A#3 note frequency calculator
A#3 is MIDI note 58, -11 semitones from A4. At the standard A4 = 440 Hz that puts it at 233.082 Hz.
- Period
- 0.004 290 34 s
- Wavelength in air
- 1.4716
- Quarter wavelength
- 0.3679
- One octave up
- 466.1638 Hz
- One octave down
- 116.5409 Hz
- Equal-tempered fifth above
- 349.2282 Hz
- Just fifth above
- 349.6228 Hz
- How flat the tempered fifth is
- 1.9550 cents
- String length at that tension
- 0.2713
- MIDI note number
- 58
Show the working
- Reference pitch for A4 = 440
- Detune = 0
- Speed of sound = 343
- String tension = 80
- String mass per metre = 0.005
- semitones = -11 = -11
- Frequency = 440 * 2^(-11/12) * 2^(0/1200) = 233.082
- Period = 233.082 > 0 ? 1/233.082 : 0 = 0.004 290 34
- Wavelength in air = 233.082 > 0 ? 343 / 233.082 : 0 = 1.471 59
- Quarter wavelength = 1.471 59 / 4 = 0.367 896
- One octave up = 233.082 * 2 = 466.164
- One octave down = 233.082 / 2 = 116.541
- Equal-tempered fifth above = 233.082 * 2^(7/12) = 349.228
- Just fifth above = 233.082 * 1.5 = 349.623
- How flat the tempered fifth is = 349.228 > 0 ? 1200 * log2(349.623/349.228) : 0 = 1.955
- String length at that tension = 233.082 > 0 ? sqrt(80 / 0.005) / (2 * 233.082) : 0 = 0.271 345
- MIDI note number = 58 = 58
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#3 at different concert pitches
| A4 reference | A#3 frequency |
|---|---|
| 415 Hz | 219.839 Hz |
| 430 Hz | 227.785 Hz |
| 432 Hz | 228.844 Hz |
| 435 Hz | 230.433 Hz |
| 440 Hz | 233.082 Hz |
| 442 Hz | 234.141 Hz |
| 443 Hz | 234.671 Hz |
| 444 Hz | 235.201 Hz |
Frequently asked
What frequency is A#3?
233.082 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.