The formula behind the chart
In twelve-tone equal temperament an octave is a frequency ratio of 2 to 1 and it is divided into 12 equal semitones, so each semitone multiplies the frequency by the twelfth root of 2, 1.059463. Give every note a number such that A4 is 69 and each semitone adds one, which is the MIDI numbering, and the frequency of any note is:
The UNSW music acoustics notes give the same formula and the convention behind it: A4 is often set at 440 Hz. Middle C is n = 60, nine semitones below A4, so 440 × 2−9/12 = 261.63 Hz. The tone generator plays any frequency you type, and the online tuner works the formula backwards, from the frequency it hears to the nearest note and the distance in cents.
Note frequencies from C0 to B8
Octaves run from C to B, and the octave number changes at C, so B3 is followed by C4. C4 is middle C, A4 the 440 Hz reference, and the chart runs from C0 (16.35 Hz) to B8 (7902 Hz). Values are in hertz, rounded to two decimals below 1,000 Hz and to whole hertz above.
| Note | Octave 0 | Octave 1 | Octave 2 | Octave 3 | Octave 4 | Octave 5 | Octave 6 | Octave 7 | Octave 8 |
|---|---|---|---|---|---|---|---|---|---|
| C | 16.35 | 32.70 | 65.41 | 130.81 | 261.63 | 523.25 | 1047 | 2093 | 4186 |
| C♯/D♭ | 17.32 | 34.65 | 69.30 | 138.59 | 277.18 | 554.37 | 1109 | 2217 | 4435 |
| D | 18.35 | 36.71 | 73.42 | 146.83 | 293.66 | 587.33 | 1175 | 2349 | 4699 |
| D♯/E♭ | 19.45 | 38.89 | 77.78 | 155.56 | 311.13 | 622.25 | 1245 | 2489 | 4978 |
| E | 20.60 | 41.20 | 82.41 | 164.81 | 329.63 | 659.26 | 1319 | 2637 | 5274 |
| F | 21.83 | 43.65 | 87.31 | 174.61 | 349.23 | 698.46 | 1397 | 2794 | 5588 |
| F♯/G♭ | 23.12 | 46.25 | 92.50 | 185.00 | 369.99 | 739.99 | 1480 | 2960 | 5920 |
| G | 24.50 | 49.00 | 98.00 | 196.00 | 392.00 | 783.99 | 1568 | 3136 | 6272 |
| G♯/A♭ | 25.96 | 51.91 | 103.83 | 207.65 | 415.30 | 830.61 | 1661 | 3322 | 6645 |
| A | 27.50 | 55.00 | 110.00 | 220.00 | 440.00 | 880.00 | 1760 | 3520 | 7040 |
| A♯/B♭ | 29.14 | 58.27 | 116.54 | 233.08 | 466.16 | 932.33 | 1865 | 3729 | 7459 |
| B | 30.87 | 61.74 | 123.47 | 246.94 | 493.88 | 987.77 | 1976 | 3951 | 7902 |
Two patterns make the chart easy to use without a calculator. Across a row, each cell is exactly double the one to its left. Down a column, every twelve rows the frequency doubles, and the A column is 27.5, 55, 110, 220, 440, 880 and so on, which is why A is the reference note: its frequencies are round numbers.
Open strings of common instruments
Standard tunings, with the frequency of each open string at A4 = 440 Hz. The tuner's instrument presets use the same values.
| Instrument | Strings, low to high | Frequencies in Hz |
|---|---|---|
| Guitar, standard | E2, A2, D3, G3, B3, E4 | 82.41, 110.00, 146.83, 196.00, 246.94, 329.63 |
| Bass, four strings | E1, A1, D2, G2 | 41.20, 55.00, 73.42, 98.00 |
| Violin | G3, D4, A4, E5 | 196.00, 293.66, 440.00, 659.26 |
| Ukulele, re-entrant | G4, C4, E4, A4 | 392.00, 261.63, 329.63, 440.00 |
| Cello | C2, G2, D3, A3 | 65.41, 98.00, 146.83, 220.00 |
The guitar's two E strings, E2 and E4, are two octaves apart, a factor of four: 82.41 and 329.63 Hz. The ukulele's first string is tuned higher than its second, which is what re-entrant means, so its lowest note is the C4 in the middle of the set.
Cents: how far out of tune
A cent is one hundredth of an equal-tempered semitone: 100 cents to the semitone, 1,200 to the octave. As a ratio one cent is 21/1200, about 1.000578, so at A4 one cent is about 0.25 Hz and at A2 about 0.064 Hz. The same number of cents is a smaller number of hertz the lower the note, which is why tuners show cents rather than hertz. The distance between two frequencies in cents is 1200 × log₂(f₂ ÷ f₁): a string at 445 Hz against a 440 Hz reference is 19.6 cents sharp. The metronome covers the other dimension of practice, time, with the same kind of steady reference.
Other reference pitches
Change A4 and every frequency in the chart scales by the same ratio, because the formula multiplies the reference. Some orchestras tune to 442 or 443 Hz, and some players prefer 432 Hz. The table shows a few notes at each reference; the tuner lets you set A4 anywhere from 400 to 480 Hz and recomputes the rest.
| Note | A4 = 432 Hz | A4 = 440 Hz | A4 = 442 Hz | A4 = 443 Hz |
|---|---|---|---|---|
| C4 | 256.87 | 261.63 | 262.81 | 263.41 |
| E4 | 323.63 | 329.63 | 331.13 | 331.88 |
| G4 | 384.87 | 392.00 | 393.78 | 394.67 |
| A4 | 432.00 | 440.00 | 442.00 | 443.00 |
| C5 | 513.74 | 523.25 | 525.63 | 526.82 |
The difference between 440 and 442 Hz is 7.9 cents, between 440 and 432 Hz -31.8 cents, a little under a third of a semitone.
Sharps, flats and the twelve names
In equal temperament C♯ and D♭ are the same frequency, which is why the chart has one row for each pair. There are twelve rows because an octave has twelve semitones: seven natural notes, C D E F G A B, and five sharps or flats between them, with no black key between E and F or between B and C. Instruments without fixed pitch, such as the violin or the voice, can and do play C♯ and D♭ slightly differently when the harmony calls for it; the chart gives the equal-tempered compromise that keyboards, frets and electronic tuners use.
Frequently asked questions
What frequency is middle C?
Middle C is C4, MIDI note 60, and with A4 at 440 Hz it is 261.63 Hz. The C an octave above, C5, is 523.25 Hz, and the C below, C3, is 130.81 Hz. Each octave doubles or halves the frequency.
Why is A4 440 Hz?
By convention. The UNSW music acoustics notes put it the same way: A4 is often set at 440 Hz. Every other note in equal temperament follows from that reference, so an orchestra that tunes to 442 or 443 Hz, or a player who prefers 432, shifts the whole table by the same ratio. The tables on this page use 440 and show the alternatives for a few notes.
How do I calculate the frequency of any note?
Number the notes so that A4 is 69 and each semitone adds one, which is the MIDI convention, then f = 440 × 2^((n − 69) ÷ 12). For C4, n = 60: 440 × 2^(−9 ÷ 12) = 261.63 Hz. Going the other way, n = 69 + 12 × log₂(f ÷ 440).
What is a cent?
A hundredth of an equal-tempered semitone, so 1,200 cents make an octave. One cent is a frequency ratio of 2^(1/1200), about 1.000578, which at 440 Hz is about a quarter of a hertz. Tuners show how far a note is from the nearest pitch in cents.
Why does a guitar's low E read 82 Hz and not 330 Hz?
Because the low E string is E2 and the high E string is E4, two octaves apart. E2 is 82.41 Hz and E4 is 329.63 Hz, a factor of four. A tuner that shows 164.81 Hz is hearing E3, one octave up, which can happen when the string's second harmonic is louder than its fundamental.