E5 note frequency calculator
E5 is MIDI note 76, 7 semitones from A4. At the standard A4 = 440 Hz that puts it at 659.255 Hz.
- Period
- 0.001 516 86 s
- Wavelength in air
- 0.5203
- Quarter wavelength
- 0.1301
- One octave up
- 1318.5102 Hz
- One octave down
- 329.6276 Hz
- Equal-tempered fifth above
- 987.7666 Hz
- Just fifth above
- 988.8827 Hz
- How flat the tempered fifth is
- 1.9550 cents
- String length at that tension
- 0.0959
- MIDI note number
- 76
Show the working
- Reference pitch for A4 = 440
- Detune = 0
- Speed of sound = 343
- String tension = 80
- String mass per metre = 0.005
- semitones = 7 = 7
- Frequency = 440 * 2^(7/12) * 2^(0/1200) = 659.255
- Period = 659.255 > 0 ? 1/659.255 : 0 = 0.001 516 86
- Wavelength in air = 659.255 > 0 ? 343 / 659.255 : 0 = 0.520 284
- Quarter wavelength = 0.520 284 / 4 = 0.130 071
- One octave up = 659.255 * 2 = 1318.51
- One octave down = 659.255 / 2 = 329.628
- Equal-tempered fifth above = 659.255 * 2^(7/12) = 987.767
- Just fifth above = 659.255 * 1.5 = 988.883
- How flat the tempered fifth is = 987.767 > 0 ? 1200 * log2(988.883/987.767) : 0 = 1.955
- String length at that tension = 659.255 > 0 ? sqrt(80 / 0.005) / (2 * 659.255) : 0 = 0.095 934 9
- MIDI note number = 76 = 76
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.
E5 at different concert pitches
| A4 reference | E5 frequency |
|---|---|
| 415 Hz | 621.797 Hz |
| 430 Hz | 644.272 Hz |
| 432 Hz | 647.269 Hz |
| 435 Hz | 651.764 Hz |
| 440 Hz | 659.255 Hz |
| 442 Hz | 662.252 Hz |
| 443 Hz | 663.750 Hz |
| 444 Hz | 665.248 Hz |
Frequently asked
What frequency is E5?
659.255 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.