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Piano key frequencies

From Wikipedia, the free encyclopedia

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] Since every octave is made of twelve steps and since a jump of one octave doubles the frequency (for example, the fifth A is 440 Hz and the higher octave A is 880 Hz), each successive 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 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 (or just by the sixth root of two, approximately 1.122462). To go from A4 to C5 (which is a minor third), multiply 440 three times by the twelfth root of two, (or just 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 of the nth key, as shown in the table:[1]

(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)
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. (A 108-key piano that extends from C0 to B8 was first built in 2018 by Stuart & Sons.[4])

Key number Helmholtz name[5] Scientific name[5] Frequency (Hz) (Equal temperament) [6] Corresponding open strings
Violin Viola Cello Bass Guitar Ukulele
108 b′′′′′ B8 7902.133
107 a′′′′′/b′′′′′ A8/B8 7458.620
106 a′′′′′ A8 7040.000
105 g′′′′′/a′′′′′ G8/A8 6644.875
104 g′′′′′ G8 6271.927
103 f′′′′′/g′′′′′ F8/G8 5919.911
102 f′′′′′ F8 5587.652
101 e′′′′′ E8 5274.041
100 d′′′′′/e′′′′′ D8/E8 4978.032
99 d′′′′′ D8 4698.636
98 c′′′′′/d′′′′′ C8/D8 4434.922
88 c′′′′′ 5-line octave C8 Eighth octave 4186.009
87 b′′′′ B7 3951.066
86 a′′′′/b′′′′ A7/B7 3729.310
85 a′′′′ A7 3520.000
84 g′′′′/a′′′′ G7/A7 3322.438
83 g′′′′ G7 3135.963
82 f′′′′/g′′′′ F7/G7 2959.955
81 f′′′′ F7 2793.826
80 e′′′′ E7 2637.020
79 d′′′′/e′′′′ D7/E7 2489.016
78 d′′′′ D7 2349.318
77 c′′′′/d′′′′ C7/D7 2217.461
76 c′′′′ 4-line octave C7 Double high C 2093.005
75 b′′′ B6 1975.533
74 a′′′/b′′′ A6/B6 1864.655
73 a′′′ A6 1760.000
72 g′′′/a′′′ G6/A6 1661.219
71 g′′′ G6 1567.982
70 f′′′/g′′′ F6/G6 1479.978
69 f′′′ F6 1396.913
68 e′′′ E6 1318.510
67 d′′′/e′′′ D6/E6 1244.508
66 d′′′ D6 1174.659
65 c′′′/d′′′ C6/D6 1108.731
64 c′′′ 3-line octave C6 Soprano C (High C) 1046.502
63 b′′ B5 987.7666
62 a′′/b′′ A5/B5 932.3275
61 a′′ A5 880.0000
60 g′′/a′′ G5/A5 830.6094
59 g′′ G5 783.9909
58 f′′/g′′ F5/G5 739.9888
57 f′′ F5 698.4565
56 e′′ E5 659.2551 E E (5 String Viola)
55 d′′/e′′ D5/E5 622.2540
54 d′′ D5 587.3295
53 c′′/d′′ C5/D5 554.3653
52 c′′ 2-line octave C5 Tenor C 523.2511
51 b′ B4 493.8833 High B (Optional for 12 String Guitar)
50 a′/b A4/B4 466.1638
49 a′ A4 A440 440.0000 A A High A (Optional) A
48 g′/a G4/A4 415.3047 High Ab (12 Single String Bass)
47 g′ G4 391.9954 High G
46 f′/g F4/G4 369.9944
45 f′ F4 349.2282
44 e′ E4 329.6276 High E (5 String Cello) High E E
43 d′/e D4/E4 311.1270 High Eb (12 String Single String Bass)
42 d′ D4 293.6648 D D
41 c′/d C4/D4 277.1826
40 c′ 1-line octave C4 Middle C 261.6256 C
39 b B3 246.9417 B
38 a/b A3/B3 233.0819
37 a A3 220.0000 A
36 g/a G3/A3 207.6523
35 g G3 195.9977 G G G Low G
34 f/g F3/G3 184.9972 High F (7 String)
33 f F3 174.6141
32 e E3 164.8138
31 d/e D3/E3 155.5635
30 d D3 146.8324 D D
29 c/d C3/D3 138.5913
28 c small octave C3 130.8128 C (5 String) C C (6 string)
27 B B2 123.4708
26 A/B A2/B2 116.5409
25 A A2 110.0000 A
24 G/A G2/A2 103.8262
23 G G2 97.99886 G G
22 F/G F2/G2 92.49861
21 F F2 87.30706 F (6 String) F (6 String)
20 E E2 82.40689 Low E
19 D/E D2/E2 77.78175
18 D D2 73.41619 D
17 C/D C2/D2 69.29566
16 C great octave C2 Deep C 65.40639 C
15 B1 61.73541 Low B (7 string)
14 A͵/B͵ A1/B1 58.27047
13 A1 55.00000 A
12 G͵/A͵ G1/A1 51.91309
11 G1 48.99943
10 F͵/G͵ F1/G1 46.24930 Low F (8 string)
9 F1 43.65353
8 E1 41.20344 E
7 D͵/E͵ D1/E1 38.89087
6 D1 36.70810
5 C͵/D͵ C1/D1 34.64783 Low C#(9 String)
4 C͵ contra-octave C1 Pedal C 32.70320
3 B͵͵ B0 30.86771 B (5 string)
2 A͵͵/B͵͵ A0/B0 29.13524
1 A͵͵ A0 27.50000
97 G͵͵/A͵͵ G0/A0 25.95654 Low G# (10 String)
96 G͵͵ G0 24.49971
95 F͵͵/G͵͵ F0/G0 23.12465
94 F͵͵ F0 21.82676
93 E͵͵ E0 20.60172
92 D͵͵/E͵͵ D0/E0 19.44544
91 D͵͵ D0 18.35405
90 C͵͵/D͵͵ C0/D0 17.32391
89 C͵͵ sub-contra-octave C0 Double Pedal C 16.35160

See also

External links

References

  1. ^ 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.
  2. ^ a b 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. ^ a b 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.
This page was last edited on 10 April 2021, at 19:31
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