F#2 note frequency calculator
F#2 is MIDI note 42, -27 semitones from A4. At the standard A4 = 440 Hz that puts it at 92.499 Hz.
- Period
- 0.010 811 s
- Wavelength in air
- 3.7082
- Quarter wavelength
- 0.9270
- One octave up
- 184.9972 Hz
- One octave down
- 46.2493 Hz
- Equal-tempered fifth above
- 138.5913 Hz
- Just fifth above
- 138.7479 Hz
- How flat the tempered fifth is
- 1.9550 cents
- String length at that tension
- 0.6837
- MIDI note number
- 42
Show the working
- Reference pitch for A4 = 440
- Detune = 0
- Speed of sound = 343
- String tension = 80
- String mass per metre = 0.005
- semitones = -27 = -27
- Frequency = 440 * 2^(-27/12) * 2^(0/1200) = 92.4986
- Period = 92.4986 > 0 ? 1/92.4986 : 0 = 0.010 811
- Wavelength in air = 92.4986 > 0 ? 343 / 92.4986 : 0 = 3.708 16
- Quarter wavelength = 3.708 16 / 4 = 0.927 041
- One octave up = 92.4986 * 2 = 184.997
- One octave down = 92.4986 / 2 = 46.2493
- Equal-tempered fifth above = 92.4986 * 2^(7/12) = 138.591
- Just fifth above = 92.4986 * 1.5 = 138.748
- How flat the tempered fifth is = 138.591 > 0 ? 1200 * log2(138.748/138.591) : 0 = 1.955
- String length at that tension = 92.4986 > 0 ? sqrt(80 / 0.005) / (2 * 92.4986) : 0 = 0.683 746
- MIDI note number = 42 = 42
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#2 at different concert pitches
| A4 reference | F#2 frequency |
|---|---|
| 415 Hz | 87.243 Hz |
| 430 Hz | 90.396 Hz |
| 432 Hz | 90.817 Hz |
| 435 Hz | 91.447 Hz |
| 440 Hz | 92.499 Hz |
| 442 Hz | 92.919 Hz |
| 443 Hz | 93.129 Hz |
| 444 Hz | 93.340 Hz |
Frequently asked
What frequency is F#2?
92.499 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.