D2 note frequency calculator
D2 is MIDI note 38, -31 semitones from A4. At the standard A4 = 440 Hz that puts it at 73.416 Hz.
- Period
- 0.013 621 s
- Wavelength in air
- 4.6720
- Quarter wavelength
- 1.1680
- One octave up
- 146.8324 Hz
- One octave down
- 36.7081 Hz
- Equal-tempered fifth above
- 110.0000 Hz
- Just fifth above
- 110.1243 Hz
- How flat the tempered fifth is
- 1.9550 cents
- String length at that tension
- 0.8615
- MIDI note number
- 38
Show the working
- Reference pitch for A4 = 440
- Detune = 0
- Speed of sound = 343
- String tension = 80
- String mass per metre = 0.005
- semitones = -31 = -31
- Frequency = 440 * 2^(-31/12) * 2^(0/1200) = 73.4162
- Period = 73.4162 > 0 ? 1/73.4162 : 0 = 0.013 621
- Wavelength in air = 73.4162 > 0 ? 343 / 73.4162 : 0 = 4.671 99
- Quarter wavelength = 4.671 99 / 4 = 1.168
- One octave up = 73.4162 * 2 = 146.832
- One octave down = 73.4162 / 2 = 36.7081
- Equal-tempered fifth above = 73.4162 * 2^(7/12) = 110
- Just fifth above = 73.4162 * 1.5 = 110.124
- How flat the tempered fifth is = 110 > 0 ? 1200 * log2(110.124/110) : 0 = 1.955
- String length at that tension = 73.4162 > 0 ? sqrt(80 / 0.005) / (2 * 73.4162) : 0 = 0.861 466
- MIDI note number = 38 = 38
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.
D2 at different concert pitches
| A4 reference | D2 frequency |
|---|---|
| 415 Hz | 69.245 Hz |
| 430 Hz | 71.748 Hz |
| 432 Hz | 72.081 Hz |
| 435 Hz | 72.582 Hz |
| 440 Hz | 73.416 Hz |
| 442 Hz | 73.750 Hz |
| 443 Hz | 73.917 Hz |
| 444 Hz | 74.084 Hz |
Frequently asked
What frequency is D2?
73.416 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.