Note Frequencies

There are countless ways of calculating the frequency of a given note, but here's the formula I've seen most often:

f = f_0 \cdot 2^{\left( \frac{c}{1200} \right)}

Where f is the frequency we're after, f0 is the reference frequency, and c is the pitch shift in cents. 100 cents are a semitone and 1200 cents are an octave. Doubling the frequency of a note puts it up an octave and halving the frequency of a note puts it down an octave.

The reference note to use is A-4 (sometimes called "Concert A"), which, at least in the Equal Tempered Scale, is exactly 440Hz. "Middle C" is C-4. Many physics textbooks claim that its frequency is 256Hz, probably because 256 is a power of two so fun ensues when you need to shift it up or down octaves. Its real value is closer to 262Hz.

Piano

Here's a handy reference chart of the fourth and fifth octaves:

NoteFrequency (Hz) NoteFrequency (Hz)
C-4261.63 C-5523.25
C#4277.18 C#5554.37
D-4293.66 D-5587.33
D#4311.13 D#5622.25
E-4329.63 E-5659.26
F-4349.23 F-5698.46
F#4369.99 F#5739.99
G-4392.00 G-5783.99
G#4415.30 G#5830.61
A-4440.00 A-5880.00
A#4466.16 A#5932.33
B-4493.88 B-5987.77

Notice that, unlike the alphabet, musical octaves start with a C, not an A.

A semitone on a piano is the next key along, including the sharps (the ebonies.) To find notes in other frequencies either double or halve the frequencies in the table above, depending on whether you're going up or down an octave, respectively.

Guitar

One fret on a guitar string is one semitone. Here's the classical tuning for a six-string guitar:

NoteFrequency (Hz)
E-2 82.41
A-2110.00
D-3146.83
G-3196.00
B-3246.94
E-4329.63

For a bass guitar:

NoteFrequency (Hz)
E-141.21
A-155.00
D-273.42
G-298.00

See also

Hz to note converter (PERL script)
“Concert A” Pitch Since 1511


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