G#2 note frequency calculator
G#2 is MIDI note 44, -25 semitones from A4. At the standard A4 = 440 Hz that puts it at 103.826 Hz.
- Period
- 0.009 631 48 s
- Wavelength in air
- 3.3036
- Quarter wavelength
- 0.8259
- One octave up
- 207.6523 Hz
- One octave down
- 51.9131 Hz
- Equal-tempered fifth above
- 155.5635 Hz
- Just fifth above
- 155.7393 Hz
- How flat the tempered fifth is
- 1.9550 cents
- String length at that tension
- 0.6091
- MIDI note number
- 44
Show the working
- Reference pitch for A4 = 440
- Detune = 0
- Speed of sound = 343
- String tension = 80
- String mass per metre = 0.005
- semitones = -25 = -25
- Frequency = 440 * 2^(-25/12) * 2^(0/1200) = 103.826
- Period = 103.826 > 0 ? 1/103.826 : 0 = 0.009 631 48
- Wavelength in air = 103.826 > 0 ? 343 / 103.826 : 0 = 3.3036
- Quarter wavelength = 3.3036 / 4 = 0.8259
- One octave up = 103.826 * 2 = 207.652
- One octave down = 103.826 / 2 = 51.9131
- Equal-tempered fifth above = 103.826 * 2^(7/12) = 155.563
- Just fifth above = 103.826 * 1.5 = 155.739
- How flat the tempered fifth is = 155.563 > 0 ? 1200 * log2(155.739/155.563) : 0 = 1.955
- String length at that tension = 103.826 > 0 ? sqrt(80 / 0.005) / (2 * 103.826) : 0 = 0.609 148
- MIDI note number = 44 = 44
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#2 at different concert pitches
| A4 reference | G#2 frequency |
|---|---|
| 415 Hz | 97.927 Hz |
| 430 Hz | 101.466 Hz |
| 432 Hz | 101.938 Hz |
| 435 Hz | 102.646 Hz |
| 440 Hz | 103.826 Hz |
| 442 Hz | 104.298 Hz |
| 443 Hz | 104.534 Hz |
| 444 Hz | 104.770 Hz |
Frequently asked
What frequency is G#2?
103.826 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.