D5 note frequency calculator
D5 is MIDI note 74, 5 semitones from A4. At the standard A4 = 440 Hz that puts it at 587.330 Hz.
- Period
- 0.001 702 62 s
- Wavelength in air
- 0.5840
- Quarter wavelength
- 0.1460
- One octave up
- 1174.6591 Hz
- One octave down
- 293.6648 Hz
- Equal-tempered fifth above
- 880.0000 Hz
- Just fifth above
- 880.9943 Hz
- How flat the tempered fifth is
- 1.9550 cents
- String length at that tension
- 0.1077
- MIDI note number
- 74
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) = 587.33
- Period = 587.33 > 0 ? 1/587.33 : 0 = 0.001 702 62
- Wavelength in air = 587.33 > 0 ? 343 / 587.33 : 0 = 0.583 999
- Quarter wavelength = 0.583 999 / 4 = 0.146
- One octave up = 587.33 * 2 = 1174.66
- One octave down = 587.33 / 2 = 293.665
- Equal-tempered fifth above = 587.33 * 2^(7/12) = 880
- Just fifth above = 587.33 * 1.5 = 880.994
- How flat the tempered fifth is = 880 > 0 ? 1200 * log2(880.994/880) : 0 = 1.955
- String length at that tension = 587.33 > 0 ? sqrt(80 / 0.005) / (2 * 587.33) : 0 = 0.107 683
- MIDI note number = 74 = 74
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.
D5 at different concert pitches
| A4 reference | D5 frequency |
|---|---|
| 415 Hz | 553.959 Hz |
| 430 Hz | 573.981 Hz |
| 432 Hz | 576.651 Hz |
| 435 Hz | 580.655 Hz |
| 440 Hz | 587.330 Hz |
| 442 Hz | 589.999 Hz |
| 443 Hz | 591.334 Hz |
| 444 Hz | 592.669 Hz |
Frequently asked
What frequency is D5?
587.330 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.