Piano Key Frequencies
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Piano Key Frequencies

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). 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?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 (or just by the sixth root of two, approximately 1.12246). 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:

(a' = A4 = A440 is the 49th key on the idealized standard piano)

Alternatively, this can be written as:

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

List

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

Values in bold are exact on an ideal piano. Keys shaded gray are rare and only appear on extended pianos. The normally included 88 keys have been numbered 1-88, with the extra low keys numbered 89-97 and the extra high keys numbered 98-108. (108-key pianos do not yet exist, but one is being built in the first half of 2018 by Stuart & Sons; the current record is a 102-key piano from C0 to F8.)

Key
number
Helmholtz
name
Scientific
name
Frequency (Hz) Corresponding Open Strings
Violin Viola Cello Bass Guitar
108 b B8 7902.13
107 a?/b? A?8/B?8 7458.62
106 a A8 7040.00
105 g?/a? G?8/A?8 6644.88
104 g G8 6271.93
103 f?/g? F?8/G?8 5919.91
102 f F8 5587.65
101 e E8 5274.04
100 d?/e? D?8/E?8 4978.03
99 d D8 4698.64
98 c?/d? C?8/D?8 4434.92
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 C7Double 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 C6Soprano C (High 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 C5Tenor C 523.251
51 b? B4 493.883
50 a??/b?? A?4/B?4 466.164
49 a? A4A440 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 C4Middle 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 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 C2Deep C 65.4064 C
15 B? B1 61.7354 Low B (7 string)
14 A??/B?? A?1/B?1 58.2705
13 A? A1 55.0000 A
12 G??/A?? G?1/A?1 51.9131
11 G? G1 48.9994
10 F??/G?? F?1/G?1 46.2493
9 F? F1 43.6535
8 E? E1 41.2034 E
7 D??/E?? D?1/E?1 38.8909
6 D? D1 36.7081
5 C??/D?? C?1/D?1 34.6478
4 C? contra-octave C1 Pedal C 32.7032
3 B B0 30.8677 B (5 string)
2 A?/B? A?0/B?0 29.1352
1 A A0 27.5000
97 G?/A? G?0/A?0 25.9565
96 G G0 24.4997
95 F?/G? F?0/G?0 23.1247
94 F F0 21.8268
93 E E0 20.6017
92 D?/E? D?0/E?0 19.4454
91 D D0 18.3540
90 C?/D? C?0/D?0 17.3239
89 C sub-contra-octave C0 Double Pedal C 16.3516

See also

External links


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