F3 note frequency calculator
F3 is MIDI note 53, -16 semitones from A4. At the standard A4 = 440 Hz that puts it at 174.614 Hz.
- Period
- 0.005 726 91 s
- Wavelength in air
- 1.9643
- Quarter wavelength
- 0.4911
- One octave up
- 349.2282 Hz
- One octave down
- 87.3071 Hz
- Equal-tempered fifth above
- 261.6256 Hz
- Just fifth above
- 261.9212 Hz
- How flat the tempered fifth is
- 1.9550 cents
- String length at that tension
- 0.3622
- MIDI note number
- 53
Show the working
- Reference pitch for A4 = 440
- Detune = 0
- Speed of sound = 343
- String tension = 80
- String mass per metre = 0.005
- semitones = -16 = -16
- Frequency = 440 * 2^(-16/12) * 2^(0/1200) = 174.614
- Period = 174.614 > 0 ? 1/174.614 : 0 = 0.005 726 91
- Wavelength in air = 174.614 > 0 ? 343 / 174.614 : 0 = 1.964 33
- Quarter wavelength = 1.964 33 / 4 = 0.491 083
- One octave up = 174.614 * 2 = 349.228
- One octave down = 174.614 / 2 = 87.3071
- Equal-tempered fifth above = 174.614 * 2^(7/12) = 261.626
- Just fifth above = 174.614 * 1.5 = 261.921
- How flat the tempered fifth is = 261.626 > 0 ? 1200 * log2(261.921/261.626) : 0 = 1.955
- String length at that tension = 174.614 > 0 ? sqrt(80 / 0.005) / (2 * 174.614) : 0 = 0.362 202
- MIDI note number = 53 = 53
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.
F3 at different concert pitches
| A4 reference | F3 frequency |
|---|---|
| 415 Hz | 164.693 Hz |
| 430 Hz | 170.646 Hz |
| 432 Hz | 171.439 Hz |
| 435 Hz | 172.630 Hz |
| 440 Hz | 174.614 Hz |
| 442 Hz | 175.408 Hz |
| 443 Hz | 175.805 Hz |
| 444 Hz | 176.202 Hz |
Frequently asked
What frequency is F3?
174.614 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.