C4 note frequency calculator
C4 is MIDI note 60, -9 semitones from A4. At the standard A4 = 440 Hz that puts it at 261.626 Hz.
- Period
- 0.003 822 26 s
- Wavelength in air
- 1.3110
- Quarter wavelength
- 0.3278
- One octave up
- 523.2511 Hz
- One octave down
- 130.8128 Hz
- Equal-tempered fifth above
- 391.9954 Hz
- Just fifth above
- 392.4383 Hz
- How flat the tempered fifth is
- 1.9550 cents
- String length at that tension
- 0.2417
- MIDI note number
- 60
Show the working
- Reference pitch for A4 = 440
- Detune = 0
- Speed of sound = 343
- String tension = 80
- String mass per metre = 0.005
- semitones = -9 = -9
- Frequency = 440 * 2^(-9/12) * 2^(0/1200) = 261.626
- Period = 261.626 > 0 ? 1/261.626 : 0 = 0.003 822 26
- Wavelength in air = 261.626 > 0 ? 343 / 261.626 : 0 = 1.311 03
- Quarter wavelength = 1.311 03 / 4 = 0.327 758
- One octave up = 261.626 * 2 = 523.251
- One octave down = 261.626 / 2 = 130.813
- Equal-tempered fifth above = 261.626 * 2^(7/12) = 391.995
- Just fifth above = 261.626 * 1.5 = 392.438
- How flat the tempered fifth is = 391.995 > 0 ? 1200 * log2(392.438/391.995) : 0 = 1.955
- String length at that tension = 261.626 > 0 ? sqrt(80 / 0.005) / (2 * 261.626) : 0 = 0.241 741
- MIDI note number = 60 = 60
Values are shown to six significant figures here; the arithmetic itself runs on exact fractions and is only rounded where a number is printed.
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The formula
- f = 440 x 2^((n - 69)/12), with n the MIDI note number
- one cent is 2^(1/1200), so a detune of c cents multiplies by 2^(c/1200)
- string frequency = sqrt(tension / linear density) / (2 x length)
Equal temperament divides the octave into twelve equal ratios of 2^(1/12), which is irrational. Every interval except the octave is therefore slightly out of tune against the simple whole-number ratios the ear prefers.
The tempered fifth is about 1.955 cents flat of a just fifth, which is close enough that almost nobody notices.
Concert pitch is not universal: many orchestras tune to 442 or 443 Hz, and baroque performance often uses 415.
C4 at different concert pitches
| A4 reference | C4 frequency |
|---|---|
| 415 Hz | 246.760 Hz |
| 430 Hz | 255.680 Hz |
| 432 Hz | 256.869 Hz |
| 435 Hz | 258.653 Hz |
| 440 Hz | 261.626 Hz |
| 442 Hz | 262.815 Hz |
| 443 Hz | 263.409 Hz |
| 444 Hz | 264.004 Hz |
Frequently asked
What frequency is C4?
261.626 Hz in equal temperament with A4 at 440 Hz.
How is the frequency of a note calculated?
Multiply the reference pitch by two raised to the number of semitones divided by twelve.