D#5 note frequency calculator
D#5 is MIDI note 75, 6 semitones from A4. At the standard A4 = 440 Hz that puts it at 622.254 Hz.
- Period
- 0.001 607 06 s
- Wavelength in air
- 0.5512
- Quarter wavelength
- 0.1378
- One octave up
- 1244.5079 Hz
- One octave down
- 311.1270 Hz
- Equal-tempered fifth above
- 932.3275 Hz
- Just fifth above
- 933.3810 Hz
- How flat the tempered fifth is
- 1.9550 cents
- String length at that tension
- 0.1016
- MIDI note number
- 75
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) = 622.254
- Period = 622.254 > 0 ? 1/622.254 : 0 = 0.001 607 06
- Wavelength in air = 622.254 > 0 ? 343 / 622.254 : 0 = 0.551 222
- Quarter wavelength = 0.551 222 / 4 = 0.137 805
- One octave up = 622.254 * 2 = 1244.51
- One octave down = 622.254 / 2 = 311.127
- Equal-tempered fifth above = 622.254 * 2^(7/12) = 932.328
- Just fifth above = 622.254 * 1.5 = 933.381
- How flat the tempered fifth is = 932.328 > 0 ? 1200 * log2(933.381/932.328) : 0 = 1.955
- String length at that tension = 622.254 > 0 ? sqrt(80 / 0.005) / (2 * 622.254) : 0 = 0.101 639
- MIDI note number = 75 = 75
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#5 at different concert pitches
| A4 reference | D#5 frequency |
|---|---|
| 415 Hz | 586.899 Hz |
| 430 Hz | 608.112 Hz |
| 432 Hz | 610.940 Hz |
| 435 Hz | 615.183 Hz |
| 440 Hz | 622.254 Hz |
| 442 Hz | 625.082 Hz |
| 443 Hz | 626.497 Hz |
| 444 Hz | 627.911 Hz |
Frequently asked
What frequency is D#5?
622.254 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.