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).[1][2] 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).[1][2] For example, to get the frequency one semitone up from A4 (A♯4), 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.[3] This deviation from equal temperament is called the Railsback curve.

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

where n is shown in the table below.[1]

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

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 idealized standard piano. Keys shaded gray are rare and only appear on extended pianos. The normal 88 keys were numbered 1–88, with the extra low keys numbered 89–97 and the extra high keys numbered 98–108. A 108-key piano that extends from C0 to B8 was first built in 2018 by Stuart & Sons.[4] (Note: these piano key numbers 1-108 are not the n keys in the equations or the table.)

Piano key number MIDI note number Helmholtz name[5] Scientific pitch name[5] n Frequency f(n) (Hz) (Equal temperament) [6] Corresponding open strings on other instruments
Violin Viola Cello Bass Guitar Ukulele
108 119 b′′′′′B8997902.133
107 118 a♯′′′′′/b♭′′′′′ A♯8/B♭8 98 7458.620
106 117 a′′′′′ A8 97 7040.000
105 116 g♯′′′′′/a♭′′′′′ G♯8/A♭8 96 6644.875
104 115 g′′′′′ G8 95 6271.927
103 114 f♯′′′′′/g♭′′′′′ F♯8/G♭8 94 5919.911
102 113 f′′′′′ F8 93 5587.652
101 112 e′′′′′ E8 92 5274.041
100 111 d♯′′′′′/e♭′′′′′ D♯8/E♭8 91 4978.032
99 110 d′′′′′ D8 90 4698.636
98 109 c♯′′′′′/d♭′′′′′ C♯8/D♭8 89 4434.922
88 108 c′′′′′ 5-line octave C8 Eighth octave 88 4186.009
87 107 b′′′′ B7 87 3951.066
86 106 a♯′′′′/b♭′′′′ A♯7/B♭7 86 3729.310
85 105 a′′′′ A7 85 3520.000
84 104 g♯′′′′/a♭′′′′ G♯7/A♭7 84 3322.438
83 103 g′′′′ G7 83 3135.963
82 102 f♯′′′′/g♭′′′′ F♯7/G♭7 82 2959.955
81 101 f′′′′ F7 81 2793.826
80 100 e′′′′ E7 80 2637.020
79 99 d♯′′′′/e♭′′′′ D♯7/E♭7 79 2489.016
78 98 d′′′′ D7 78 2349.318
77 97 c♯′′′′/d♭′′′′ C♯7/D♭7 77 2217.461
76 96 c′′′′ 4-line octave C7 Double high C 76 2093.005
75 95 b′′′ B6 75 1975.533
74 94 a♯′′′/b♭′′′ A♯6/B♭6 74 1864.655
73 93 a′′′ A6 73 1760.000
72 92 g♯′′′/a♭′′′ G♯6/A♭6 72 1661.219
71 91 g′′′ G6 71 1567.982
70 90 f♯′′′/g♭′′′ F♯6/G♭6 70 1479.978
69 89 f′′′ F6 69 1396.913
68 88 e′′′ E6 68 1318.510
67 87 d♯′′′/e♭′′′ D♯6/E♭6 67 1244.508
66 86 d′′′ D6 66 1174.659
65 85 c♯′′′/d♭′′′ C♯6/D♭6 65 1108.731
64 84 c′′′ 3-line octave C6 Soprano C (High C) 64 1046.502
63 83 b′′ B5 63 987.7666
62 82 a♯′′/b♭′′ A♯5/B♭5 62 932.3275
61 81 a′′ A5 61 880.0000
60 80 g♯′′/a♭′′ G♯5/A♭5 60 830.6094
59 79 g′′ G5 59 783.9909
58 78 f♯′′/g♭′′ F♯5/G♭5 58 739.9888
57 77 f′′ F5 57 698.4565
56 76 e′′ E5 56 659.2551 E E (5 String Viola)
55 75 d♯′′/e♭′′ D♯5/E♭5 55 622.2540
54 74 d′′ D5 54 587.3295
53 73 c♯′′/d♭′′ C♯5/D♭5 53 554.3653
52 72 c′′ 2-line octave C5 Tenor C 52 523.2511
51 71 b′ B4 51 493.8833 High B (Optional for 12 String Guitar)
50 70 a♯′/b♭′ A♯4/B♭4 50 466.1638
49 69 a′ A4 A440 49 440.0000 A A High A (Optional) A
48 68 g♯′/a♭′ G♯4/A♭4 48 415.3047 High Ab (12 Single String Bass)
47 67 g′ G4 47 391.9954 High G
46 66 f♯′/g♭′ F♯4/G♭4 46 369.9944
45 65 f′ F4 45 349.2282
44 64 e′ E4 44 329.6276 High E (5 String Cello) High E E
43 63 d♯′/e♭′ D♯4/E♭4 43 311.1270 High Eb (12 String Single String Bass)
42 62 d′ D4 42 293.6648 D D
41 61 c♯′/d♭′ C♯4/D♭4 41 277.1826
40 60 c′ 1-line octave C4 Middle C 40 261.6256 C
39 59 b B3 39 246.9417 B
38 58 a♯/b♭ A♯3/B♭3 38 233.0819
37 57 a A3 37 220.0000 A
36 56 g♯/a♭ G♯3/A♭3 36 207.6523
35 55 g G3 35 195.9977 G G G Low G
34 54 f♯/g♭ F♯3/G♭3 34 184.9972 High F (7 String)
33 53 f F3 33 174.6141
32 52 e E3 32 164.8138
31 51 d♯/e♭ D♯3/E♭3 31 155.5635
30 50 d D3 30 146.8324 D D
29 49 c♯/d♭ C♯3/D♭3 29 138.5913
28 48 c small octave C3 28 130.8128 C (5 String) C C (6 string)
27 47 B B2 27 123.4708
26 46 A♯/B♭ A♯2/B♭2 26 116.5409
25 45 A A2 25 110.0000 A
24 44 G♯/A♭ G♯2/A♭2 24 103.8262
23 43 G G2 23 97.99886 G G
22 42 F♯/G♭ F♯2/G♭2 22 92.49861
21 41 F F2 21 87.30706 F (6 String) F (6 String)
20 40 E E2 20 82.40689 Low E
19 39 D♯/E♭ D♯2/E♭2 19 77.78175
18 38 D D2 18 73.41619 D
17 37 C♯/D♭ C♯2/D♭2 17 69.29566
16 36 C great octave C2 Deep C 16 65.40639 C
15 35 B͵ B1 15 61.73541 Low B (7 string)
14 34 A♯͵/B♭͵ A♯1/B♭1 14 58.27047
13 33 A͵ A1 13 55.00000 A
12 32 G♯͵/A♭͵ G♯1/A♭1 12 51.91309
11 31 G͵ G1 11 48.99943
10 30 F♯͵/G♭͵ F♯1/G♭1 10 46.24930 Low F♯ (8 string)
9 29 F͵ F1 9 43.65353
8 28 E͵ E1 8 41.20344 E
7 27 D♯͵/E♭͵ D♯1/E♭1 7 38.89087
6 26 D͵ D1 6 36.70810
5 25 C♯͵/D♭͵ C♯1/D♭1 5 34.64783 Low C#(9 String)
4 24 C͵ contra-octave C1 Pedal C 4 32.70320 C (Upright Extension)
3 23 B͵͵ B0 3 30.86771 B (5 string)
2 22 A♯͵͵/B♭͵͵ A♯0/B♭0 2 29.13524
1 21 A͵͵ A0 1 27.50000
97 20 G♯͵͵/A♭͵͵ G♯0/A♭0 0 25.95654 Low G# (10 String)
96 19 G͵͵ G0 -1 24.49971
95 18 F♯͵͵/G♭͵͵ F♯0/G♭0 -2 23.12465
94 17 F͵͵ F0 -3 21.82676
93 16 E͵͵ E0 -4 20.60172
92 15 D♯͵͵/E♭͵͵ D♯0/E♭0 -5 19.44544
91 14 D͵͵ D0 -6 18.35405
90 13 C♯͵͵/D♭͵͵ C♯0/D♭0 -7 17.32391
89 12 C͵͵ sub-contra-octave C0 Double Pedal C -8 16.35160

See also

References
  1. Weisstein, Eric. "Equal Temperament -- from Eric Weisstein's Treasure Trove of Music". Eric Weisstein's Treasure Trove of Music. Archived from the original on 2019-06-14. Retrieved 2019-12-26.
  2. Nov, Yuval. "Explaining the Equal Temperament". www.yuvalnov.org. Archived from the original on 2019-05-26. Retrieved 2019-12-26.
  3. Citak, Ray. "Information on Piano Tuning". www.pianotechnician.com. Archived from the original on 2019-02-26. Retrieved 2019-12-26.
  4. Wills, Oscar; King, Rosie (2018-09-15). "Australian behind world's grandest piano". ABC News. Australia. Archived from the original on 2019-06-11. Retrieved 2019-12-26.
  5. Goss, Clint (2019-02-18). "Octave Notation". Flutopedia. Archived from the original on 2019-05-12. Retrieved 2019-12-26.
  6. Suits, Bryan (1998). "Frequencies of Musical Notes, A4 = 440 Hz". Physics of Music — Notes. Michigan Tech University. Archived from the original on 2019-12-16. Retrieved 2019-12-26.
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