F#5 note frequency calculator
F#5 is MIDI note 78, 9 semitones from A4. At the standard A4 = 440 Hz that puts it at 739.989 Hz.
- Period
- 0.001 351 37 s
- Wavelength in air
- 0.4635
- Quarter wavelength
- 0.1159
- One octave up
- 1479.9777 Hz
- One octave down
- 369.9944 Hz
- Equal-tempered fifth above
- 1108.7305 Hz
- Just fifth above
- 1109.9833 Hz
- How flat the tempered fifth is
- 1.9550 cents
- String length at that tension
- 0.0855
- MIDI note number
- 78
Show the working
- Reference pitch for A4 = 440
- Detune = 0
- Speed of sound = 343
- String tension = 80
- String mass per metre = 0.005
- semitones = 9 = 9
- Frequency = 440 * 2^(9/12) * 2^(0/1200) = 739.989
- Period = 739.989 > 0 ? 1/739.989 : 0 = 0.001 351 37
- Wavelength in air = 739.989 > 0 ? 343 / 739.989 : 0 = 0.463 521
- Quarter wavelength = 0.463 521 / 4 = 0.115 88
- One octave up = 739.989 * 2 = 1479.98
- One octave down = 739.989 / 2 = 369.994
- Equal-tempered fifth above = 739.989 * 2^(7/12) = 1108.73
- Just fifth above = 739.989 * 1.5 = 1109.98
- How flat the tempered fifth is = 1108.73 > 0 ? 1200 * log2(1109.98/1108.73) : 0 = 1.955
- String length at that tension = 739.989 > 0 ? sqrt(80 / 0.005) / (2 * 739.989) : 0 = 0.085 468 3
- MIDI note number = 78 = 78
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#5 at different concert pitches
| A4 reference | F#5 frequency |
|---|---|
| 415 Hz | 697.944 Hz |
| 430 Hz | 723.171 Hz |
| 432 Hz | 726.535 Hz |
| 435 Hz | 731.580 Hz |
| 440 Hz | 739.989 Hz |
| 442 Hz | 743.352 Hz |
| 443 Hz | 745.034 Hz |
| 444 Hz | 746.716 Hz |
Frequently asked
What frequency is F#5?
739.989 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.