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Cents Calculator

Calculate the difference in cents between two frequencies. A cent is 1/100th of a semitone - essential for precise tuning and intonation analysis.

Difference

7.85 cents

Frequency Ratio:
1.00455
Semitones:
0.08
Perception:
Barely noticeable
Direction:
F2 is sharper
Cents Reference Chart
Cents Musical Meaning Perception
1-5 Micro-adjustment Usually imperceptible
5-15 Fine tuning difference Noticeable to trained ears
15-30 Slightly out of tune Clearly audible
50 Quarter tone Very obvious
100 Semitone (half step) Different note
200 Whole tone Two semitones
1200 Octave Same note, higher/lower

The Formulas

Cents from Two Frequencies:
cents = 1200 × log₂(f₂ / f₁)

Where f₁ and f₂ are the two frequencies being compared.

Frequency from Cents:
f₂ = f₁ × 2^(cents / 1200)

Add cents to a base frequency to get the new frequency.

Why Use Cents?

  • Precision: Cents allow for much finer measurements than semitones
  • Universal: Same scale works across all octaves and frequencies
  • Perception-based: Cents roughly correspond to how we perceive pitch differences
  • Standard: Used worldwide by musicians, luthiers, and audio engineers

Frequently Asked Questions

Most people can detect pitch differences of about 5-10 cents when notes are played sequentially. When played simultaneously, differences as small as 2-3 cents can create audible "beating" (wavering sound). Professional musicians often tune to within 1-2 cents.

The difference is approximately 31.2 cents, or about one-third of a semitone. This is clearly audible to most listeners and explains why instruments tuned to different standards sound noticeably different when played together.

The cents system was designed by Alexander Ellis in the 1880s specifically to have 100 cents per semitone, making calculations intuitive. Since there are 12 semitones in an octave, there are exactly 1200 cents in an octave. The logarithmic scale ensures equal perception across all registers.
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