A5 note frequency calculator
A5 is MIDI note 81, 12 semitones from A4. At the standard A4 = 440 Hz that puts it at 880.000 Hz.
- Period
- 0.001 136 36 s
- Wavelength in air
- 0.3898
- Quarter wavelength
- 0.0974
- One octave up
- 1760.0000 Hz
- One octave down
- 440.0000 Hz
- Equal-tempered fifth above
- 1318.5102 Hz
- Just fifth above
- 1320.0000 Hz
- How flat the tempered fifth is
- 1.9550 cents
- String length at that tension
- 0.0719
- MIDI note number
- 81
Show the working
- Reference pitch for A4 = 440
- Detune = 0
- Speed of sound = 343
- String tension = 80
- String mass per metre = 0.005
- semitones = 12 = 12
- Frequency = 440 * 2^(12/12) * 2^(0/1200) = 880
- Period = 880 > 0 ? 1/880 : 0 = 0.001 136 36
- Wavelength in air = 880 > 0 ? 343 / 880 : 0 = 0.389 773
- Quarter wavelength = 0.389 773 / 4 = 0.097 443 2
- One octave up = 880 * 2 = 1760
- One octave down = 880 / 2 = 440
- Equal-tempered fifth above = 880 * 2^(7/12) = 1318.51
- Just fifth above = 880 * 1.5 = 1320
- How flat the tempered fifth is = 1318.51 > 0 ? 1200 * log2(1320/1318.51) : 0 = 1.955
- String length at that tension = 880 > 0 ? sqrt(80 / 0.005) / (2 * 880) : 0 = 0.071 869 9
- MIDI note number = 81 = 81
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.
A5 at different concert pitches
| A4 reference | A5 frequency |
|---|---|
| 415 Hz | 830.000 Hz |
| 430 Hz | 860.000 Hz |
| 432 Hz | 864.000 Hz |
| 435 Hz | 870.000 Hz |
| 440 Hz | 880.000 Hz |
| 442 Hz | 884.000 Hz |
| 443 Hz | 886.000 Hz |
| 444 Hz | 888.000 Hz |
Frequently asked
What frequency is A5?
880.000 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.