Frequencies of Notes

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This article uses material from the Wikipedia page available here. It is released under the Creative Commons Attribution-Share-Alike License 3.0.

Frequencies of Notes

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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 A_{4}), tuned to 440 Hz (referred to as A440). Since every octave is made of twelve steps and equals two times 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 previous by the twelfth root of two (approximately 1.059463). For example, to get the frequency a semitone up from A_{4} (A♯_{4}), multiply 440 by the twelfth root of two. To go from A_{4} to B_{4} (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 A_{4} to C_{5} (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. This deviation from equal temperament is called the Railsback curve.

The following equation gives the frequency f of the n^{th} key, as shown in the table:

(a' = A_{4} = 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:

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 C_{0} to B_{8} was first built in 2018 by Stuart & Sons.)

Key number |
Helmholtz name |
Scientific name |
Frequency (Hz) | Corresponding Open Strings | ||||
---|---|---|---|---|---|---|---|---|

Violin | Viola | Cello | Bass | Guitar | ||||

108 | b | B_{8} |
7902.133 | |||||

107 | a♯/b♭ | A♯_{8}/B♭_{8} |
7458.620 | |||||

106 | a | A_{8} |
7040.000 |
|||||

105 | g♯/a♭ | G♯_{8}/A♭_{8} |
6644.875 | |||||

104 | g | G_{8} |
6271.927 | |||||

103 | f♯/g♭ | F♯_{8}/G♭_{8} |
5919.911 | |||||

102 | f | F_{8} |
5587.652 | |||||

101 | e | E_{8} |
5274.041 | |||||

100 | d♯/e♭ | D♯_{8}/E♭_{8} |
4978.032 | |||||

99 | d | D_{8} |
4698.636 | |||||

98 | c♯/d♭ | C♯_{8}/D♭_{8} |
4434.922 | |||||

88 | c 5-line octave | C_{8} Eighth octave |
4186.009 | |||||

87 | b? | B_{7} |
3951.066 | |||||

86 | a♯?/b♭? | A♯_{7}/B♭_{7} |
3729.310 | |||||

85 | a? | A_{7} |
3520.000 |
|||||

84 | g♯?/a♭? | G♯_{7}/A♭_{7} |
3322.438 | |||||

83 | g? | G_{7} |
3135.963 | |||||

82 | f♯?/g♭? | F♯_{7}/G♭_{7} |
2959.955 | |||||

81 | f? | F_{7} |
2793.826 | |||||

80 | e? | E_{7} |
2637.020 | |||||

79 | d♯?/e♭? | D♯_{7}/E♭_{7} |
2489.016 | |||||

78 | d? | D_{7} |
2349.318 | |||||

77 | c♯?/d♭? | C♯_{7}/D♭_{7} |
2217.461 | |||||

76 | c? 4-line octave | C_{7}Double high C |
2093.005 | |||||

75 | b | B_{6} |
1975.533 | |||||

74 | a♯/b♭ | A♯_{6}/B♭_{6} |
1864.655 | |||||

73 | a | A_{6} |
1760.000 |
|||||

72 | g♯/a♭ | G♯_{6}/A♭_{6} |
1661.219 | |||||

71 | g | G_{6} |
1567.982 | |||||

70 | f♯/g♭ | F♯_{6}/G♭_{6} |
1479.978 | |||||

69 | f | F_{6} |
1396.913 | |||||

68 | e | E_{6} |
1318.510 | |||||

67 | d♯/e♭ | D♯_{6}/E♭_{6} |
1244.508 | |||||

66 | d | D_{6} |
1174.659 | |||||

65 | c♯/d♭ | C♯_{6}/D♭_{6} |
1108.731 | |||||

64 | c 3-line octave | C_{6}Soprano C (High C) |
1046.502 | |||||

63 | b | B_{5} |
987.7666 | |||||

62 | a♯/b♭ | A♯_{5}/B♭_{5} |
932.3275 | |||||

61 | a | A_{5} |
880.0000 |
|||||

60 | g♯/a♭ | G♯_{5}/A♭_{5} |
830.6094 | |||||

59 | g | G_{5} |
783.9909 | |||||

58 | f♯/g♭ | F♯_{5}/G♭_{5} |
739.9888 | |||||

57 | f | F_{5} |
698.4565 | |||||

56 | e | E_{5} |
659.2551 | E | ||||

55 | d♯/e♭ | D♯_{5}/E♭_{5} |
622.2540 | |||||

54 | d | D_{5} |
587.3295 | |||||

53 | c♯/d♭ | C♯_{5}/D♭_{5} |
554.3653 | |||||

52 | c 2-line octave | C_{5}Tenor C |
523.2511 | |||||

51 | b? | B_{4} |
493.8833 | |||||

50 | a♯?/b♭? | A♯_{4}/B♭_{4} |
466.1638 | |||||

49 | a? | A_{4}A440 |
440.0000 |
A | A | |||

48 | g♯?/a♭? | G♯_{4}/A♭_{4} |
415.3047 | |||||

47 | g? | G_{4} |
391.9954 | |||||

46 | f♯?/g♭? | F♯_{4}/G♭_{4} |
369.9944 | |||||

45 | f? | F_{4} |
349.2282 | |||||

44 | e? | E_{4} |
329.6276 | High E | ||||

43 | d♯?/e♭? | D♯_{4}/E♭_{4} |
311.1270 | |||||

42 | d? | D_{4} |
293.6648 | D | D | |||

41 | c♯?/d♭? | C♯_{4}/D♭_{4} |
277.1826 | |||||

40 | c? 1-line octave | C_{4}Middle C |
261.6256 | |||||

39 | b | B_{3} |
246.9417 | B | ||||

38 | a♯/b♭ | A♯_{3}/B♭_{3} |
233.0819 | |||||

37 | a | A_{3} |
220.0000 |
A | ||||

36 | g♯/a♭ | G♯_{3}/A♭_{3} |
207.6523 | |||||

35 | g | G_{3} |
195.9977 | G | G | G | ||

34 | f♯/g♭ | F♯_{3}/G♭_{3} |
184.9972 | |||||

33 | f | F_{3} |
174.6141 | |||||

32 | e | E_{3} |
164.8138 | |||||

31 | d♯/e♭ | D♯_{3}/E♭_{3} |
155.5635 | |||||

30 | d | D_{3} |
146.8324 | D | D | |||

29 | c♯/d♭ | C♯_{3}/D♭_{3} |
138.5913 | |||||

28 | c small octave | C_{3} |
130.8128 | C | ||||

27 | B | B_{2} |
123.4708 | |||||

26 | A♯/B♭ | A♯_{2}/B♭_{2} |
116.5409 | |||||

25 | A | A_{2} |
110.0000 |
A | ||||

24 | G♯/A♭ | G♯_{2}/A♭_{2} |
103.8262 | |||||

23 | G | G_{2} |
97.99886 | G | G | |||

22 | F♯/G♭ | F♯_{2}/G♭_{2} |
92.49861 | |||||

21 | F | F_{2} |
87.30706 | |||||

20 | E | E_{2} |
82.40689 | Low E | ||||

19 | D♯/E♭ | D♯_{2}/E♭_{2} |
77.78175 | |||||

18 | D | D_{2} |
73.41619 | D | ||||

17 | C♯/D♭ | C♯_{2}/D♭_{2} |
69.29566 | |||||

16 | C great octave | C_{2}Deep C |
65.40639 | C | ||||

15 | B? | B_{1} |
61.73541 | Low B (7 string) | ||||

14 | A♯?/B♭? | A♯_{1}/B♭_{1} |
58.27047 | |||||

13 | A? | A_{1} |
55.00000 |
A | ||||

12 | G♯?/A♭? | G♯_{1}/A♭_{1} |
51.91309 | |||||

11 | G? | G_{1} |
48.99943 | |||||

10 | F♯?/G♭? | F♯_{1}/G♭_{1} |
46.24930 | |||||

9 | F? | F_{1} |
43.65353 | |||||

8 | E? | E_{1} |
41.20344 | E | ||||

7 | D♯?/E♭? | D♯_{1}/E♭_{1} |
38.89087 | |||||

6 | D? | D_{1} |
36.70810 | |||||

5 | C♯?/D♭? | C♯_{1}/D♭_{1} |
34.64783 | |||||

4 | C? contra-octave | C_{1} Pedal C |
32.70320 | |||||

3 | B | B_{0} |
30.86771 | B (5 string) | ||||

2 | A♯/B♭ | A♯_{0}/B♭_{0} |
29.13524 | |||||

1 | A | A_{0} |
27.50000 |
|||||

97 | G♯/A♭ | G♯_{0}/A♭_{0} |
25.95654 | |||||

96 | G | G_{0} |
24.49971 | |||||

95 | F♯/G♭ | F♯_{0}/G♭_{0} |
23.12465 | |||||

94 | F | F_{0} |
21.82676 | |||||

93 | E | E_{0} |
20.60172 | |||||

92 | D♯/E♭ | D♯_{0}/E♭_{0} |
19.44544 | |||||

91 | D | D_{0} |
18.35405 | |||||

90 | C♯/D♭ | C♯_{0}/D♭_{0} |
17.32391 | |||||

89 | C sub-contra-octave | C_{0} Double Pedal C |
16.35160 |

- interactive piano frequency table - A PHP script allowing the reference pitch of A4 to be altered from 440 Hz.
- PySynth - A simple Python-based software synthesizer that prints the key frequencies table and then creates a few demo songs based on that table.
- "Keyboard and frequencies",
*SengpielAudio.com*. - Notefreqs - A complete table of note frequencies and ratios for midi, piano, guitar, bass, and violin. Includes fret measurements (in cm and inches) for building instruments.

This article uses material from the Wikipedia page available here. It is released under the Creative Commons Attribution-Share-Alike License 3.0.

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