C#4 note frequency calculator
C#4 is MIDI note 61, -8 semitones from A4. At the standard A4 = 440 Hz that puts it at 277.183 Hz.
- Period
- 0.003 607 73 s
- Wavelength in air
- 1.2375
- Quarter wavelength
- 0.3094
- One octave up
- 554.3653 Hz
- One octave down
- 138.5913 Hz
- Equal-tempered fifth above
- 415.3047 Hz
- Just fifth above
- 415.7739 Hz
- How flat the tempered fifth is
- 1.9550 cents
- String length at that tension
- 0.2282
- MIDI note number
- 61
Show the working
- Reference pitch for A4 = 440
- Detune = 0
- Speed of sound = 343
- String tension = 80
- String mass per metre = 0.005
- semitones = -8 = -8
- Frequency = 440 * 2^(-8/12) * 2^(0/1200) = 277.183
- Period = 277.183 > 0 ? 1/277.183 : 0 = 0.003 607 73
- Wavelength in air = 277.183 > 0 ? 343 / 277.183 : 0 = 1.237 45
- Quarter wavelength = 1.237 45 / 4 = 0.309 363
- One octave up = 277.183 * 2 = 554.365
- One octave down = 277.183 / 2 = 138.591
- Equal-tempered fifth above = 277.183 * 2^(7/12) = 415.305
- Just fifth above = 277.183 * 1.5 = 415.774
- How flat the tempered fifth is = 415.305 > 0 ? 1200 * log2(415.774/415.305) : 0 = 1.955
- String length at that tension = 277.183 > 0 ? sqrt(80 / 0.005) / (2 * 277.183) : 0 = 0.228 173
- MIDI note number = 61 = 61
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#4 at different concert pitches
| A4 reference | C#4 frequency |
|---|---|
| 415 Hz | 261.434 Hz |
| 430 Hz | 270.883 Hz |
| 432 Hz | 272.143 Hz |
| 435 Hz | 274.033 Hz |
| 440 Hz | 277.183 Hz |
| 442 Hz | 278.443 Hz |
| 443 Hz | 279.073 Hz |
| 444 Hz | 279.702 Hz |
Frequently asked
What frequency is C#4?
277.183 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.