G4 note frequency calculator
G4 is MIDI note 67, -2 semitones from A4. At the standard A4 = 440 Hz that puts it at 391.995 Hz.
- Period
- 0.002 551 05 s
- Wavelength in air
- 0.8750
- Quarter wavelength
- 0.2188
- One octave up
- 783.9909 Hz
- One octave down
- 195.9977 Hz
- Equal-tempered fifth above
- 587.3295 Hz
- Just fifth above
- 587.9932 Hz
- How flat the tempered fifth is
- 1.9550 cents
- String length at that tension
- 0.1613
- MIDI note number
- 67
Show the working
- Reference pitch for A4 = 440
- Detune = 0
- Speed of sound = 343
- String tension = 80
- String mass per metre = 0.005
- semitones = -2 = -2
- Frequency = 440 * 2^(-2/12) * 2^(0/1200) = 391.995
- Period = 391.995 > 0 ? 1/391.995 : 0 = 0.002 551 05
- Wavelength in air = 391.995 > 0 ? 343 / 391.995 : 0 = 0.875 01
- Quarter wavelength = 0.875 01 / 4 = 0.218 753
- One octave up = 391.995 * 2 = 783.991
- One octave down = 391.995 / 2 = 195.998
- Equal-tempered fifth above = 391.995 * 2^(7/12) = 587.33
- Just fifth above = 391.995 * 1.5 = 587.993
- How flat the tempered fifth is = 587.33 > 0 ? 1200 * log2(587.993/587.33) : 0 = 1.955
- String length at that tension = 391.995 > 0 ? sqrt(80 / 0.005) / (2 * 391.995) : 0 = 0.161 343
- MIDI note number = 67 = 67
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.
G4 at different concert pitches
| A4 reference | G4 frequency |
|---|---|
| 415 Hz | 369.723 Hz |
| 430 Hz | 383.086 Hz |
| 432 Hz | 384.868 Hz |
| 435 Hz | 387.541 Hz |
| 440 Hz | 391.995 Hz |
| 442 Hz | 393.777 Hz |
| 443 Hz | 394.668 Hz |
| 444 Hz | 395.559 Hz |
Frequently asked
What frequency is G4?
391.995 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.