C#2 note frequency calculator
C#2 is MIDI note 37, -32 semitones from A4. At the standard A4 = 440 Hz that puts it at 69.296 Hz.
- Period
- 0.014 430 9 s
- Wavelength in air
- 4.9498
- Quarter wavelength
- 1.2375
- One octave up
- 138.5913 Hz
- One octave down
- 34.6478 Hz
- Equal-tempered fifth above
- 103.8262 Hz
- Just fifth above
- 103.9435 Hz
- How flat the tempered fifth is
- 1.9550 cents
- String length at that tension
- 0.9127
- MIDI note number
- 37
Show the working
- Reference pitch for A4 = 440
- Detune = 0
- Speed of sound = 343
- String tension = 80
- String mass per metre = 0.005
- semitones = -32 = -32
- Frequency = 440 * 2^(-32/12) * 2^(0/1200) = 69.2957
- Period = 69.2957 > 0 ? 1/69.2957 : 0 = 0.014 430 9
- Wavelength in air = 69.2957 > 0 ? 343 / 69.2957 : 0 = 4.949 81
- Quarter wavelength = 4.949 81 / 4 = 1.237 45
- One octave up = 69.2957 * 2 = 138.591
- One octave down = 69.2957 / 2 = 34.6478
- Equal-tempered fifth above = 69.2957 * 2^(7/12) = 103.826
- Just fifth above = 69.2957 * 1.5 = 103.943
- How flat the tempered fifth is = 103.826 > 0 ? 1200 * log2(103.943/103.826) : 0 = 1.955
- String length at that tension = 69.2957 > 0 ? sqrt(80 / 0.005) / (2 * 69.2957) : 0 = 0.912 691
- MIDI note number = 37 = 37
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.
C#2 at different concert pitches
| A4 reference | C#2 frequency |
|---|---|
| 415 Hz | 65.358 Hz |
| 430 Hz | 67.721 Hz |
| 432 Hz | 68.036 Hz |
| 435 Hz | 68.508 Hz |
| 440 Hz | 69.296 Hz |
| 442 Hz | 69.611 Hz |
| 443 Hz | 69.768 Hz |
| 444 Hz | 69.926 Hz |
Frequently asked
What frequency is C#2?
69.296 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.