F#3 note frequency calculator
F#3 is MIDI note 54, -15 semitones from A4. At the standard A4 = 440 Hz that puts it at 184.997 Hz.
- Period
- 0.005 405 49 s
- Wavelength in air
- 1.8541
- Quarter wavelength
- 0.4635
- One octave up
- 369.9944 Hz
- One octave down
- 92.4986 Hz
- Equal-tempered fifth above
- 277.1826 Hz
- Just fifth above
- 277.4958 Hz
- How flat the tempered fifth is
- 1.9550 cents
- String length at that tension
- 0.3419
- MIDI note number
- 54
Show the working
- Reference pitch for A4 = 440
- Detune = 0
- Speed of sound = 343
- String tension = 80
- String mass per metre = 0.005
- semitones = -15 = -15
- Frequency = 440 * 2^(-15/12) * 2^(0/1200) = 184.997
- Period = 184.997 > 0 ? 1/184.997 : 0 = 0.005 405 49
- Wavelength in air = 184.997 > 0 ? 343 / 184.997 : 0 = 1.854 08
- Quarter wavelength = 1.854 08 / 4 = 0.463 521
- One octave up = 184.997 * 2 = 369.994
- One octave down = 184.997 / 2 = 92.4986
- Equal-tempered fifth above = 184.997 * 2^(7/12) = 277.183
- Just fifth above = 184.997 * 1.5 = 277.496
- How flat the tempered fifth is = 277.183 > 0 ? 1200 * log2(277.496/277.183) : 0 = 1.955
- String length at that tension = 184.997 > 0 ? sqrt(80 / 0.005) / (2 * 184.997) : 0 = 0.341 873
- MIDI note number = 54 = 54
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.
F#3 at different concert pitches
| A4 reference | F#3 frequency |
|---|---|
| 415 Hz | 174.486 Hz |
| 430 Hz | 180.793 Hz |
| 432 Hz | 181.634 Hz |
| 435 Hz | 182.895 Hz |
| 440 Hz | 184.997 Hz |
| 442 Hz | 185.838 Hz |
| 443 Hz | 186.259 Hz |
| 444 Hz | 186.679 Hz |
Frequently asked
What frequency is F#3?
184.997 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.