D4 note frequency calculator
D4 is MIDI note 62, -7 semitones from A4. At the standard A4 = 440 Hz that puts it at 293.665 Hz.
- Period
- 0.003 405 24 s
- Wavelength in air
- 1.1680
- Quarter wavelength
- 0.2920
- One octave up
- 587.3295 Hz
- One octave down
- 146.8324 Hz
- Equal-tempered fifth above
- 440.0000 Hz
- Just fifth above
- 440.4972 Hz
- How flat the tempered fifth is
- 1.9550 cents
- String length at that tension
- 0.2154
- MIDI note number
- 62
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) = 293.665
- Period = 293.665 > 0 ? 1/293.665 : 0 = 0.003 405 24
- Wavelength in air = 293.665 > 0 ? 343 / 293.665 : 0 = 1.168
- Quarter wavelength = 1.168 / 4 = 0.292
- One octave up = 293.665 * 2 = 587.33
- One octave down = 293.665 / 2 = 146.832
- Equal-tempered fifth above = 293.665 * 2^(7/12) = 440
- Just fifth above = 293.665 * 1.5 = 440.497
- How flat the tempered fifth is = 440 > 0 ? 1200 * log2(440.497/440) : 0 = 1.955
- String length at that tension = 293.665 > 0 ? sqrt(80 / 0.005) / (2 * 293.665) : 0 = 0.215 366
- MIDI note number = 62 = 62
Values are shown to six significant figures here; the arithmetic itself runs on exact fractions and is only rounded where a number is printed.
Scenarios & local history
Compare a saved scenario
Recent calculations
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.
D4 at different concert pitches
| A4 reference | D4 frequency |
|---|---|
| 415 Hz | 276.979 Hz |
| 430 Hz | 286.991 Hz |
| 432 Hz | 288.325 Hz |
| 435 Hz | 290.328 Hz |
| 440 Hz | 293.665 Hz |
| 442 Hz | 295.000 Hz |
| 443 Hz | 295.667 Hz |
| 444 Hz | 296.334 Hz |
Frequently asked
What frequency is D4?
293.665 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.