Piano key frequencies

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Template:Short description Template:More citations needed This is a list of the fundamental frequencies in hertz (cycles per second) of the keys of a modern 88-key standard or 108-key extended piano in twelve-tone equal temperament, with the 49th key, the fifth A (called A4), tuned to 440 Hz (referred to as A440).<ref name=":0">{{#invoke:citation/CS1|citation |CitationClass=web }}</ref><ref name=":1">{{#invoke:citation/CS1|citation |CitationClass=web }}</ref> Every octave is made of twelve steps called semitones. A jump from the lowest semitone to the highest semitone in one octave doubles the frequency (for example, the fifth A is 440 Hz and the sixth A is 880 Hz). The frequency of a pitch is derived by multiplying (ascending) or dividing (descending) the frequency of the previous pitch by the twelfth root of two (approximately 1.059463).<ref name=":0" /><ref name=":1" /> For example, to get the frequency one semitone up from A4 (ATemplate:Music4), multiply 440 Hz by the twelfth root of two. To go from A4 up two semitones (one whole tone) to B4, multiply 440 twice by the twelfth root of two (or once by the sixth root of two, approximately 1.122462). To go from A4 up three semitones to C5 (a minor third), multiply 440 Hz three times by the twelfth root of two (or once by the fourth root of two, approximately 1.189207). For other tuning schemes, refer to musical tuning.

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. To compensate for this, octaves are tuned slightly wide, stretched according to the inharmonic characteristics of each instrument.<ref>{{#invoke:citation/CS1|citation |CitationClass=web }}</ref> This deviation from equal temperament is called the Railsback curve.

The following equation gives the frequency Template:Mvar (Hz) of the Template:Mvarth key on the idealized standard piano with the 49th key tuned to A4 at 440 Hz:

<math>

f(n) = \left(\sqrt[12]{2}\,\right)^{n-49} \times 440 \,\text{Hz}\, = 2^{\frac{n-49}{12}} \times 440 \,\text{Hz}\, </math> where Template:Mvar is shown in the table below.<ref name=":0" />

Conversely, the key number of a pitch with a frequency Template:Mvar (Hz) on the idealized standard piano is:

<math>

n = 12 \, \log_2\left({\frac{f}{440 \,\text{Hz}}}\right) + 49 </math>

List

Piano Keyboard
An 88-key piano, with the octaves numbered and with Middle C (cyan) and A440 (yellow) highlighted
A printable version of the standard 88 keys' frequencies

Values in bold are exact on an idealized standard piano. Keys shaded gray are rare and only appear on extended pianos. The normal 88 keys are numbered 1 to 88; extra low and high keys which only appear on extended pianos are numbered -8 to 0 and 89 to 99 respectively. A 108-key piano that extends from C0 to B8 was first built in 2018 by Stuart & Sons.<ref>{{#invoke:citation/CS1|citation |CitationClass=web }}</ref>

Piano key number MIDI note number Helmholtz name<ref name=":2">{{#invoke:citation/CS1|citation CitationClass=web

}}</ref>

Scientific pitch name<ref name=":2" /> Frequency Template:Mvar(Template:Mvar) (Hz) (Equal temperament) <ref>{{#invoke:citation/CS1|citation CitationClass=web

}}</ref>

Corresponding open strings on other instruments Vocal Ranges
width="7%" Template:Vert header width="7%" Template:Vert header width="7%" Template:Vert header width="12%" Template:Vert header width="12%" Template:Vert header width="7%" Template:Vert header width="3%" Template:Vert header width="3%" Template:Vert header width="3%" Template:Vert header width="3%" Template:Vert header width="3%" Template:Vert header width="3%" Template:Vert header
99 119 b′′′′′ B8 7902.133
98 118 aTemplate:Music′′′′′/bTemplate:Music′′′′′ ATemplate:Music8/BTemplate:Music8 7458.620
97 117 a′′′′′ A8 7040.000
96 116 gTemplate:Music′′′′′/aTemplate:Music′′′′′ GTemplate:Music8/ATemplate:Music8 6644.875
95 115 g′′′′′ G8 6271.927
94 114 fTemplate:Music′′′′′/gTemplate:Music′′′′′ FTemplate:Music8/GTemplate:Music8 5919.911
93 113 f′′′′′ F8 5587.652
92 112 e′′′′′ E8 5274.041
91 111 dTemplate:Music′′′′′/eTemplate:Music′′′′′ DTemplate:Music8/ETemplate:Music8 4978.032
90 110 d′′′′′ D8 4698.636
89 109 cTemplate:Music′′′′′/dTemplate:Music′′′′′ CTemplate:Music8/DTemplate:Music8 4434.922
88 108 c′′′′′ 5-line octave C8 Eighth octave 4186.009
87 107 b′′′′ B7 3951.066
86 106 aTemplate:Music′′′′/bTemplate:Music′′′′ ATemplate:Music7/BTemplate:Music7 3729.310
85 105 a′′′′ A7 3520.000
84 104 gTemplate:Music′′′′/aTemplate:Music′′′′ GTemplate:Music7/ATemplate:Music7 3322.438
83 103 g′′′′ G7 3135.963
82 102 fTemplate:Music′′′′/gTemplate:Music′′′′ FTemplate:Music7/GTemplate:Music7 2959.955
81 101 f′′′′ F7 2793.826
80 100 e′′′′ E7 2637.020
79 99 dTemplate:Music′′′′/eTemplate:Music′′′′ DTemplate:Music7/ETemplate:Music7 2489.016
78 98 d′′′′ D7 2349.318
77 97 cTemplate:Music′′′′/dTemplate:Music′′′′ CTemplate:Music7/DTemplate:Music7 2217.461
76 96 c′′′′ 4-line octave C7 Double high C 2093.005
75 95 b′′′ B6 1975.533
74 94 aTemplate:Music′′′/bTemplate:Music′′′ ATemplate:Music6/BTemplate:Music6 1864.655
73 93 a′′′ A6 1760.000
72 92 gTemplate:Music′′′/aTemplate:Music′′′ GTemplate:Music6/ATemplate:Music6 1661.219
71 91 g′′′ G6 1567.982
70 90 fTemplate:Music′′′/gTemplate:Music′′′ FTemplate:Music6/GTemplate:Music6 1479.978
69 89 f′′′ F6 1396.913
68 88 e′′′ E6 1318.510
67 87 dTemplate:Music′′′/eTemplate:Music′′′ DTemplate:Music6/ETemplate:Music6 1244.508
66 86 d′′′ D6 1174.659
65 85 cTemplate:Music′′′/dTemplate:Music′′′ CTemplate:Music6/DTemplate:Music6 1108.731
64 84 c′′′ 3-line octave C6 Soprano C (High C) 1046.502 rowspan="25" Template:Yes C
63 83 b′′ B5 987.7666
62 82 aTemplate:Music′′/bTemplate:Music′′ ATemplate:Music5/BTemplate:Music5 932.3275
61 81 a′′ A5 880.0000 rowspan="25" Template:Yes C
60 80 gTemplate:Music′′/aTemplate:Music′′ GTemplate:Music5/ATemplate:Music5 830.6094
59 79 g′′ G5 783.9909
58 78 fTemplate:Music′′/gTemplate:Music′′ FTemplate:Music5/GTemplate:Music5 739.9888
57 77 f′′ F5 698.4565 rowspan="25" Template:Yes C
56 76 e′′ E5 659.2551 E E (5 string)
55 75 dTemplate:Music′′/eTemplate:Music′′ DTemplate:Music5/ETemplate:Music5 622.2540
54 74 d′′ D5 587.3295
53 73 cTemplate:Music′′/dTemplate:Music′′ CTemplate:Music5/DTemplate:Music5 554.3653
52 72 c′′ 2-line octave C5 Tenor C 523.2511 rowspan="25" Template:Yes C
51 71 b′ B4 493.8833 High B (12 string, optional)
50 70 aTemplate:Music′/bTemplate:Music′ ATemplate:Music4/BTemplate:Music4 466.1638
49 69 a′ A4 A440 440.0000 A A High A (optional) A rowspan="25" Template:Yes C
48 68 gTemplate:Music′/aTemplate:Music′ GTemplate:Music4/ATemplate:Music4 415.3047 High ATemplate:Music (12 single string)
47 67 g′ G4 391.9954 High G
46 66 fTemplate:Music′/gTemplate:Music′ FTemplate:Music4/GTemplate:Music4 369.9944
45 65 f′ F4 349.2282
44 64 e′ E4 329.6276 High E (5 string) High E E rowspan="25" Template:Yes C
43 63 dTemplate:Music′/eTemplate:Music′ DTemplate:Music4/ETemplate:Music4 311.1270 High ETemplate:Music (12 single string)
42 62 d′ D4 293.6648 D D
41 61 cTemplate:Music′/dTemplate:Music′ CTemplate:Music4/DTemplate:Music4 277.1826
40 60 c′ 1-line octave C4 Middle C 261.6256 C
39 59 b B3 246.9417 B
38 58 aTemplate:Music/bTemplate:Music ATemplate:Music3/BTemplate:Music3 233.0819
37 57 a A3 220.0000 A
36 56 gTemplate:Music/aTemplate:Music GTemplate:Music3/ATemplate:Music3 207.6523
35 55 g G3 195.9977 G G G Low G
34 54 fTemplate:Music/gTemplate:Music FTemplate:Music3/GTemplate:Music3 184.9972
33 53 f F3 174.6141 High F (7 string)
32 52 e E3 164.8138 High E (5th tuning, 5 string)
31 51 dTemplate:Music/eTemplate:Music DTemplate:Music3/ETemplate:Music3 155.5635
30 50 d D3 146.8324 D D
29 49 cTemplate:Music/dTemplate:Music CTemplate:Music3/DTemplate:Music3 138.5913
28 48 c small octave C3 130.8128 C (5 string) C C (6 string)
27 47 B B2 123.4708
26 46 ATemplate:Music/BTemplate:Music ATemplate:Music2/BTemplate:Music2 116.5409
25 45 A A2 110.0000 A (5th tuning upright) A
24 44 GTemplate:Music/ATemplate:Music GTemplate:Music2/ATemplate:Music2 103.8262
23 43 G G2 97.99886 G G
22 42 FTemplate:Music/GTemplate:Music FTemplate:Music2/GTemplate:Music2 92.49861
21 41 F F2 87.30706 Low F (6 string) Low F (6 string)
20 40 E E2 82.40689 Low E
19 39 DTemplate:Music/ETemplate:Music DTemplate:Music2/ETemplate:Music2 77.78175
18 38 D D2 73.41619 D
17 37 CTemplate:Music/DTemplate:Music CTemplate:Music2/DTemplate:Music2 69.29566
16 36 C great octave C2 Deep C 65.40639 C
15 35 B͵ B1 61.73541 Low B (7 string)
14 34 ATemplate:Music͵/BTemplate:Music͵ ATemplate:Music1/BTemplate:Music1 58.27047
13 33 A͵ A1 55.00000 A
12 32 GTemplate:Music͵/ATemplate:Music͵ GTemplate:Music1/ATemplate:Music1 51.91309
11 31 G͵ G1 48.99943 G (5th tuning upright)
10 30 FTemplate:Music͵/GTemplate:Music͵ FTemplate:Music1/GTemplate:Music1 46.24930 Low FTemplate:Music (8 string)
9 29 F͵ F1 43.65353 Low F (6 string)
8 28 E͵ E1 41.20344 E
7 27 DTemplate:Music͵/ETemplate:Music͵ DTemplate:Music1/ETemplate:Music1 38.89087
6 26 D͵ D1 36.70810
5 25 CTemplate:Music͵/DTemplate:Music͵ CTemplate:Music1/DTemplate:Music1 34.64783 Low CTemplate:Music (9 string)
4 24 C͵ contra-octave C1 Pedal C 32.70320 C (upright extension or 5th tuning)
3 23 B͵͵ B0 30.86771 B (5 string)
2 22 ATemplate:Music͵͵/BTemplate:Music͵͵ ATemplate:Music0/BTemplate:Music0 29.13524
1 21 A͵͵ A0 27.50000
0 20 GTemplate:Music͵͵/ATemplate:Music͵͵ GTemplate:Music0/ATemplate:Music0 25.95654 Low GTemplate:Music (10 string)
-1 19 G͵͵ G0 24.49971
-2 18 FTemplate:Music͵͵/GTemplate:Music͵͵ FTemplate:Music0/GTemplate:Music0 23.12465
-3 17 F͵͵ F0 21.82676
-4 16 E͵͵ E0 20.60172
-5 15 DTemplate:Music͵͵/ETemplate:Music͵͵ DTemplate:Music0/ETemplate:Music0 19.44544
-6 14 D͵͵ D0 18.35405
-7 13 CTemplate:Music͵͵/DTemplate:Music͵͵ CTemplate:Music0/DTemplate:Music0 17.32391
-8 12 C͵͵ sub-contra-octave C0 Double Pedal C 16.35160

See also

References

<references />


Template:Musical keyboards Template:Pitch (music)

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