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| This is a list of the absolute frequencies in [[hertz]] (cycles per second) of the keys of a standard modern 88-key [[piano]] in [[Equal temperament#Twelve-tone equal temperament|twelve-tone equal temperament]], with the 49th key, the fifth A (called A4), tuned to 440 Hz (referred to as [[A440 (pitch standard)|A440]]). Each successive pitch is derived by multiplying (ascending) or dividing (descending) the previous by the [[twelfth root of two]] (approximately 1.05946...). For example, to get the [[frequency]] a [[semitone]] up from A4 (A{{music|#}}4), multiply 440 by the twelfth root of two. To go from A4 to B4 (up a [[whole tone]], or two semitones), multiply 440 twice by the twelfth root of two. For other tuning schemes refer to [[musical tuning]].
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| This list of frequencies is for a theoretically ideal piano. On an actual piano the ratio between semitones is slightly larger, especially at the high and low ends, where string stiffness causes [[inharmonicity]], i.e., the tendency for the [[harmonic]] makeup of each note to run [[sharp (music)|sharp]]. To compensate for this, octaves are tuned slightly wide, [[stretched octave|stretched]] according to the inharmonic characteristics of each instrument. This deviation from equal temperament is called the [[Railsback curve]].
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| The following equation gives the frequency {{mvar|f}} of the {{mvar|n}}<sup>th</sup> key, as shown in the table:
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| :<math>
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| f(n) = (\sqrt[12]{2}\,)^{n-49} \times 440 \,\text{Hz}\,
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| </math>
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| (a' is the 49th key on the idealized piano)
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| Alternatively, this can be written as:
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| :<math>
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| f(n) = 2^{\frac{n-49}{12}} \times 440 \,\text{Hz}\,
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| </math>
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| Conversely, starting from a frequency on the idealized piano tuned to A440, one obtains the key number by:
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| :<math>
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| n = 12 \, \log_2\left({\frac{f}{440 \,\text{Hz}}}\right) + 49
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| </math>
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| ==List==
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| [[File:Piano Frequencies.svg|frame|alt=Piano Keyboard|An 88-key piano, with the octaves numbered and [[Middle C]] (cyan) and [[A440 (pitch standard)|A440]] (yellow) highlighted.]]
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| [[File:Piano key frequencies.png|thumb|left|50px|A printable version of the chart below.]]
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| <br clear='all'> | |
| {| class="wikitable" style="text-align: center"
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| !rowspan="2"| Key<br>number ||rowspan="2"| [[Helmholtz pitch notation|Helmholtz]]<br>name ||rowspan="2"|[[Scientific pitch notation|Scientific]]<br>name ||rowspan="2"| Frequency (Hz) || colspan="5"| Corresponding Open Strings
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| |-
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| ! [[Violin]] || [[Viola]] || [[Cello]] || [[Double bass|Bass]] || [[Guitar]]
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| |-
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| | bgcolor="white" | 88 || c′′′′′ 5-line [[octave]]|| [[Eighth octave C|C8]] Eighth octave || 4186.01 || || || || ||
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| |-
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| | bgcolor="white" | 87 || b′′′′ || B7 || 3951.07 || || || || ||
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| |-
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| | bgcolor="black" style="color:white" | 86 || a{{music|#}}′′′′/b{{music|b}}′′′′ || A{{music|#}}7/B{{music|b}}7 || 3729.31 || || || || ||
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| |-
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| | bgcolor="white" | 85 || a′′′′ || A7 || 3520.00 || || || || ||
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| |-
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| | bgcolor="black" style="color:white" | 84 || g{{music|#}}′′′′/a{{music|b}}′′′′ || G{{music|#}}7/A{{music|b}}7 || 3322.44 || || || || ||
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| |-
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| | bgcolor="white" | 83 || g′′′′ || G7 || 3135.96 || || || || ||
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| |-
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| | bgcolor="black" style="color:white" | 82 || f{{music|#}}′′′′/g{{music|b}}′′′′ || F{{music|#}}7/G{{music|b}}7 || 2959.96 || || || || ||
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| |-
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| | bgcolor="white" | 81 || f′′′′ || F7 || 2793.83 || || || || ||
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| |-
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| | bgcolor="white" | 80 || e′′′′ || E7 || 2637.02 || || || || ||
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| |-
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| | bgcolor="black" style="color:white" | 79 || d{{music|#}}′′′′/e{{music|b}}′′′′ || D{{music|#}}7/E{{music|b}}7 || 2489.02 || || || || ||
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| |-
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| | bgcolor="white" | 78 || d′′′′ || D7 || 2349.32 || || || || ||
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| |-
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| | bgcolor="black" style="color:white" | 77 || c{{music|#}}′′′′/d{{music|b}}′′′′ || C{{music|#}}7/D{{music|b}}7 || 2217.46 || || || || ||
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| |-
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| | bgcolor="white" | 76 || c′′′′ 4-line octave|| C7 [[Double high C]] || 2093.00 || || || || ||
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| |-
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| | bgcolor="white" | 75 || b′′′ || B6 || 1975.53 || || || || ||
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| |-
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| | bgcolor="black" style="color:white" | 74 || a{{music|#}}′′′/b{{music|b}}′′′ || A{{music|#}}6/B{{music|b}}6 || 1864.66 || || || || ||
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| |-
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| | bgcolor="white" | 73 || a′′′ || A6 || 1760.00 || || || || ||
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| |-
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| | bgcolor="black" style="color:white" | 72 || g{{music|#}}′′′/a{{music|b}}′′′ || G{{music|#}}6/A{{music|b}}6 || 1661.22 || || || || ||
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| |-
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| | bgcolor="white" | 71 || g′′′ || G6 || 1567.98 || || || || ||
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| |-
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| | bgcolor="black" style="color:white" | 70 || f{{music|#}}′′′/g{{music|b}}′′′ || F{{music|#}}6/G{{music|b}}6 || 1479.98 || || || || ||
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| |-
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| | bgcolor="white" | 69 || f′′′ || F6 || 1396.91 || || || || ||
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| |-
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| | bgcolor="white" | 68 || e′′′ || E6 || 1318.51 || || || || ||
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| |-
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| | bgcolor="black" style="color:white" | 67 || d{{music|#}}′′′/e{{music|b}}′′′ || D{{music|#}}6/E{{music|b}}6 || 1244.51 || || || || ||
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| |-
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| | bgcolor="white" | 66 || d′′′ || D6 || 1174.66 || || || || ||
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| |-
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| | bgcolor="black" style="color:white" | 65 || c{{music|#}}′′′/d{{music|b}}′′′ || C{{music|#}}6/D{{music|b}}6 || 1108.73 || || || || ||
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| |-
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| | bgcolor="white" | 64 || c′′′ 3-line octave|| C6 [[Soprano C]] (High C) || 1046.50 || || || || ||
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| |-
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| | bgcolor="white" | 63 || b′′ || B5 || 987.767 || || || || ||
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| |-
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| | bgcolor="black" style="color:white" | 62 || a{{music|#}}′′/b{{music|b}}′′ || A{{music|#}}5/B{{music|b}}5 || 932.328 || || || || ||
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| |-
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| | bgcolor="white" | 61 || a′′ || A5 || 880.000 || || || || ||
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| |-
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| | bgcolor="black" style="color:white" | 60 || g{{music|#}}′′/a{{music|b}}′′ || G{{music|#}}5/A{{music|b}}5 || 830.609 || || || || ||
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| |-
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| | bgcolor="white" | 59 || g′′ || G5 || 783.991 || || || || ||
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| |-
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| | bgcolor="black" style="color:white" | 58 || f{{music|#}}′′/g{{music|b}}′′ || F{{music|#}}5/G{{music|b}}5 || 739.989 || || || || ||
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| |-
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| | bgcolor="white" | 57 || f′′ || F5 || 698.456 || || || || ||
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| |-
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| | bgcolor="white" | 56 || e′′ || E5 || 659.255 || E || || || ||
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| |-
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| | bgcolor="black" style="color:white" | 55 || d{{music|#}}′′/e{{music|b}}′′ || D{{music|#}}5/E{{music|b}}5 || 622.254 || || || || ||
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| |-
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| | bgcolor="white" | 54 || d′′ ||D5 || 587.330 || || || || ||
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| |-
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| | bgcolor="black" style="color:white" | 53 || c{{music|#}}′′/d{{music|b}}′′ || C{{music|#}}5/D{{music|b}}5 || 554.365 || || || || ||
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| |-
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| | bgcolor="white" | 52 || c′′ 2-line octave || C5 [[Tenor C]] || 523.251 || || || || ||
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| |-
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| | bgcolor="white" | 51 || b′ || B4 || 493.883 || || || || ||
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| |-
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| | bgcolor="black" style="color:white" | 50 || a{{music|#}}′/b{{music|b}}′|| A{{music|#}}4/B{{music|b}}4 || 466.164 || || || || ||
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| |-
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| | bgcolor="white" |49 || a′ || A4 [[A440 (pitch standard)|A440]] || bgcolor="yellow" | 440.000 || A || A || || || High A (Optional)
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| | bgcolor="black" style="color:white" | 48 || g{{music|#}}′/a{{music|b}}′ || G{{music|#}}4/A{{music|b}}4 || 415.305 || || || || ||
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| |-
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| | bgcolor="white" | 47 || g′|| G4 || 391.995 || || || || ||
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| | bgcolor="black" style="color:white" | 46 || f{{music|#}}′/g{{music|b}}′ || F{{music|#}}4/G{{music|b}}4 || 369.994 || || || || ||
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| |-
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| | bgcolor="white" | 45 || f′ || F4 || 349.228 || || || || ||
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| |-
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| | bgcolor="white" | 44 || e′ || E4 || 329.628 || || || || || High E
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| |-
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| | bgcolor="black" style="color:white" | 43 || d{{music|#}}′/e{{music|b}}′ || D{{music|#}}4/E{{music|b}}4 || 311.127 || || || || ||
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| | bgcolor="white" | 42 || d′ || D4 || 293.665 || D || D || || ||
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| |-
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| | bgcolor="black" style="color:white" | 41 || c{{music|#}}′/d{{music|b}}′ || C{{music|#}}4/D{{music|b}}4 || 277.183 || || || || ||
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| | bgcolor="white" | 40 || c′ 1-line octave || C4 [[Middle C]] || bgcolor="skyblue" | 261.626 || || || || ||
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| | bgcolor="white" | 39 || b || B3 || 246.942 || || || || || B
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| |-
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| | bgcolor="black" style="color:white" | 38 || a{{music|#}}/b{{music|b}} || A{{music|#}}3/B{{music|b}}3 || 233.082 || || || || ||
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| | bgcolor="white" | 37 || a || A3 || 220.000 || || || A || ||
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| | bgcolor="black" style="color:white" | 36 || g{{music|#}}/a{{music|b}} || G{{music|#}}3/A{{music|b}}3 || 207.652 || || || || ||
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| | bgcolor="white" | 35 || g || G3 || 195.998 || G || G || || || G
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| | bgcolor="black" style="color:white" | 34 || f{{music|#}}/g{{music|b}} || F{{music|#}}3/G{{music|b}}3 || 184.997 || || || || ||
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| | bgcolor="white" | 33 || f || F3 || 174.614 || || || || F (7 string)||
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| | bgcolor="white" | 32 || e || E3 || 164.814 || || || || ||
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| | bgcolor="black" style="color:white" | 31 || d{{music|#}}/e{{music|b}} || D{{music|#}}3/E{{music|b}}3 || 155.563 || || || || ||
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| | bgcolor="white" | 30 || d || D3 || 146.832 || || || D || || D
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| | bgcolor="black" style="color:white" | 29 || c{{music|#}}/d{{music|b}} || C{{music|#}}3/D{{music|b}}3 || 138.591 || || || || ||
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| | bgcolor="white" | 28 || c small octave|| C3 [[Low C]] || 130.813 || C (5 string) || C || || C (6 string) ||
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| | bgcolor="white" | 27 || B || B2 || 123.471 || || || || ||
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| | bgcolor="black" style="color:white" | 26 || A{{music|#}}/B{{music|b}} || A{{music|#}}2/B{{music|b}}2 || 116.541 || || || || ||
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| | bgcolor="white" | 25 || A || A2 || 110.000 || || || || || A
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| | bgcolor="black" style="color:white" | 24 || G{{music|#}}/A{{music|b}} ||G{{music|#}}2/A{{music|b}}2 || 103.826 || || || || ||
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| | bgcolor="white" | 23 || G || G2 || 97.9989 || || || G || G ||
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| | bgcolor="black" style="color:white" | 22 || F{{music|#}}/G{{music|b}} ||F{{music|#}}2/G{{music|b}}2 || 92.4986 || || || || ||
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| | bgcolor="white" | 21 || F || F2 || 87.3071 || F (6 string) || || || ||
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| | bgcolor="white" | 20 || E || E2 || 82.4069 || || || || || Low E
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| | bgcolor="black" style="color:white" | 19 || D{{music|#}}/E{{music|b}} ||D{{music|#}}2/E{{music|b}}2 || 77.7817 || || || || ||
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| | bgcolor="white" | 18 || D || D2 || 73.4162 || || || || D ||
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| | bgcolor="black" style="color:white" | 17 || C{{music|#}}/D{{music|b}} ||C{{music|#}}2/D{{music|b}}2 || 69.2957 || || || || ||
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| | bgcolor="white" | 16 || C great octave || C2 [[Deep C]] || 65.4064 || || || C || ||
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| | bgcolor="white" | 15 || B͵ || B1 || 61.7354 || || || || || B (7 string)
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| | bgcolor="black" style="color:white" | 14 || A{{music|#}}͵/B{{music|b}}͵ || A{{music|#}}1/B{{music|b}}1 || 58.2705 || B{{music|b}} (7 string) || || || ||
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| | bgcolor="white" | 13 || A͵ || A1 || 55.0000 || || || || A ||
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| | bgcolor="black" style="color:white" | 12 || G{{music|#}}͵/A{{music|b}}͵ || G{{music|#}}1/A{{music|b}}1 || 51.9131 || || || || ||
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| | bgcolor="white" | 11 || G͵ || G1 || 48.9994 || || || || ||
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| | bgcolor="black" style="color:white" | 10 || F{{music|#}}͵/G{{music|b}}͵ || F{{music|#}}1/G{{music|b}}1 || 46.2493 || || || || || F{{music|#}} (8 string)
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| | bgcolor="white" | 9 || F͵ || F1 || 43.6535 || || || || ||
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| | bgcolor="white" | 8 || E͵ || E1 || 41.2034 || || || || E ||
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| | bgcolor="black" style="color:white" | 7 || D{{music|#}}͵/E{{music|b}}͵ || D{{music|#}}1/E{{music|b}}1 || 38.8909 || || || || ||
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| | bgcolor="white" | 6 || D͵ || D1 || 36.7081 || || || || ||
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| | bgcolor="black" style="color:white" | 5 || C{{music|#}}͵/D{{music|b}}͵ || C{{music|#}}1/D{{music|b}}1 || 34.6478 || || || || || C{{music|#}} (9 string)
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| | bgcolor="white" | 4 || C͵ contra-octave|| C1 Pedal C|| 32.7032 || || || || ||
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| | bgcolor="white" | 3 || B͵͵ || B0 || 30.8677 || || || || B (5 string) ||
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| | bgcolor="black" style="color:white" | 2 || A{{music|#}}͵͵/B{{music|b}}͵͵ || A{{music|#}}0/B{{music|b}}0 || 29.1352 || || || || ||
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| | bgcolor="white" | 1 || A͵͵ sub-contra-octave|| A0 Double Pedal A|| 27.5000 || || || || ||
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| |}
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| ==See also==
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| *[[Piano tuning]]
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| *[[Scientific pitch notation]]
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| *[[Music and mathematics]]
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| ==External links==
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| *[http://shakahara.com/pianopitch2.php interactive piano frequency table] — A php script allowing the reference pitch of A4 to be altered from 440 Hz.
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| *[http://home.arcor.de/mdoege/pysynth/ PySynth] — A simple [[Python (programming language)|Python]]-based [[software synthesizer]] that prints the key frequencies table and then creates a few demo songs based on that table.
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| *"[http://www.sengpielaudio.com/calculator-notenames.htm Keyboard and frequencies]", ''SengpielAudio.com''.
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| {{Pitch (music)}}
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| [[Category:Piano|Key frequencies]]
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| [[Category:Musical tuning]]
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