G#3 note frequency calculator
G#3 is MIDI note 56, -13 semitones from A4. At the standard A4 = 440 Hz that puts it at 207.652 Hz.
- Period
- 0.004 815 74 s
- Wavelength in air
- 1.6518
- Quarter wavelength
- 0.4129
- One octave up
- 415.3047 Hz
- One octave down
- 103.8262 Hz
- Equal-tempered fifth above
- 311.1270 Hz
- Just fifth above
- 311.4785 Hz
- How flat the tempered fifth is
- 1.9550 cents
- String length at that tension
- 0.3046
- MIDI note number
- 56
Show the working
- Reference pitch for A4 = 440
- Detune = 0
- Speed of sound = 343
- String tension = 80
- String mass per metre = 0.005
- semitones = -13 = -13
- Frequency = 440 * 2^(-13/12) * 2^(0/1200) = 207.652
- Period = 207.652 > 0 ? 1/207.652 : 0 = 0.004 815 74
- Wavelength in air = 207.652 > 0 ? 343 / 207.652 : 0 = 1.6518
- Quarter wavelength = 1.6518 / 4 = 0.412 95
- One octave up = 207.652 * 2 = 415.305
- One octave down = 207.652 / 2 = 103.826
- Equal-tempered fifth above = 207.652 * 2^(7/12) = 311.127
- Just fifth above = 207.652 * 1.5 = 311.479
- How flat the tempered fifth is = 311.127 > 0 ? 1200 * log2(311.479/311.127) : 0 = 1.955
- String length at that tension = 207.652 > 0 ? sqrt(80 / 0.005) / (2 * 207.652) : 0 = 0.304 574
- MIDI note number = 56 = 56
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#3 at different concert pitches
| A4 reference | G#3 frequency |
|---|---|
| 415 Hz | 195.854 Hz |
| 430 Hz | 202.933 Hz |
| 432 Hz | 203.877 Hz |
| 435 Hz | 205.293 Hz |
| 440 Hz | 207.652 Hz |
| 442 Hz | 208.596 Hz |
| 443 Hz | 209.068 Hz |
| 444 Hz | 209.540 Hz |
Frequently asked
What frequency is G#3?
207.652 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.