F4 note frequency calculator
F4 is MIDI note 65, -4 semitones from A4. At the standard A4 = 440 Hz that puts it at 349.228 Hz.
- Period
- 0.002 863 46 s
- Wavelength in air
- 0.9822
- Quarter wavelength
- 0.2455
- One octave up
- 698.4565 Hz
- One octave down
- 174.6141 Hz
- Equal-tempered fifth above
- 523.2511 Hz
- Just fifth above
- 523.8423 Hz
- How flat the tempered fifth is
- 1.9550 cents
- String length at that tension
- 0.1811
- MIDI note number
- 65
Show the working
- Reference pitch for A4 = 440
- Detune = 0
- Speed of sound = 343
- String tension = 80
- String mass per metre = 0.005
- semitones = -4 = -4
- Frequency = 440 * 2^(-4/12) * 2^(0/1200) = 349.228
- Period = 349.228 > 0 ? 1/349.228 : 0 = 0.002 863 46
- Wavelength in air = 349.228 > 0 ? 343 / 349.228 : 0 = 0.982 166
- Quarter wavelength = 0.982 166 / 4 = 0.245 541
- One octave up = 349.228 * 2 = 698.456
- One octave down = 349.228 / 2 = 174.614
- Equal-tempered fifth above = 349.228 * 2^(7/12) = 523.251
- Just fifth above = 349.228 * 1.5 = 523.842
- How flat the tempered fifth is = 523.251 > 0 ? 1200 * log2(523.842/523.251) : 0 = 1.955
- String length at that tension = 349.228 > 0 ? sqrt(80 / 0.005) / (2 * 349.228) : 0 = 0.181 101
- MIDI note number = 65 = 65
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.
F4 at different concert pitches
| A4 reference | F4 frequency |
|---|---|
| 415 Hz | 329.386 Hz |
| 430 Hz | 341.291 Hz |
| 432 Hz | 342.879 Hz |
| 435 Hz | 345.260 Hz |
| 440 Hz | 349.228 Hz |
| 442 Hz | 350.816 Hz |
| 443 Hz | 351.609 Hz |
| 444 Hz | 352.403 Hz |
Frequently asked
What frequency is F4?
349.228 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.