Semitone Calculator
Calculate the distance between any two frequencies in semitones and cents. Find the closest musical note for each frequency with this free online music interval tool.
About This Calculator
The Semitone Calculator computes the musical interval between any two frequencies in hertz (Hz). Whether you are a musician comparing tunings, an audio engineer calibrating equipment, a music student studying intervals, or a producer working with alternate temperaments, this tool gives you instant results in semitones, cents, frequency ratio, and the closest equal-temperament note names.
In Western music, the smallest pitch interval is the semitone — also called a half step. In 12-tone equal temperament (the most common tuning system), the octave is divided into 12 equally spaced semitones. The calculator uses the formula n = 12 × log₂(f₂ / f₁) to compute the number of semitones between any two frequencies and cents = 1200 × log₂(f₂ / f₁) for the more precise cent measurement. Each frequency is also mapped to its closest note name (C through B) and octave number based on the MIDI standard where A4 = 440 Hz.
Regional Notes
Music theory and the 12-tone equal temperament system are universal — semitones, cents, and note names are identical across all regions. The ISO standard of A4 = 440 Hz is recognized worldwide (ISO 16:1975). However, regional and historical variations exist: some European orchestras tune to A4 = 442 Hz, Baroque ensembles often use A4 = 415 Hz, Indian classical music uses a reference of C4 = 256 Hz (Shadja at 256 Hz or 240 Hz depending on the tradition), and some contemporary musicians prefer A4 = 432 Hz tuning. The calculator works with any frequency you enter, so you can explore these different standards.
Frequently Asked Questions
What is a semitone?
A semitone, also called a half step or half tone, is the smallest musical interval used in Western music. It represents the distance between two consecutive notes on a piano — from C to C♯, or from E to F. In terms of frequency, one semitone corresponds to a frequency ratio of 2 to the power of 1/12, approximately 1.0595.
How do you calculate the number of semitones between two frequencies?
The number of semitones n between two frequencies f₁ and f₂ is calculated as n = 12 × log₂(f₂ / f₁). For example, between 440 Hz (A4) and 880 Hz (A5), n = 12 × log₂(880/440) = 12 × log₂(2) = 12 semitones, which is exactly one octave.
What is a cent in music?
A cent is a logarithmic unit of measure used to express musical intervals. One octave is divided into 1200 cents. Since one octave contains 12 semitones, each semitone equals exactly 100 cents. Cents allow precise measurement of intervals smaller than a semitone and are commonly used for tuning comparisons.
How many cents are in a semitone?
There are exactly 100 cents in one semitone. The 12-tone equal temperament system divides the octave into 12 equally spaced semitones, each spanning 100 cents. This means an octave contains 1200 cents total.
How do I find the closest musical note to a frequency?
The closest musical note in 12-tone equal temperament is found by calculating the cents offset from A4 (440 Hz). The formula is cents = 1200 × log₂(f / 440), then the closest MIDI note number is round(cents/100) + 69. Each MIDI note maps to a note name (C, C♯, D, etc.) and octave number. The deviation in cents shows how far the frequency is from that note.
Is A4 always tuned to 440 Hz?
440 Hz for A4 is the modern standard (ISO 16:1975) used worldwide. However, historical and alternative tunings exist: Baroque music often uses A4 = 415 Hz (one semitone lower), some orchestras tune to A4 = 442 Hz for a brighter sound, and scientific tuning uses C4 = 256 Hz. Many contemporary musicians also use A4 = 432 Hz tuning.
What is the frequency ratio of a semitone?
The frequency ratio of one equal-temperament semitone is the 12th root of 2, approximately 1.059463. This means multiplying a frequency by 1.059463 raises it by one semitone. Two semitones (a whole tone) give a ratio of about 1.1225, and 12 semitones (one octave) give exactly a ratio of 2.
How many cents are between 432 Hz and 440 Hz?
The difference between 432 Hz and 440 Hz is approximately 31.77 cents. Using the formula cents = 1200 × log₂(432/440), we get about -31.77 cents. This means 432 Hz is about 31.8 cents (roughly one third of a semitone) lower than the standard A4 at 440 Hz.