This list of frequencies is for a theoretical ideal piano. On an actual piano the ratio between semitones is slightly larger, especially at the high and low ends, where string thickness causesinharmonicity due to the nonzero force required to bend stee lpiano wire in the absence of tension. This effect is sometimes known as stretched octaves, and the pattern ofdeviation is called the Railsback curve.
The following equation will give the frequency F of the nth key, as shown in the table:
An 88-key piano, with the octaves numbered and Middle C (cyan) and A440 (yellow) highlighted.
| Key number |
Helmholtz name |
Scientific name |
Frequency (Hz) | Corresponding Open Strings | ||||
|---|---|---|---|---|---|---|---|---|
| Violin | Viola | Cello | Bass | Guitar | ||||
| 88 | c′′′′′ 5-line octave | C8 Eighth octave | 4186.01 | |||||
| 87 | b′′′′ | B7 | 3951.07 | |||||
| 86 | a♯′′′′/b♭′′′′ | A♯7/B♭7 | 3729.31 | |||||
| 85 | a′′′′ | A7 | 3520.00 | |||||
| 84 | g♯′′′′/a♭′′′′ | G♯7/A♭7 | 3322.44 | |||||
| 83 | g′′′′ | G7 | 3135.96 | |||||
| 82 | f♯′′′′/g♭′′′′ | F♯7/G♭7 | 2959.96 | |||||
| 81 | f′′′′ | F7 | 2793.83 | |||||
| 80 | e′′′′ | E7 | 2637.02 | |||||
| 79 | d♯′′′′/e♭′′′′ | D♯7/E♭7 | 2489.02 | |||||
| 78 | d′′′′ | D7 | 2349.32 | |||||
| 77 | c♯′′′′/d♭′′′′ | C♯7/D♭7 | 2217.46 | |||||
| 76 | c′′′′ 4-line octave | C7 Double high C | 2093.00 | |||||
| 75 | b′′′ | B6 | 1975.53 | |||||
| 74 | a♯′′′/b♭′′′ | A♯6/B♭6 | 1864.66 | |||||
| 73 | a′′′ | A6 | 1760.00 | |||||
| 72 | g♯′′′/a♭′′′ | G♯6/A♭6 | 1661.22 | |||||
| 71 | g′′′ | G6 | 1567.98 | |||||
| 70 | f♯′′′/g♭′′′ | F♯6/G♭6 | 1479.98 | |||||
| 69 | f′′′ | F6 | 1396.91 | |||||
| 68 | e′′′ | E6 | 1318.51 | |||||
| 67 | d♯′′′/e♭′′′ | D♯6/E♭6 | 1244.51 | |||||
| 66 | d′′′ | D6 | 1174.66 | |||||
| 65 | c♯′′′/d♭′′′ | C♯6/D♭6 | 1108.73 | |||||
| 64 | c′′′ 3-line octave | C6 Soprano C | 1046.50 | |||||
| 63 | b′′ | B5 | 987.767 | |||||
| 62 | a♯′′/b♭′′ | A♯5/B♭5 | 932.328 | |||||
| 61 | a′′ | A5 | 880.000 | |||||
| 60 | g♯′′/a♭′′ | G♯5/A♭5 | 830.609 | |||||
| 59 | g′′ | G5 | 783.991 | |||||
| 58 | f♯′′/g♭′′ | F♯5/G♭5 | 739.989 | |||||
| 57 | f′′ | F5 | 698.456 | |||||
| 56 | e′′ | E5 | 659.255 | E | ||||
| 55 | d♯′′/e♭′′ | D♯5/E♭5 | 622.254 | |||||
| 54 | d′′ | D5 | 587.330 | |||||
| 53 | c♯′′/d♭′′ | C♯5/D♭5 | 554.365 | |||||
| 52 | c′′ 2-line octave | C5 Tenor C | 523.251 | |||||
| 51 | b′ | B4 | 493.883 | |||||
| 50 | a♯′/b♭′ | A♯4/B♭4 | 466.164 | |||||
| 49 | a′ | A4 A440 | 440.000 | A | A | |||
| 48 | g♯′/a♭′ | G♯4/A♭4 | 415.305 | |||||
| 47 | g′ | G4 | 391.995 | |||||
| 46 | f♯′/g♭′ | F♯4/G♭4 | 369.994 | |||||
| 45 | f′ | F4 | 349.228 | |||||
| 44 | e′ | E4 | 329.628 | High E | ||||
| 43 | d♯′/e♭′ | D♯4/E♭4 | 311.127 | |||||
| 42 | d′ | D4 | 293.665 | D | D | |||
| 41 | c♯′/d♭′ | C♯4/D♭4 | 277.183 | |||||
| 40 | c′ 1-line octave | C4 Middle C | 261.626 | |||||
| 39 | b | B3 | 246.942 | B | ||||
| 38 | a♯/b♭ | A♯3/B♭3 | 233.082 | |||||
| 37 | a | A3 | 220.000 | A | ||||
| 36 | g♯/a♭ | G♯3/A♭3 | 207.652 | |||||
| 35 | g | G3 | 195.998 | G | G | G | ||
| 34 | f♯/g♭ | F♯3/G♭3 | 184.997 | |||||
| 33 | f | F3 | 174.614 | |||||
| 32 | e | E3 | 164.814 | |||||
| 31 | d♯/e♭ | D♯3/E♭3 | 155.563 | |||||
| 30 | d | D3 | 146.832 | D | D | |||
| 29 | c♯/d♭ | C♯3/D♭3 | 138.591 | |||||
| 28 | c small octave | C3 Low C | 130.813 | C | ||||
| 27 | B | B2 | 123.471 | |||||
| 26 | A♯/B♭ | A♯2/B♭2 | 116.541 | |||||
| 25 | A | A2 | 110.000 | A | ||||
| 24 | G♯/A♭ | G♯2/A♭2 | 103.826 | |||||
| 23 | G | G2 | 97.9989 | G | G | |||
| 22 | F♯/G♭ | F♯2/G♭2 | 92.4986 | |||||
| 21 | F | F2 | 87.3071 | |||||
| 20 | E | E2 | 82.4069 | Low E | ||||
| 19 | D♯/E♭ | D♯2/E♭2 | 77.7817 | |||||
| 18 | D | D2 | 73.4162 | D | ||||
| 17 | C♯/D♭ | C♯2/D♭2 | 69.2957 | |||||
| 16 | C great octave | C2 Deep C | 65.4064 | C | ||||
| 15 | Bˌ | B1 | 61.7354 | |||||
| 14 | A♯ˌ/B♭ˌ | A♯1/B♭1 | 58.2705 | |||||
| 13 | Aˌ | A1 | 55.0000 | A | ||||
| 12 | G♯ˌ/A♭ˌ | G♯1/A♭1 | 51.9131 | |||||
| 11 | Gˌ | G1 | 48.9994 | |||||
| 10 | F♯ˌ/G♭ˌ | F♯1/G♭1 | 46.2493 | |||||
| 9 | Fˌ | F1 | 43.6535 | |||||
| 8 | Eˌ | E1 | 41.2034 | E | ||||
| 7 | D♯ˌ/E♭ˌ | D♯1/E♭1 | 38.8909 | |||||
| 6 | Dˌ | D1 | 36.7081 | |||||
| 5 | C♯ˌ/D♭ˌ | C♯1/D♭1 | 34.6478 | |||||
| 4 | Cˌ contra-octave | C1 Pedal C | 32.7032 | |||||
| 3 | Bˌˌ | B0 | 30.8677 | B | ||||
| 2 | A♯ˌˌ/B♭ˌˌ | A♯0/B♭0 | 29.1352 | |||||
| 1 | Aˌˌ sub-contra-octave | A0 Double Pedal A | 27.5000 | |||||