D#2 note frequency calculator
D#2 is MIDI note 39, -30 semitones from A4. At the standard A4 = 440 Hz that puts it at 77.782 Hz.
- Period
- 0.012 856 5 s
- Wavelength in air
- 4.4098
- Quarter wavelength
- 1.1024
- One octave up
- 155.5635 Hz
- One octave down
- 38.8909 Hz
- Equal-tempered fifth above
- 116.5409 Hz
- Just fifth above
- 116.6726 Hz
- How flat the tempered fifth is
- 1.9550 cents
- String length at that tension
- 0.8131
- MIDI note number
- 39
Show the working
- Reference pitch for A4 = 440
- Detune = 0
- Speed of sound = 343
- String tension = 80
- String mass per metre = 0.005
- semitones = -30 = -30
- Frequency = 440 * 2^(-30/12) * 2^(0/1200) = 77.7817
- Period = 77.7817 > 0 ? 1/77.7817 : 0 = 0.012 856 5
- Wavelength in air = 77.7817 > 0 ? 343 / 77.7817 : 0 = 4.409 78
- Quarter wavelength = 4.409 78 / 4 = 1.102 44
- One octave up = 77.7817 * 2 = 155.563
- One octave down = 77.7817 / 2 = 38.8909
- Equal-tempered fifth above = 77.7817 * 2^(7/12) = 116.541
- Just fifth above = 77.7817 * 1.5 = 116.673
- How flat the tempered fifth is = 116.541 > 0 ? 1200 * log2(116.673/116.541) : 0 = 1.955
- String length at that tension = 77.7817 > 0 ? sqrt(80 / 0.005) / (2 * 77.7817) : 0 = 0.813 116
- MIDI note number = 39 = 39
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#2 at different concert pitches
| A4 reference | D#2 frequency |
|---|---|
| 415 Hz | 73.362 Hz |
| 430 Hz | 76.014 Hz |
| 432 Hz | 76.368 Hz |
| 435 Hz | 76.898 Hz |
| 440 Hz | 77.782 Hz |
| 442 Hz | 78.135 Hz |
| 443 Hz | 78.312 Hz |
| 444 Hz | 78.489 Hz |
Frequently asked
What frequency is D#2?
77.782 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.