B3 note frequency calculator
B3 is MIDI note 59, -10 semitones from A4. At the standard A4 = 440 Hz that puts it at 246.942 Hz.
- Period
- 0.004 049 54 s
- Wavelength in air
- 1.3890
- Quarter wavelength
- 0.3472
- One octave up
- 493.8833 Hz
- One octave down
- 123.4708 Hz
- Equal-tempered fifth above
- 369.9944 Hz
- Just fifth above
- 370.4125 Hz
- How flat the tempered fifth is
- 1.9550 cents
- String length at that tension
- 0.2561
- MIDI note number
- 59
Show the working
- Reference pitch for A4 = 440
- Detune = 0
- Speed of sound = 343
- String tension = 80
- String mass per metre = 0.005
- semitones = -10 = -10
- Frequency = 440 * 2^(-10/12) * 2^(0/1200) = 246.942
- Period = 246.942 > 0 ? 1/246.942 : 0 = 0.004 049 54
- Wavelength in air = 246.942 > 0 ? 343 / 246.942 : 0 = 1.388 99
- Quarter wavelength = 1.388 99 / 4 = 0.347 248
- One octave up = 246.942 * 2 = 493.883
- One octave down = 246.942 / 2 = 123.471
- Equal-tempered fifth above = 246.942 * 2^(7/12) = 369.994
- Just fifth above = 246.942 * 1.5 = 370.412
- How flat the tempered fifth is = 369.994 > 0 ? 1200 * log2(370.412/369.994) : 0 = 1.955
- String length at that tension = 246.942 > 0 ? sqrt(80 / 0.005) / (2 * 246.942) : 0 = 0.256 115
- MIDI note number = 59 = 59
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.
B3 at different concert pitches
| A4 reference | B3 frequency |
|---|---|
| 415 Hz | 232.911 Hz |
| 430 Hz | 241.329 Hz |
| 432 Hz | 242.452 Hz |
| 435 Hz | 244.135 Hz |
| 440 Hz | 246.942 Hz |
| 442 Hz | 248.064 Hz |
| 443 Hz | 248.625 Hz |
| 444 Hz | 249.187 Hz |
Frequently asked
What frequency is B3?
246.942 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.