D#4 note frequency calculator
D#4 is MIDI note 63, -6 semitones from A4. At the standard A4 = 440 Hz that puts it at 311.127 Hz.
- Period
- 0.003 214 12 s
- Wavelength in air
- 1.1024
- Quarter wavelength
- 0.2756
- One octave up
- 622.2540 Hz
- One octave down
- 155.5635 Hz
- Equal-tempered fifth above
- 466.1638 Hz
- Just fifth above
- 466.6905 Hz
- How flat the tempered fifth is
- 1.9550 cents
- String length at that tension
- 0.2033
- MIDI note number
- 63
Show the working
- Reference pitch for A4 = 440
- Detune = 0
- Speed of sound = 343
- String tension = 80
- String mass per metre = 0.005
- semitones = -6 = -6
- Frequency = 440 * 2^(-6/12) * 2^(0/1200) = 311.127
- Period = 311.127 > 0 ? 1/311.127 : 0 = 0.003 214 12
- Wavelength in air = 311.127 > 0 ? 343 / 311.127 : 0 = 1.102 44
- Quarter wavelength = 1.102 44 / 4 = 0.275 611
- One octave up = 311.127 * 2 = 622.254
- One octave down = 311.127 / 2 = 155.563
- Equal-tempered fifth above = 311.127 * 2^(7/12) = 466.164
- Just fifth above = 311.127 * 1.5 = 466.69
- How flat the tempered fifth is = 466.164 > 0 ? 1200 * log2(466.69/466.164) : 0 = 1.955
- String length at that tension = 311.127 > 0 ? sqrt(80 / 0.005) / (2 * 311.127) : 0 = 0.203 279
- MIDI note number = 63 = 63
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.
D#4 at different concert pitches
| A4 reference | D#4 frequency |
|---|---|
| 415 Hz | 293.449 Hz |
| 430 Hz | 304.056 Hz |
| 432 Hz | 305.470 Hz |
| 435 Hz | 307.591 Hz |
| 440 Hz | 311.127 Hz |
| 442 Hz | 312.541 Hz |
| 443 Hz | 313.248 Hz |
| 444 Hz | 313.955 Hz |
Frequently asked
What frequency is D#4?
311.127 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.