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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
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
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
editValues 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 | Vocal Ranges | ||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
Soprano
|
Mezzo-soprano
|
Contralto
|
Tenor
|
Baritone
|
Bass
| ||||||||||||
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 | ||||||||||||
33 | 53 | f | F3 | 33 | 174.6141 | High F (7 String) | |||||||||||
32 | 52 | e | E3 | 32 | 164.8138 | High E (5th tunig, 5 String Bass) | |||||||||||
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 (5th tuning Upright) | 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 | Low F (6 String) | Low 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 | G (5th tuning Upright) | |||||||||||
10 | 30 | F♯͵/G♭͵ | F♯1/G♭1 | 10 | 46.24930 | Low F♯ (8 string) | |||||||||||
9 | 29 | F͵ | F1 | 9 | 43.65353 | Low F (6 String) | |||||||||||
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 or 5th tuning) | |||||||||||
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
editReferences
edit- ^ 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.
- ^ 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.