G#4 note frequency calculator
G#4 is MIDI note 68, -1 semitones from A4. At the standard A4 = 440 Hz that puts it at 415.305 Hz.
- Period
- 0.002 407 87 s
- Wavelength in air
- 0.8259
- Quarter wavelength
- 0.2065
- One octave up
- 830.6094 Hz
- One octave down
- 207.6523 Hz
- Equal-tempered fifth above
- 622.2540 Hz
- Just fifth above
- 622.9570 Hz
- How flat the tempered fifth is
- 1.9550 cents
- String length at that tension
- 0.1523
- MIDI note number
- 68
Show the working
- Reference pitch for A4 = 440
- Detune = 0
- Speed of sound = 343
- String tension = 80
- String mass per metre = 0.005
- semitones = -1 = -1
- Frequency = 440 * 2^(-1/12) * 2^(0/1200) = 415.305
- Period = 415.305 > 0 ? 1/415.305 : 0 = 0.002 407 87
- Wavelength in air = 415.305 > 0 ? 343 / 415.305 : 0 = 0.8259
- Quarter wavelength = 0.8259 / 4 = 0.206 475
- One octave up = 415.305 * 2 = 830.609
- One octave down = 415.305 / 2 = 207.652
- Equal-tempered fifth above = 415.305 * 2^(7/12) = 622.254
- Just fifth above = 415.305 * 1.5 = 622.957
- How flat the tempered fifth is = 622.254 > 0 ? 1200 * log2(622.957/622.254) : 0 = 1.955
- String length at that tension = 415.305 > 0 ? sqrt(80 / 0.005) / (2 * 415.305) : 0 = 0.152 287
- MIDI note number = 68 = 68
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.
G#4 at different concert pitches
| A4 reference | G#4 frequency |
|---|---|
| 415 Hz | 391.708 Hz |
| 430 Hz | 405.866 Hz |
| 432 Hz | 407.754 Hz |
| 435 Hz | 410.585 Hz |
| 440 Hz | 415.305 Hz |
| 442 Hz | 417.192 Hz |
| 443 Hz | 418.136 Hz |
| 444 Hz | 419.080 Hz |
Frequently asked
What frequency is G#4?
415.305 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.