Back
Cents & Frequency
The logarithmic language of pitch — how musicians measure the spaces between notes
The Cents Scale
Cents measure pitch logarithmically: cents = 1200 · log₂(f / f₁). The octave spans exactly 1200 cents; a semitone is 100 cents. This lets us compare intervals across any reference pitch with a single number — a perfect fifth is ~702 cents, a major third ~386 cents, regardless of the base frequency.
Cents & Frequency Calculator
cents = 1200 · log₂(f / f₁). An octave is 1200¢, a semitone 100¢. Convert any note + cents offset to its exact frequency.
Base C#4277.18 Hz
+25¢ offset×1.014545
Result frequency281.21 Hz
Example from the physics of music: C#4 + 25¢ = 281.21 Hz (base 277.18 × 2^(25/1200))
Perception Is Logarithmic
We hear pitch ratios, not pitch differences. The distance from 100 Hz to 200 Hz (an octave) feels the same as from 1000 Hz to 2000 Hz (also an octave) — even though the first is a 100 Hz gap and the second a 1000 Hz gap. The cents scale mirrors this: equal steps in cents correspond to equal perceptual distances.
Pitch Ladder (Logarithmic)
Perception is logarithmic — each octave feels equal in distance though frequencies double. Drag to feel the equal spacing of cents.
-1200¢
-700¢
-500¢
-400¢
-300¢
-200¢
-100¢
0¢
+100¢
+200¢
+300¢
+400¢
+500¢
+700¢
+1200¢
0¢ from C4261.63 Hz
Turning Notes Into Frequencies
What is the frequency of C#4 + 25 cents? C#4 is 277.18 Hz. Multiply by 2^(25/1200) = 1.01455, and you get 281.21 Hz. This is how microtonal music, orchestral tuning adjustments, and historical temperaments are all expressed — in cents, the universal unit of pitch distance.
Reflect
If hearing is logarithmic, does a 'small' pitch adjustment feel bigger or smaller than it actually is? Try the calculator and notice.