F5 note frequency calculator
F5 is MIDI note 77, 8 semitones from A4. At the standard A4 = 440 Hz that puts it at 698.456 Hz.
- Period
- 0.001 431 73 s
- Wavelength in air
- 0.4911
- Quarter wavelength
- 0.1228
- One octave up
- 1396.9129 Hz
- One octave down
- 349.2282 Hz
- Equal-tempered fifth above
- 1046.5023 Hz
- Just fifth above
- 1047.6847 Hz
- How flat the tempered fifth is
- 1.9550 cents
- String length at that tension
- 0.0906
- MIDI note number
- 77
Show the working
- Reference pitch for A4 = 440
- Detune = 0
- Speed of sound = 343
- String tension = 80
- String mass per metre = 0.005
- semitones = 8 = 8
- Frequency = 440 * 2^(8/12) * 2^(0/1200) = 698.456
- Period = 698.456 > 0 ? 1/698.456 : 0 = 0.001 431 73
- Wavelength in air = 698.456 > 0 ? 343 / 698.456 : 0 = 0.491 083
- Quarter wavelength = 0.491 083 / 4 = 0.122 771
- One octave up = 698.456 * 2 = 1396.91
- One octave down = 698.456 / 2 = 349.228
- Equal-tempered fifth above = 698.456 * 2^(7/12) = 1046.5
- Just fifth above = 698.456 * 1.5 = 1047.68
- How flat the tempered fifth is = 1046.5 > 0 ? 1200 * log2(1047.68/1046.5) : 0 = 1.955
- String length at that tension = 698.456 > 0 ? sqrt(80 / 0.005) / (2 * 698.456) : 0 = 0.090 550 5
- MIDI note number = 77 = 77
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.
F5 at different concert pitches
| A4 reference | F5 frequency |
|---|---|
| 415 Hz | 658.771 Hz |
| 430 Hz | 682.582 Hz |
| 432 Hz | 685.757 Hz |
| 435 Hz | 690.519 Hz |
| 440 Hz | 698.456 Hz |
| 442 Hz | 701.631 Hz |
| 443 Hz | 703.219 Hz |
| 444 Hz | 704.806 Hz |
Frequently asked
What frequency is F5?
698.456 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.