D#3 note frequency calculator
D#3 is MIDI note 51, -18 semitones from A4. At the standard A4 = 440 Hz that puts it at 155.563 Hz.
- Period
- 0.006 428 24 s
- Wavelength in air
- 2.2049
- Quarter wavelength
- 0.5512
- One octave up
- 311.1270 Hz
- One octave down
- 77.7817 Hz
- Equal-tempered fifth above
- 233.0819 Hz
- Just fifth above
- 233.3452 Hz
- How flat the tempered fifth is
- 1.9550 cents
- String length at that tension
- 0.4066
- MIDI note number
- 51
Show the working
- Reference pitch for A4 = 440
- Detune = 0
- Speed of sound = 343
- String tension = 80
- String mass per metre = 0.005
- semitones = -18 = -18
- Frequency = 440 * 2^(-18/12) * 2^(0/1200) = 155.563
- Period = 155.563 > 0 ? 1/155.563 : 0 = 0.006 428 24
- Wavelength in air = 155.563 > 0 ? 343 / 155.563 : 0 = 2.204 89
- Quarter wavelength = 2.204 89 / 4 = 0.551 222
- One octave up = 155.563 * 2 = 311.127
- One octave down = 155.563 / 2 = 77.7817
- Equal-tempered fifth above = 155.563 * 2^(7/12) = 233.082
- Just fifth above = 155.563 * 1.5 = 233.345
- How flat the tempered fifth is = 233.082 > 0 ? 1200 * log2(233.345/233.082) : 0 = 1.955
- String length at that tension = 155.563 > 0 ? sqrt(80 / 0.005) / (2 * 155.563) : 0 = 0.406 558
- MIDI note number = 51 = 51
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#3 at different concert pitches
| A4 reference | D#3 frequency |
|---|---|
| 415 Hz | 146.725 Hz |
| 430 Hz | 152.028 Hz |
| 432 Hz | 152.735 Hz |
| 435 Hz | 153.796 Hz |
| 440 Hz | 155.563 Hz |
| 442 Hz | 156.271 Hz |
| 443 Hz | 156.624 Hz |
| 444 Hz | 156.978 Hz |
Frequently asked
What frequency is D#3?
155.563 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.