How to Use the Semitone Calculator
Begin by entering two frequencies in hertz into the Frequency 1 and Frequency 2 fields. The calculator immediately displays the interval between them in both semitones and cents—the two most useful ways to express pitch distances.
You can also work backwards: input one frequency and the number of semitones (or cents) separating it from another note to find the target frequency. For instance, if you want to know the frequency that lies 12 semitones (one octave) above 440 Hz, enter 440 and 12 semitones; the tool returns 880 Hz.
All results appear in real time, making this especially useful for:
- Audio engineering and frequency matching
- Musical instrument tuning
- Pitch analysis and comparison
- Understanding tuning standards
Understanding Semitones and Musical Intervals
A semitone, or half step, is the smallest interval in Western music. On a keyboard, it's the distance between any two adjacent keys (white or black). On a guitar fretboard, it's one fret. Within a 12-tone equal temperament system—the standard tuning method—an octave spans exactly 12 semitones, each equally spaced.
This equal spacing means the frequency ratio between consecutive semitones is constant: each step multiplies the frequency by the 12th root of 2 (approximately 1.0595). That's why moving up an octave (12 semitones) always doubles the frequency, regardless of which note you start from.
Musically, semitones define scales and chords. A major scale follows the pattern: whole step, whole step, half step, whole step, whole step, whole step, half step. This precise interval structure is why the same major scale sounds identical on any instrument, from C major to F♯ major.
Converting Between Frequencies and Semitones
To find the number of semitones between two frequencies, take the logarithm of their ratio. To find a frequency at a given interval from a known pitch, multiply by a power of two.
f₂ = f₁ × (2^(n/12))
n = 12 × log₂(f₂ / f₁)
cents = 100 × n
f₁, f₂— Frequencies in hertz (Hz)n— Number of semitonescents— Interval measured in cents (1/100th of a semitone)
The Cent: A Fine-Grained Unit of Pitch
While semitones suit musical conversation, cents provide finer precision for technical work. Defined in 1885 by Alexander Ellis, a cent divides an octave into 1200 equal parts. This means one semitone equals 100 cents, making conversions straightforward: multiply semitones by 100.
Cents are invaluable because the same frequency difference in cents remains identical across octaves, whereas the hertz difference compounds. For example, the interval from 220 Hz to 440 Hz (one octave) measures 1200 cents, and so does the interval from 440 Hz to 880 Hz. But in hertz, the first spans 220 Hz while the second spans 440 Hz—the same musical interval, different physical distance.
This unit proves essential for:
- Precise instrument tuning (a well-tuned note usually stays within ±5 cents)
- Comparing tuning standards (A440 vs. A432 differs by about 32 cents)
- Analyzing audio deviations from target pitch
Common Pitfalls When Working with Pitch Intervals
Avoid these frequent mistakes when calculating or thinking about frequency relationships.
- Confusing Hz differences with interval size — A 10 Hz jump is tiny at 440 Hz but enormous at 55 Hz—both are the same musical interval (about 39 cents). Always use semitones or cents to compare intervals meaningfully across the audio spectrum.
- Forgetting the logarithmic nature of pitch — Frequency ratios, not differences, determine intervals. Doubling a frequency always increases pitch by one octave (1200 cents), whether you go from 100 Hz to 200 Hz or 4000 Hz to 8000 Hz. This is why musical scales feel evenly spaced despite unequal hertz spacing.
- Assuming tuning standards don't matter — The reference pitch A (often 440 Hz internationally, but sometimes 432 Hz or 442 Hz in orchestras) shifts all other notes proportionally. If your source material uses a non-standard reference, you may observe pitch discrepancies across semitones—check the tuning standard first.
- Rounding prematurely in multi-step calculations — When converting frequencies to semitones and then to cents, intermediate rounding compounds errors. Maintain full precision until the final result, especially for small intervals where cents precision matters.