Piano key frequencies
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This is a list of the
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
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
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′′′′′ | B8 | 99 | 7902.133 | ||||||
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
- ^ a b c 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.
- ^ a b Nov, Yuval. "Explaining the Equal Temperament". www.yuvalnov.org. Archived from the original on 2019-05-26. Retrieved 2019-12-26.
- ^ Citak, Ray. "Information on Piano Tuning". www.pianotechnician.com. Archived from the original on 2019-02-26. Retrieved 2019-12-26.
- ^ 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.
- ^ a b Goss, Clint (2019-02-18). "Octave Notation". Flutopedia. Archived from the original on 2019-05-12. Retrieved 2019-12-26.
- Michigan Tech University. Archivedfrom the original on 2019-12-16. Retrieved 2019-12-26.