B5 note frequency calculator
B5 is MIDI note 83, 14 semitones from A4. At the standard A4 = 440 Hz that puts it at 987.767 Hz.
- Period
- 0.001 012 38 s
- Wavelength in air
- 0.3472
- Quarter wavelength
- 0.0868
- One octave up
- 1975.5332 Hz
- One octave down
- 493.8833 Hz
- Equal-tempered fifth above
- 1479.9777 Hz
- Just fifth above
- 1481.6499 Hz
- How flat the tempered fifth is
- 1.9550 cents
- String length at that tension
- 0.0640
- MIDI note number
- 83
Show the working
- Reference pitch for A4 = 440
- Detune = 0
- Speed of sound = 343
- String tension = 80
- String mass per metre = 0.005
- semitones = 14 = 14
- Frequency = 440 * 2^(14/12) * 2^(0/1200) = 987.767
- Period = 987.767 > 0 ? 1/987.767 : 0 = 0.001 012 38
- Wavelength in air = 987.767 > 0 ? 343 / 987.767 : 0 = 0.347 248
- Quarter wavelength = 0.347 248 / 4 = 0.086 812
- One octave up = 987.767 * 2 = 1975.53
- One octave down = 987.767 / 2 = 493.883
- Equal-tempered fifth above = 987.767 * 2^(7/12) = 1479.98
- Just fifth above = 987.767 * 1.5 = 1481.65
- How flat the tempered fifth is = 1479.98 > 0 ? 1200 * log2(1481.65/1479.98) : 0 = 1.955
- String length at that tension = 987.767 > 0 ? sqrt(80 / 0.005) / (2 * 987.767) : 0 = 0.064 028 8
- MIDI note number = 83 = 83
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.
B5 at different concert pitches
| A4 reference | B5 frequency |
|---|---|
| 415 Hz | 931.644 Hz |
| 430 Hz | 965.317 Hz |
| 432 Hz | 969.807 Hz |
| 435 Hz | 976.542 Hz |
| 440 Hz | 987.767 Hz |
| 442 Hz | 992.256 Hz |
| 443 Hz | 994.501 Hz |
| 444 Hz | 996.746 Hz |
Frequently asked
What frequency is B5?
987.767 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.