B2 note frequency calculator
B2 is MIDI note 47, -22 semitones from A4. At the standard A4 = 440 Hz that puts it at 123.471 Hz.
- Period
- 0.008 099 08 s
- Wavelength in air
- 2.7780
- Quarter wavelength
- 0.6945
- One octave up
- 246.9417 Hz
- One octave down
- 61.7354 Hz
- Equal-tempered fifth above
- 184.9972 Hz
- Just fifth above
- 185.2062 Hz
- How flat the tempered fifth is
- 1.9550 cents
- String length at that tension
- 0.5122
- MIDI note number
- 47
Show the working
- Reference pitch for A4 = 440
- Detune = 0
- Speed of sound = 343
- String tension = 80
- String mass per metre = 0.005
- semitones = -22 = -22
- Frequency = 440 * 2^(-22/12) * 2^(0/1200) = 123.471
- Period = 123.471 > 0 ? 1/123.471 : 0 = 0.008 099 08
- Wavelength in air = 123.471 > 0 ? 343 / 123.471 : 0 = 2.777 98
- Quarter wavelength = 2.777 98 / 4 = 0.694 496
- One octave up = 123.471 * 2 = 246.942
- One octave down = 123.471 / 2 = 61.7354
- Equal-tempered fifth above = 123.471 * 2^(7/12) = 184.997
- Just fifth above = 123.471 * 1.5 = 185.206
- How flat the tempered fifth is = 184.997 > 0 ? 1200 * log2(185.206/184.997) : 0 = 1.955
- String length at that tension = 123.471 > 0 ? sqrt(80 / 0.005) / (2 * 123.471) : 0 = 0.512 231
- MIDI note number = 47 = 47
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.
B2 at different concert pitches
| A4 reference | B2 frequency |
|---|---|
| 415 Hz | 116.455 Hz |
| 430 Hz | 120.665 Hz |
| 432 Hz | 121.226 Hz |
| 435 Hz | 122.068 Hz |
| 440 Hz | 123.471 Hz |
| 442 Hz | 124.032 Hz |
| 443 Hz | 124.313 Hz |
| 444 Hz | 124.593 Hz |
Frequently asked
What frequency is B2?
123.471 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.