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 sixth 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 one semitone up from A4 (A♯4), multiply 440 by the twelfth root of two. To go from A4 to B4 (up one whole tone, or two semitones), multiply 440 twice by the twelfth root of two (or once 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 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 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:
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 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])
^ abcWeisstein, Eric. "Equal Temperament -- from Eric Weisstein's Treasure Trove of Music". Eric Weisstein's Treasure Trove of Music. from the original on 2019-06-14. Retrieved 2019-12-26.
^ abNov, Yuval. "Explaining the Equal Temperament". www.yuvalnov.org. from the original on 2019-05-26. Retrieved 2019-12-26.
^Citak, Ray. "Information on Piano Tuning". www.pianotechnician.com. 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. from the original on 2019-06-11. Retrieved 2019-12-26.
^ abGoss, Clint (2019-02-18). "Octave Notation". Flutopedia. 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. from the original on 2019-12-16. Retrieved 2019-12-26.
External links
interactive piano frequency table – A PHP script allowing the reference pitch of A4 to be altered from 440 Hz.
– 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.
February 19, 2023
piano, frequencies, this, article, needs, additional, citations, verification, please, help, improve, this, article, adding, citations, reliable, sources, unsourced, material, challenged, removed, find, sources, news, newspapers, books, scholar, jstor, decembe. This article needs additional citations for verification Please help improve this article by adding citations to reliable sources Unsourced material may be challenged and removed Find sources Piano key frequencies news newspapers books scholar JSTOR December 2019 Learn how and when to remove this template message 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 sixth 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 one semitone up from A4 A 4 multiply 440 by the twelfth root of two To go from A4 to B4 up one whole tone or two semitones multiply 440 twice by the twelfth root of two or once 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 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 of the n th key as shown in the table 1 f n 2 12 n 49 440 Hz displaystyle f n left sqrt 12 2 right n 49 times 440 text Hz a A4 A440 is the 49th key on the idealized standard piano Alternatively this can be written as f n 2 n 49 12 440 Hz displaystyle f n 2 frac n 49 12 times 440 text Hz Conversely starting from a frequency on the idealized standard piano tuned to A440 one obtains the key number by n 12 log 2 f 440 Hz 49 displaystyle n 12 log 2 left frac f 440 text Hz right 49 Contents 1 List 2 See also 3 References 4 External linksList Edit 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 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 amp Sons 4 Key number MIDI note Helmholtz name 5 Scientific name 5 Frequency Hz Equal temperament 6 Corresponding open stringsViolin Viola Cello Bass Guitar Ukulele108 119 b B8 7902 133107 118 a b A 8 B 8 7458 620106 117 a A8 7040 000105 116 g a G 8 A 8 6644 875104 115 g G8 6271 927103 114 f g F 8 G 8 5919 911102 113 f F8 5587 652101 112 e E8 5274 041100 111 d e D 8 E 8 4978 03299 110 d D8 4698 63698 109 c d C 8 D 8 4434 92288 108 c 5 line octave C8 Eighth octave 4186 00987 107 b B7 3951 06686 106 a b A 7 B 7 3729 31085 105 a A7 3520 00084 104 g a G 7 A 7 3322 43883 103 g G7 3135 96382 102 f g F 7 G 7 2959 95581 101 f F7 2793 82680 100 e E7 2637 02079 99 d e D 7 E 7 2489 01678 98 d D7 2349 31877 97 c d C 7 D 7 2217 46176 96 c 4 line octave C7 Double high C 2093 00575 95 b B6 1975 53374 94 a b A 6 B 6 1864 65573 93 a A6 1760 00072 92 g a G 6 A 6 1661 21971 91 g G6 1567 98270 90 f g F 6 G 6 1479 97869 89 f F6 1396 91368 88 e E6 1318 51067 87 d e D 6 E 6 1244 50866 86 d D6 1174 65965 85 c d C 6 D 6 1108 73164 84 c 3 line octave C6 Soprano C High C 1046 50263 83 b B5 987 766662 82 a b A 5 B 5 932 327561 81 a A5 880 000060 80 g a G 5 A 5 830 609459 79 g G5 783 990958 78 f g F 5 G 5 739 988857 77 f F5 698 456556 76 e E5 659 2551 E E 5 String Viola 55 75 d e D 5 E 5 622 254054 74 d D5 587 329553 73 c d C 5 D 5 554 365352 72 c 2 line octave C5 Tenor C 523 251151 71 b B4 493 8833 High B Optional for 12 String Guitar 50 70 a b A 4 B 4 466 163849 69 a A4 A440 440 0000 A A High A Optional A48 68 g a G 4 A 4 415 3047 High Ab 12 Single String Bass 47 67 g G4 391 9954 High G46 66 f g F 4 G 4 369 994445 65 f F4 349 228244 64 e E4 329 6276 High E 5 String Cello High E E43 63 d e D 4 E 4 311 1270 High Eb 12 String Single String Bass 42 62 d D4 293 6648 D D41 61 c d C 4 D 4 277 182640 60 c 1 line octave C4 Middle C 261 6256 C39 59 b B3 246 9417 B38 58 a b A 3 B 3 233 081937 57 a A3 220 0000 A36 56 g a G 3 A 3 207 652335 55 g G3 195 9977 G G G Low G34 54 f g F 3 G 3 184 9972 High F 7 String 33 53 f F3 174 614132 52 e E3 164 813831 51 d e D 3 E 3 155 563530 50 d D3 146 8324 D D29 49 c d C 3 D 3 138 591328 48 c small octave C3 130 8128 C 5 String C C 6 string 27 47 B B2 123 470826 46 A B A 2 B 2 116 540925 45 A A2 110 0000 A24 44 G A G 2 A 2 103 826223 43 G G2 97 99886 G G22 42 F G F 2 G 2 92 4986121 41 F F2 87 30706 F 6 String F 6 String 20 40 E E2 82 40689 Low E19 39 D E D 2 E 2 77 7817518 38 D D2 73 41619 D17 37 C D C 2 D 2 69 2956616 36 C great octave C2 Deep C 65 40639 C15 35 B B1 61 73541 Low B 7 string 14 34 A B A 1 B 1 58 2704713 33 A A1 55 00000 A12 32 G A G 1 A 1 51 9130911 31 G G1 48 9994310 30 F G F 1 G 1 46 24930 Low F 8 string 9 29 F F1 43 653538 28 E E1 41 20344 E7 27 D E D 1 E 1 38 890876 26 D D1 36 708105 25 C D C 1 D 1 34 64783 Low C 9 String 4 24 C contra octave C1 Pedal C 32 70320 C Upright Extension 3 23 B B0 30 86771 B 5 string 2 22 A B A 0 B 0 29 135241 21 A A0 27 5000097 20 G A G 0 A 0 25 95654 Low G 10 String 96 19 G G0 24 4997195 18 F G F 0 G 0 23 1246594 17 F F0 21 8267693 16 E E0 20 6017292 15 D E D 0 E 0 19 4454491 14 D D0 18 3540590 13 C D C 0 D 0 17 3239189 12 C sub contra octave C0 Double Pedal C 16 35160See also EditPiano tuning Scientific pitch notation Music and mathematicsReferences 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 External links Editinteractive 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 Retrieved from https en wikipedia org w index php title Piano key frequencies amp oldid 1133218592, wikipedia, wiki, book, books, library,
