C5 note frequency calculator
C5 is MIDI note 72, 3 semitones from A4. At the standard A4 = 440 Hz that puts it at 523.251 Hz.
- Period
- 0.001 911 13 s
- Wavelength in air
- 0.6555
- Quarter wavelength
- 0.1639
- One octave up
- 1046.5023 Hz
- One octave down
- 261.6256 Hz
- Equal-tempered fifth above
- 783.9909 Hz
- Just fifth above
- 784.8767 Hz
- How flat the tempered fifth is
- 1.9550 cents
- String length at that tension
- 0.1209
- MIDI note number
- 72
Show the working
- Reference pitch for A4 = 440
- Detune = 0
- Speed of sound = 343
- String tension = 80
- String mass per metre = 0.005
- semitones = 3 = 3
- Frequency = 440 * 2^(3/12) * 2^(0/1200) = 523.251
- Period = 523.251 > 0 ? 1/523.251 : 0 = 0.001 911 13
- Wavelength in air = 523.251 > 0 ? 343 / 523.251 : 0 = 0.655 517
- Quarter wavelength = 0.655 517 / 4 = 0.163 879
- One octave up = 523.251 * 2 = 1046.5
- One octave down = 523.251 / 2 = 261.626
- Equal-tempered fifth above = 523.251 * 2^(7/12) = 783.991
- Just fifth above = 523.251 * 1.5 = 784.877
- How flat the tempered fifth is = 783.991 > 0 ? 1200 * log2(784.877/783.991) : 0 = 1.955
- String length at that tension = 523.251 > 0 ? sqrt(80 / 0.005) / (2 * 523.251) : 0 = 0.120 87
- MIDI note number = 72 = 72
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.
C5 at different concert pitches
| A4 reference | C5 frequency |
|---|---|
| 415 Hz | 493.521 Hz |
| 430 Hz | 511.359 Hz |
| 432 Hz | 513.737 Hz |
| 435 Hz | 517.305 Hz |
| 440 Hz | 523.251 Hz |
| 442 Hz | 525.630 Hz |
| 443 Hz | 526.819 Hz |
| 444 Hz | 528.008 Hz |
Frequently asked
What frequency is C5?
523.251 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.