Pitch is perceived logarithmically: each doubling of frequency sounds like the same step, an octave, whether it goes from 110 to 220 Hz or from 1,000 to 2,000 Hz. Musicians therefore measure the distance between two frequencies by their ratio, not their difference. In equal temperament an octave has 12 semitones and a semitone 100 cents, so the number of semitones between two frequencies is 12 × log₂ of their ratio.
Cents are the unit of fine tuning. Tuners show how many cents a string is off, and differences of about 5 cents are just noticeable to trained ears. Comparing 432 Hz with 440 Hz, for example, gives 31.77 cents – about a third of a semitone.
Enter any two frequencies to get the interval between them; the calculator also gives the beat frequency (their difference), the nearest equal-tempered note for each with its deviation, and the closest named interval. It works for tuning, pitch-shifting by a ratio, analysing harmonics or comparing reference pitches.
How to use the Semitone Calculator
- Frequency 1 (f₁)
- Frequency 2 (f₂)
- Reference pitch A4 (for note names)
Everything is calculated in your browser, so results appear instantly and nothing you type is sent to a server.
How it works
The ratio f₂ ÷ f₁ is converted with a base-2 logarithm: 12 × log₂ gives semitones, 1,200 × log₂ gives cents. Each frequency is also compared with the equal-tempered scale based on your A4 reference to find the nearest note and the deviation in cents.
Worked example
From 432 Hz to 440 Hz: the ratio is 440 ÷ 432 = 1.018519, log₂ of that is 0.026472, so the interval is 12 × 0.026472 = 0.3177 semitones = 31.77 cents. 440 Hz is exactly A4; 432 Hz is A4 − 31.77 cents. The two tones together beat 8 times per second. From 36.71 Hz to 698.46 Hz the result is 51.0 semitones (5,100 cents).
Semitones and frequency ratios
| Semitones | Cents | Ratio |
|---|---|---|
| 1 | 100 | 1.059463 |
| 2 | 200 | 1.122462 |
| 3 | 300 | 1.189207 |
| 4 | 400 | 1.259921 |
| 5 | 500 | 1.334840 |
| 6 | 600 | 1.414214 |
| 7 | 700 | 1.498307 |
| 12 | 1200 | 2.000000 |
| 24 | 2400 | 4.000000 |
Formula
n = 12 × log₂(f₂ ÷ f₁) semitones
cents = 1200 × log₂(f₂ ÷ f₁) = 100 × n
Nearest note: 69 + 12 × log₂(f ÷ A4), rounded
Worked example
Inputs — Frequency 1 (f₁): 432 Hz; Frequency 2 (f₂): 440 Hz; Reference pitch A4 (for note names): 440 Hz.
Results — Interval = 0.318 semitones; Cents = 31.77 ¢; Frequency ratio f₂ ÷ f₁ = 1.018519; Octaves = 0.0265; Nearest named interval = Perfect unison (nearest whole semitone: 0); Nearest note to f₁ = A4 −31.77 cents.
Key terms
- Semitone
- 1/12 of an octave, a frequency ratio of 2^(1/12).
- Cent
- 1/100 of a semitone, 1/1200 of an octave.
- Octave
- A doubling of frequency.
- Beat frequency
- The rate of loudness fluctuation when two close tones sound together.
Frequently asked questions
How many cents is 432 Hz from 440 Hz?
1200 × log₂(440/432) = 31.77 cents; 432 Hz is A4 − 31.77 cents.
How many semitones between 36.71 Hz and 698.46 Hz?
12 × log₂(698.46/36.71) = 51.0 semitones (D1 to F5), i.e. 5,100 cents.
How many cents are in a semitone?
100; an octave has 1,200 cents.
What frequency ratio is one semitone?
2^(1/12) ≈ 1.059463 – about 5.95% higher.
How do I convert semitones to a frequency ratio?
Ratio = 2^(n/12). Seven semitones (a fifth) = 1.4983.
Can the interval be negative?
Yes – if f₂ is lower than f₁ the result is negative (a downward interval).
How small a difference can people hear?
Around 5–10 cents for sustained tones; two close tones also produce audible beats at |f₂ − f₁| Hz.