C3 note frequency calculator
C3 is MIDI note 48, -21 semitones from A4. At the standard A4 = 440 Hz that puts it at 130.813 Hz.
- Period
- 0.007 644 51 s
- Wavelength in air
- 2.6221
- Quarter wavelength
- 0.6555
- One octave up
- 261.6256 Hz
- One octave down
- 65.4064 Hz
- Equal-tempered fifth above
- 195.9977 Hz
- Just fifth above
- 196.2192 Hz
- How flat the tempered fifth is
- 1.9550 cents
- String length at that tension
- 0.4835
- MIDI note number
- 48
Show the working
- Reference pitch for A4 = 440
- Detune = 0
- Speed of sound = 343
- String tension = 80
- String mass per metre = 0.005
- semitones = -21 = -21
- Frequency = 440 * 2^(-21/12) * 2^(0/1200) = 130.813
- Period = 130.813 > 0 ? 1/130.813 : 0 = 0.007 644 51
- Wavelength in air = 130.813 > 0 ? 343 / 130.813 : 0 = 2.622 07
- Quarter wavelength = 2.622 07 / 4 = 0.655 517
- One octave up = 130.813 * 2 = 261.626
- One octave down = 130.813 / 2 = 65.4064
- Equal-tempered fifth above = 130.813 * 2^(7/12) = 195.998
- Just fifth above = 130.813 * 1.5 = 196.219
- How flat the tempered fifth is = 195.998 > 0 ? 1200 * log2(196.219/195.998) : 0 = 1.955
- String length at that tension = 130.813 > 0 ? sqrt(80 / 0.005) / (2 * 130.813) : 0 = 0.483 481
- MIDI note number = 48 = 48
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.
C3 at different concert pitches
| A4 reference | C3 frequency |
|---|---|
| 415 Hz | 123.380 Hz |
| 430 Hz | 127.840 Hz |
| 432 Hz | 128.434 Hz |
| 435 Hz | 129.326 Hz |
| 440 Hz | 130.813 Hz |
| 442 Hz | 131.407 Hz |
| 443 Hz | 131.705 Hz |
| 444 Hz | 132.002 Hz |
Frequently asked
What frequency is C3?
130.813 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.