimal ratio directly into the frequency ratio field instead.

How to Use the Cents & Transpose Calculator

Choose the conversion direction Depending on whether you are starting from a cent value or a frequency ratio, use the matching input field in the top section.
Enter the cent value or frequency ratio Type in a reading from a tuner (such as "+15 cents"), or a decimal ratio used by a tuning system, like 1.5 for a 3:2 ratio.
For transposition, enter the reference frequency and amount Provide a reference frequency in Hz and a transpose amount in semitones or cents to instantly get the transposed frequency.
Switch between semitones and cents Pick whichever unit matches your source material; semitones are usually more convenient for transposing-instrument calculations.
Check the equal temperament vs. just intonation table Compare the equal-tempered and just-intonation cent values for the main intervals to see exactly how far apart they are.

Tips for getting more out of it

You can enter positive or negative cent values. A negative value means a transposition downward, or a flat (lower) tuning offset.
To find the concert pitch of a transposing instrument (e.g. B♭ clarinet, E♭ saxophone), enter its transposition interval in semitones (e.g. -2 for B♭ clarinet) as the transpose amount.
The frequency ratio field accepts any decimal fraction used by non-equal-tempered tunings, such as just intonation or Pythagorean tuning (e.g. enter 1.5 for a 3:2 ratio).
Clicking the sample button fills in 440Hz and 12 semitones, so you can immediately verify the tool against the well-known result that transposing up an octave exactly doubles the frequency.
If a tuner shows a reading like "15 cents flat," typing that number directly into the cents field instantly gives you the corresponding frequency ratio.

Ways to Use Cents & Transpose Calculations

Fine-tuning a DAW or synthesizer

Work backward from a target frequency ratio to the exact cent value needed in a detune or fine-tune parameter on a plugin or oscillator.

Finding the concert pitch of a transposing instrument

Enter the semitone offset for instruments like the B♭ clarinet or E♭ saxophone to see the actual sounding frequency for any written note.

Interpreting a tuner's cent reading

Turn a tuner's "+15 cents" style reading into a concrete frequency ratio so you know exactly how far off pitch you really are.

Studying and comparing tuning systems

Convert the frequency ratios of just intonation, Pythagorean tuning, and others into cents for direct numeric comparison in coursework or research.

Designing pitch-shift amounts for samplers and effects

Translate a target frequency ratio or cent offset into the semitone value expected by a pitch-shifter or sampler control.

Cents & Interval Terminology

Cent: A logarithmic unit of interval size where one semitone equals 100 cents and one octave equals 1200 cents.
Equal temperament: The modern standard tuning system that divides the octave into 12 mathematically equal semitones of exactly 100 cents each, so every key sounds equally in tune.
Just intonation: A tuning system that sets intervals to simple integer frequency ratios, such as 3:2 for a perfect fifth, so specific chords sound maximally consonant, at the cost of flexibility across keys.
Transposition: Shifting a note, phrase, or whole piece upward or downward by a fixed interval, specified here in semitones or cents.
Frequency ratio: The ratio between the frequencies of two pitches — 2:1 (2.0) for an octave, or approximately 1.4983 for an equal-tempered perfect fifth.
Transposing instrument: An instrument whose written pitch differs from its sounding pitch; a B♭ clarinet, for example, sounds a major second lower than what is written.
Beating: The periodic rise and fall in loudness heard when two tones of slightly different frequency sound together, audible even from a difference of only a few cents.

Frequently Asked Questions

A cent is a logarithmic unit for measuring musical intervals, defined so that one semitone in 12-tone equal temperament equals 100 cents and one octave (a frequency doubling) equals 1200 cents. Because a fixed Hz difference represents a much smaller interval at high pitches than at low pitches, cents give musicians a consistent scale for describing interval size regardless of register.

Equal temperament divides the octave into 12 mathematically equal semitones of exactly 100 cents each, so every key sounds equally in tune. Just intonation instead tunes intervals to simple integer frequency ratios (a perfect fifth is exactly 3:2) so that specific chords sound maximally consonant; a just perfect fifth works out to about 702 cents, about 2 cents wider than the equal-tempered 700 cents, and that small gap is the source of the faint beating heard in equal-tempered chords.

Take the written pitch and shift it by the instrument's fixed transposition interval, expressed in semitones. A B♭ clarinet, for example, sounds a major second (2 semitones) lower than written, so entering -2 semitones as the transpose amount on the written pitch gives you the actual sounding frequency.

Even trained musicians can typically only reliably detect a pitch difference in a single tone of around 5 to 6 cents under good conditions, though this varies with timbre and context. That is why instrument tuning is usually considered acceptable once it is within about ±5 cents of the target pitch.

Both represent the same information, but cents are easier to work with when stacking multiple intervals (such as repeated transpositions), since they simply add together. When you need an actual frequency in Hz, however, you eventually need to convert to a ratio using 2^(cents/1200). This tool supports conversion in both directions.

Side Note — Why Musical Intervals Are Measured in Cents, Not a Simple Hz Difference

When comparing the pitch of two notes, it is tempting to simply subtract their frequencies in Hz. But a 5Hz gap between 440Hz and 445Hz sounds like an almost imperceptible difference, while the very same 5Hz gap between 220Hz and 225Hz sounds noticeably out of tune. That is because human pitch perception tracks the ratio between frequencies, not the raw difference — a property that a logarithmic unit like the cent was invented to capture numerically.

The cent was devised by the 19th-century English acoustician Alexander Ellis, who defined an octave (a 2:1 frequency ratio) as exactly 1200 cents. The number 1200 has no special physical significance; it was chosen purely so that it would divide evenly by the 100-cent semitones of 12-tone equal temperament, making transposition, tuning system comparisons, and pitch-deviation descriptions all reducible to simple cent arithmetic.

Expressing the gap between equal temperament and just intonation in cents makes the mismatch easy to see. A just perfect fifth, tuned to the simple 3:2 frequency ratio, comes out to roughly 702 cents, while equal temperament mechanically splits the octave into 12 identical pieces and lands exactly on 700 cents. That tiny 2-cent gap is precisely what produces the faint beating heard in chords on equally-tempered instruments like the piano, and it is why string players and a cappella ensembles often deliberately bend away from equal temperament to make a chord ring more purely.

Calculating a transposing instrument's concert pitch is a direct application of this same semitone-and-cent logic. Instruments like the B♭ clarinet or E♭ saxophone sound at a different pitch than what is written on the page, simply because each instrument has a fixed transposition interval built into its design; multiplying the written frequency by the corresponding frequency ratio yields the actual sounding pitch. That is also why, in an orchestra, instruments in different keys reading the same written note on the page are, in fact, sounding entirely different pitches.

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