F#4 note frequency calculator
F#4 is MIDI note 66, -3 semitones from A4. At the standard A4 = 440 Hz that puts it at 369.994 Hz.
- Period
- 0.002 702 74 s
- Wavelength in air
- 0.9270
- Quarter wavelength
- 0.2318
- One octave up
- 739.9888 Hz
- One octave down
- 184.9972 Hz
- Equal-tempered fifth above
- 554.3653 Hz
- Just fifth above
- 554.9916 Hz
- How flat the tempered fifth is
- 1.9550 cents
- String length at that tension
- 0.1709
- MIDI note number
- 66
Show the working
- Reference pitch for A4 = 440
- Detune = 0
- Speed of sound = 343
- String tension = 80
- String mass per metre = 0.005
- semitones = -3 = -3
- Frequency = 440 * 2^(-3/12) * 2^(0/1200) = 369.994
- Period = 369.994 > 0 ? 1/369.994 : 0 = 0.002 702 74
- Wavelength in air = 369.994 > 0 ? 343 / 369.994 : 0 = 0.927 041
- Quarter wavelength = 0.927 041 / 4 = 0.231 76
- One octave up = 369.994 * 2 = 739.989
- One octave down = 369.994 / 2 = 184.997
- Equal-tempered fifth above = 369.994 * 2^(7/12) = 554.365
- Just fifth above = 369.994 * 1.5 = 554.992
- How flat the tempered fifth is = 554.365 > 0 ? 1200 * log2(554.992/554.365) : 0 = 1.955
- String length at that tension = 369.994 > 0 ? sqrt(80 / 0.005) / (2 * 369.994) : 0 = 0.170 937
- MIDI note number = 66 = 66
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#4 at different concert pitches
| A4 reference | F#4 frequency |
|---|---|
| 415 Hz | 348.972 Hz |
| 430 Hz | 361.585 Hz |
| 432 Hz | 363.267 Hz |
| 435 Hz | 365.790 Hz |
| 440 Hz | 369.994 Hz |
| 442 Hz | 371.676 Hz |
| 443 Hz | 372.517 Hz |
| 444 Hz | 373.358 Hz |
Frequently asked
What frequency is F#4?
369.994 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.