A#2 note frequency calculator
A#2 is MIDI note 46, -23 semitones from A4. At the standard A4 = 440 Hz that puts it at 116.541 Hz.
- Period
- 0.008 580 68 s
- Wavelength in air
- 2.9432
- Quarter wavelength
- 0.7358
- One octave up
- 233.0819 Hz
- One octave down
- 58.2705 Hz
- Equal-tempered fifth above
- 174.6141 Hz
- Just fifth above
- 174.8114 Hz
- How flat the tempered fifth is
- 1.9550 cents
- String length at that tension
- 0.5427
- MIDI note number
- 46
Show the working
- Reference pitch for A4 = 440
- Detune = 0
- Speed of sound = 343
- String tension = 80
- String mass per metre = 0.005
- semitones = -23 = -23
- Frequency = 440 * 2^(-23/12) * 2^(0/1200) = 116.541
- Period = 116.541 > 0 ? 1/116.541 : 0 = 0.008 580 68
- Wavelength in air = 116.541 > 0 ? 343 / 116.541 : 0 = 2.943 17
- Quarter wavelength = 2.943 17 / 4 = 0.735 793
- One octave up = 116.541 * 2 = 233.082
- One octave down = 116.541 / 2 = 58.2705
- Equal-tempered fifth above = 116.541 * 2^(7/12) = 174.614
- Just fifth above = 116.541 * 1.5 = 174.811
- How flat the tempered fifth is = 174.614 > 0 ? 1200 * log2(174.811/174.614) : 0 = 1.955
- String length at that tension = 116.541 > 0 ? sqrt(80 / 0.005) / (2 * 116.541) : 0 = 0.542 69
- MIDI note number = 46 = 46
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.
A#2 at different concert pitches
| A4 reference | A#2 frequency |
|---|---|
| 415 Hz | 109.919 Hz |
| 430 Hz | 113.892 Hz |
| 432 Hz | 114.422 Hz |
| 435 Hz | 115.217 Hz |
| 440 Hz | 116.541 Hz |
| 442 Hz | 117.071 Hz |
| 443 Hz | 117.336 Hz |
| 444 Hz | 117.600 Hz |
Frequently asked
What frequency is A#2?
116.541 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.