Semitone Calculator
Calculate the distance between two frequencies in semitones and cents
Calculate Semitone Intervals
First frequency for comparison
Second frequency for comparison
Quick Presets
Interval Results
Frequency Ratio
0.000000
f₂ / f₁
Interval Direction
Same
Equal frequencies
Formula used: n = 12 × log₂(f₂ / f₁) for semitones; cents = 1200 × log₂(f₂ / f₁)
Input frequencies: f₁ = 0 Hz, f₂ = 0 Hz
Interval Analysis
Example Calculation
A4 Tuning Comparison
Standard A4: 440 Hz
Alternative A4: 432 Hz
Difference: Popular tuning debate
Calculation
n = 12 × log₂(432 / 440)
n = 12 × log₂(0.9818)
n = -0.318 semitones
cents = -31.8 cents
Common Musical Intervals
Semitone Tips
One semitone = 100 cents exactly
One octave = 12 semitones = 1200 cents
Frequency ratio of 2:1 = perfect octave
Equal temperament: 12√2 ≈ 1.0595 per semitone
Understanding Semitones and Cents
What is a Semitone?
A semitone (also called a half-step or half-tone) is the smallest musical interval commonly used in Western music. It represents the distance between two consecutive notes, such as from C to C# or from E to F on a piano keyboard.
What is a Cent?
- •A cent is 1/100 of a semitone
- •There are 1200 cents in an octave
- •Allows precise measurement of pitch differences
- •Independent of octave for same intervals
Conversion Formulas
Frequency to Semitones
n = 12 × log₂(f₂ / f₁)
Frequency to Cents
cents = 1200 × log₂(f₂ / f₁)
Semitones to Cents
cents = semitones × 100
Note: f₁ and f₂ are frequencies in Hz, n is the number of semitones