Piano key frequencies

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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 twelve-tone equal temperament, with the 49th key, the fifth A (called A4), tuned to 440 Hz (referred to as 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 (A4), 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.

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. This deviation from equal temperament is called the Railsback curve.

The following equation gives the frequency f of the nth key, as shown in the table:


f(n) = (\sqrt[12]{2}\,)^{n-49} \times 440 \,\text{Hz}\,

(a' is the 49th key on the idealized piano)

Alternatively, this can be written as:


f(n) = 2^{\frac{n-49}{12}} \times 440 \,\text{Hz}\,

Conversely, starting from a frequency on the idealized piano tuned to A440, one obtains the key number by:


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

List[edit]

Piano Keyboard
An 88-key piano, with the octaves numbered and Middle C (cyan) and A440 (yellow) highlighted.
A printable version of the chart below.


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′′′′ A7/B7 3729.31
85 a′′′′ A7 3520.00
84 g′′′′/a′′′′ G7/A7 3322.44
83 g′′′′ G7 3135.96
82 f′′′′/g′′′′ F7/G7 2959.96
81 f′′′′ F7 2793.83
80 e′′′′ E7 2637.02
79 d′′′′/e′′′′ D7/E7 2489.02
78 d′′′′ D7 2349.32
77 c′′′′/d′′′′ C7/D7 2217.46
76 c′′′′ 4-line octave C7 Double high C 2093.00
75 b′′′ B6 1975.53
74 a′′′/b′′′ A6/B6 1864.66
73 a′′′ A6 1760.00
72 g′′′/a′′′ G6/A6 1661.22
71 g′′′ G6 1567.98
70 f′′′/g′′′ F6/G6 1479.98
69 f′′′ F6 1396.91
68 e′′′ E6 1318.51
67 d′′′/e′′′ D6/E6 1244.51
66 d′′′ D6 1174.66
65 c′′′/d′′′ C6/D6 1108.73
64 c′′′ 3-line octave C6 Soprano C (High C) 1046.50
63 b′′ B5 987.767
62 a′′/b′′ A5/B5 932.328
61 a′′ A5 880.000
60 g′′/a′′ G5/A5 830.609
59 g′′ G5 783.991
58 f′′/g′′ F5/G5 739.989
57 f′′ F5 698.456
56 e′′ E5 659.255 E
55 d′′/e′′ D5/E5 622.254
54 d′′ D5 587.330
53 c′′/d′′ C5/D5 554.365
52 c′′ 2-line octave C5 523.251
51 b′ B4 493.883
50 a′/b A4/B4 466.164
49 a′ A4 A440 440.000 A A High A (Optional)
48 g′/a G4/A4 415.305
47 g′ G4 391.995
46 f′/g F4/G4 369.994
45 f′ F4 349.228
44 e′ E4 329.628 High E
43 d′/e D4/E4 311.127
42 d′ D4 293.665 D D
41 c′/d C4/D4 277.183
40 c′ 1-line octave C4 Middle C 261.626
39 b B3 246.942 B
38 a/b A3/B3 233.082
37 a A3 220.000 A
36 g/a G3/A3 207.652
35 g G3 195.998 G G G
34 f/g F3/G3 184.997
33 f F3 174.614 F (7 string)
32 e E3 164.814
31 d/e D3/E3 155.563
30 d D3 146.832 D D
29 c/d C3/D3 138.591
28 c small octave C3 Tenor C 130.813 C (5 string) C C (6 string)
27 B B2 123.471
26 A/B A2/B2 116.541
25 A A2 110.000 A
24 G/A G2/A2 103.826
23 G G2 97.9989 G G
22 F/G F2/G2 92.4986
21 F F2 87.3071 F (6 string)
20 E E2 82.4069 Low E
19 D/E D2/E2 77.7817
18 D D2 73.4162 D
17 C/D C2/D2 69.2957
16 C great octave C2 Deep C 65.4064 C
15 B1 61.7354 B (7 string)
14 A͵/B͵ A1/B1 58.2705 B (7 string)
13 A1 55.0000 A
12 G͵/A͵ G1/A1 51.9131
11 G1 48.9994
10 F͵/G͵ F1/G1 46.2493 F (8 string)
9 F1 43.6535
8 E1 41.2034 E
7 D͵/E͵ D1/E1 38.8909
6 D1 36.7081
5 C͵/D͵ C1/D1 34.6478 C (9 string)
4 C͵ contra-octave C1 Pedal C 32.7032
3 B͵͵ B0 30.8677 B (5 string)
2 A͵͵/B͵͵ A0/B0 29.1352
1 A͵͵ sub-contra-octave A0 Double Pedal A 27.5000

See also[edit]

External links[edit]