C2 note frequency calculator
C2 is MIDI note 36, -33 semitones from A4. At the standard A4 = 440 Hz that puts it at 65.406 Hz.
- Period
- 0.015 289 s
- Wavelength in air
- 5.2441
- Quarter wavelength
- 1.3110
- One octave up
- 130.8128 Hz
- One octave down
- 32.7032 Hz
- Equal-tempered fifth above
- 97.9989 Hz
- Just fifth above
- 98.1096 Hz
- How flat the tempered fifth is
- 1.9550 cents
- String length at that tension
- 0.9670
- MIDI note number
- 36
Show the working
- Reference pitch for A4 = 440
- Detune = 0
- Speed of sound = 343
- String tension = 80
- String mass per metre = 0.005
- semitones = -33 = -33
- Frequency = 440 * 2^(-33/12) * 2^(0/1200) = 65.4064
- Period = 65.4064 > 0 ? 1/65.4064 : 0 = 0.015 289
- Wavelength in air = 65.4064 > 0 ? 343 / 65.4064 : 0 = 5.244 14
- Quarter wavelength = 5.244 14 / 4 = 1.311 03
- One octave up = 65.4064 * 2 = 130.813
- One octave down = 65.4064 / 2 = 32.7032
- Equal-tempered fifth above = 65.4064 * 2^(7/12) = 97.9989
- Just fifth above = 65.4064 * 1.5 = 98.1096
- How flat the tempered fifth is = 97.9989 > 0 ? 1200 * log2(98.1096/97.9989) : 0 = 1.955
- String length at that tension = 65.4064 > 0 ? sqrt(80 / 0.005) / (2 * 65.4064) : 0 = 0.966 963
- MIDI note number = 36 = 36
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.
C2 at different concert pitches
| A4 reference | C2 frequency |
|---|---|
| 415 Hz | 61.690 Hz |
| 430 Hz | 63.920 Hz |
| 432 Hz | 64.217 Hz |
| 435 Hz | 64.663 Hz |
| 440 Hz | 65.406 Hz |
| 442 Hz | 65.704 Hz |
| 443 Hz | 65.852 Hz |
| 444 Hz | 66.001 Hz |
Frequently asked
What frequency is C2?
65.406 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.