C#3 note frequency calculator
C#3 is MIDI note 49, -20 semitones from A4. At the standard A4 = 440 Hz that puts it at 138.591 Hz.
- Period
- 0.007 215 46 s
- Wavelength in air
- 2.4749
- Quarter wavelength
- 0.6187
- One octave up
- 277.1826 Hz
- One octave down
- 69.2957 Hz
- Equal-tempered fifth above
- 207.6523 Hz
- Just fifth above
- 207.8870 Hz
- How flat the tempered fifth is
- 1.9550 cents
- String length at that tension
- 0.4563
- MIDI note number
- 49
Show the working
- Reference pitch for A4 = 440
- Detune = 0
- Speed of sound = 343
- String tension = 80
- String mass per metre = 0.005
- semitones = -20 = -20
- Frequency = 440 * 2^(-20/12) * 2^(0/1200) = 138.591
- Period = 138.591 > 0 ? 1/138.591 : 0 = 0.007 215 46
- Wavelength in air = 138.591 > 0 ? 343 / 138.591 : 0 = 2.4749
- Quarter wavelength = 2.4749 / 4 = 0.618 726
- One octave up = 138.591 * 2 = 277.183
- One octave down = 138.591 / 2 = 69.2957
- Equal-tempered fifth above = 138.591 * 2^(7/12) = 207.652
- Just fifth above = 138.591 * 1.5 = 207.887
- How flat the tempered fifth is = 207.652 > 0 ? 1200 * log2(207.887/207.652) : 0 = 1.955
- String length at that tension = 138.591 > 0 ? sqrt(80 / 0.005) / (2 * 138.591) : 0 = 0.456 346
- MIDI note number = 49 = 49
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.
C#3 at different concert pitches
| A4 reference | C#3 frequency |
|---|---|
| 415 Hz | 130.717 Hz |
| 430 Hz | 135.442 Hz |
| 432 Hz | 136.071 Hz |
| 435 Hz | 137.016 Hz |
| 440 Hz | 138.591 Hz |
| 442 Hz | 139.221 Hz |
| 443 Hz | 139.536 Hz |
| 444 Hz | 139.851 Hz |
Frequently asked
What frequency is C#3?
138.591 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.