Free Semitone Calculator

Semitone Calculator: Convert Frequency to Musical Interval

The semitone calculator is a practical frequency-to-semitone converter that determines the musical distance between two pitches in both semitones and cents. It also acts as a note frequency distance calculator, displaying the closest note name and the deviation from equal temperament. Musicians, audio engineers, and music educators use this tool to compare tuning standards, adjust instrument pitch, and explore the logarithmic relationship behind the notes.

How to Measure Intervals with This Tool

Using the calculator is straightforward:

1. Enter the first frequency (ƒ₁) in Hertz (Hz).
2. Enter the second frequency (ƒ₂) in Hz.
3. The result shows the interval in semitones and cents.
4. For each input, the closest musical note appears along with a cent deviation indicating how far it is from the standard equal-tempered pitch.

For example, inputting 432 Hz and 440 Hz yields a difference of 0.31767 semitones (31.767 cents). The tool identifies 432 Hz as A4 with a deviation of −31.767 cents, while 440 Hz matches A4 exactly. This example demonstrates how cents capture subtle tunings.

Core Concepts: Semitone and Cent

Semitone (Half Step)
A semitone is the smallest interval in Western music. On a piano keyboard, moving from any key to the immediately adjacent key—white to black or white to white—produces a semitone. In equal temperament, the frequency ratio of a semitone is exactly $2^{1/12} \approx 1.0595$. The formula to calculate the number of semitones between two frequencies is:

$$n = 12 \cdot \log_2\left(\frac{f_2}{f_1}\right)$$

Cent
A cent is a logarithmic unit that divides a semitone into 100 equal parts. Introduced by Alexander Ellis in 1885, it provides a precise way to measure intervals. An octave contains 1200 cents (12 semitones × 100 cents). The cent formula is:

$$\text{Cents} = 1200 \cdot \log_2\left(\frac{f_2}{f_1}\right)$$

Because cents are logarithmic, they represent the same ratio regardless of octave, making them ideal for comparing different tuning systems.

Practical Examples

Hz to Semitones
Two frequencies 36.71 Hz (low E on a bass) and 698.46 Hz (F5) give:

$$n = 12 \cdot \log_2\left(\frac{698.46}{36.71}\right) \approx 51\ \text{semitones}$$

This corresponds to 4 octaves and 3 semitones.

Semitones to Cents
Simply multiply semitones by 100: $51\ \text{st} \times 100 = 5100\ \text{cents}$.

432 Hz vs 440 Hz
A common question in music is the cent difference between alternative tuning (432 Hz) and standard pitch (440 Hz):

$$\text{Cents} = 1200 \cdot \log_2\left(\frac{440}{432}\right) \approx 31.767\ \text{cents}$$

Thus, 440 Hz is about 31.767 cents higher than 432 Hz.

Why This Calculator Is Useful

This musical interval calculator eliminates manual logarithm calculations. It serves as a reliable Hz-to-semitones converter and cents-between-frequencies tool for tasks like tuning instruments, comparing historical pitch standards, or teaching music theory. By providing instant results and note recognition, it supports both simple and advanced pitch analysis.