E4 note frequency calculator
E4 is MIDI note 64, -5 semitones from A4. At the standard A4 = 440 Hz that puts it at 329.628 Hz.
- Period
- 0.003 033 73 s
- Wavelength in air
- 1.0406
- Quarter wavelength
- 0.2601
- One octave up
- 659.2551 Hz
- One octave down
- 164.8138 Hz
- Equal-tempered fifth above
- 493.8833 Hz
- Just fifth above
- 494.4413 Hz
- How flat the tempered fifth is
- 1.9550 cents
- String length at that tension
- 0.1919
- MIDI note number
- 64
Show the working
- Reference pitch for A4 = 440
- Detune = 0
- Speed of sound = 343
- String tension = 80
- String mass per metre = 0.005
- semitones = -5 = -5
- Frequency = 440 * 2^(-5/12) * 2^(0/1200) = 329.628
- Period = 329.628 > 0 ? 1/329.628 : 0 = 0.003 033 73
- Wavelength in air = 329.628 > 0 ? 343 / 329.628 : 0 = 1.040 57
- Quarter wavelength = 1.040 57 / 4 = 0.260 142
- One octave up = 329.628 * 2 = 659.255
- One octave down = 329.628 / 2 = 164.814
- Equal-tempered fifth above = 329.628 * 2^(7/12) = 493.883
- Just fifth above = 329.628 * 1.5 = 494.441
- How flat the tempered fifth is = 493.883 > 0 ? 1200 * log2(494.441/493.883) : 0 = 1.955
- String length at that tension = 329.628 > 0 ? sqrt(80 / 0.005) / (2 * 329.628) : 0 = 0.191 87
- MIDI note number = 64 = 64
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.
E4 at different concert pitches
| A4 reference | E4 frequency |
|---|---|
| 415 Hz | 310.899 Hz |
| 430 Hz | 322.136 Hz |
| 432 Hz | 323.634 Hz |
| 435 Hz | 325.882 Hz |
| 440 Hz | 329.628 Hz |
| 442 Hz | 331.126 Hz |
| 443 Hz | 331.875 Hz |
| 444 Hz | 332.624 Hz |
Frequently asked
What frequency is E4?
329.628 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.