Frequency Ratio to Cents Calculator
Convert frequency ratios to cents for precise musical pitch measurement. Understand how logarithmic scales work in music theory.
Frequency Ratio Input
Enter as ratio (2:1) or decimal (1.5)
Cents Result
Enter a frequency ratio to convert it to cents
What Are Frequency Ratios and Cents?
When you hear music, you're hearing different frequencies of sound waves. A frequency ratio compares two pitches - like saying one note is twice as fast as another. But humans don't hear frequency differences linearly. We hear them logarithmically.
That's where cents come in. Cents divide the octave (the 2:1 frequency ratio) into 1200 equal parts. This logarithmic scale matches how our ears actually perceive pitch differences. A semitone (like from C to C#) is 100 cents, while a whole tone (C to D) is 200 cents.
Converting frequency ratios to cents gives us a precise, human-friendly way to talk about musical intervals.
Frequency Ratio to Cents Formula
Cents Conversion Formula
Cents = 1200 × log₂(Frequency Ratio)
This formula converts frequency ratios to cents:
- • 1200: Number of cents in an octave (2:1 ratio)
- • log₂: Base-2 logarithm (matches human pitch perception)
- • Frequency Ratio: How many times faster one frequency is than another
Example: Ratio 3:2 = 1.5
Cents = 1200 × log₂(1.5) = 702 cents
Musical Intervals in Cents
Common Musical Intervals
| Interval Name | Frequency Ratio | Cents | Example |
|---|---|---|---|
| Unison | 1:1 | 0 | Same note |
| Minor Second | 16:15 | 112 | C to C# |
| Major Second | 9:8 | 204 | C to D |
| Perfect Fourth | 4:3 | 498 | C to F |
| Perfect Fifth | 3:2 | 702 | C to G |
| Octave | 2:1 | 1200 | C to C |
These ratios come from the harmonic series and form the foundation of Western music theory.
Music Theory FAQs
Why use logarithms for pitch?
Our ears perceive pitch differences logarithmically. A note twice as high sounds like the same interval regardless of starting pitch.
What's a cent in practical terms?
One cent is about the smallest pitch difference most people can hear. Piano tuners aim for accuracy within a few cents.
How do cents help with tuning?
Cents give a precise measurement for how "in tune" or "out of tune" notes are, allowing for fine adjustments in recording and performance.