C#5 note frequency calculator
C#5 is MIDI note 73, 4 semitones from A4. At the standard A4 = 440 Hz that puts it at 554.365 Hz.
- Period
- 0.001 803 86 s
- Wavelength in air
- 0.6187
- Quarter wavelength
- 0.1547
- One octave up
- 1108.7305 Hz
- One octave down
- 277.1826 Hz
- Equal-tempered fifth above
- 830.6094 Hz
- Just fifth above
- 831.5479 Hz
- How flat the tempered fifth is
- 1.9550 cents
- String length at that tension
- 0.1141
- MIDI note number
- 73
Show the working
- Reference pitch for A4 = 440
- Detune = 0
- Speed of sound = 343
- String tension = 80
- String mass per metre = 0.005
- semitones = 4 = 4
- Frequency = 440 * 2^(4/12) * 2^(0/1200) = 554.365
- Period = 554.365 > 0 ? 1/554.365 : 0 = 0.001 803 86
- Wavelength in air = 554.365 > 0 ? 343 / 554.365 : 0 = 0.618 726
- Quarter wavelength = 0.618 726 / 4 = 0.154 681
- One octave up = 554.365 * 2 = 1108.73
- One octave down = 554.365 / 2 = 277.183
- Equal-tempered fifth above = 554.365 * 2^(7/12) = 830.609
- Just fifth above = 554.365 * 1.5 = 831.548
- How flat the tempered fifth is = 830.609 > 0 ? 1200 * log2(831.548/830.609) : 0 = 1.955
- String length at that tension = 554.365 > 0 ? sqrt(80 / 0.005) / (2 * 554.365) : 0 = 0.114 086
- MIDI note number = 73 = 73
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#5 at different concert pitches
| A4 reference | C#5 frequency |
|---|---|
| 415 Hz | 522.867 Hz |
| 430 Hz | 541.766 Hz |
| 432 Hz | 544.286 Hz |
| 435 Hz | 548.066 Hz |
| 440 Hz | 554.365 Hz |
| 442 Hz | 556.885 Hz |
| 443 Hz | 558.145 Hz |
| 444 Hz | 559.405 Hz |
Frequently asked
What frequency is C#5?
554.365 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.