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{{Short description|none}}{{More citations needed|date=December 2019}}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).WEB,www.ericweisstein.com/encyclopedias/music/EqualTemperament.html, Equal Temperament -- from Eric Weisstein’s Treasure Trove of Music, Weisstein, Eric, Eric Weisstein’s Treasure Trove of Music, live,www.ericweisstein.com/encyclopedias/music/EqualTemperament.html," title="web.archive.org/web/20190614131343www.ericweisstein.com/encyclopedias/music/EqualTemperament.html,">web.archive.org/web/20190614131343www.ericweisstein.com/encyclopedias/music/EqualTemperament.html, 2019-06-14, 2019-12-26, WEB,www.yuvalnov.org/temperament/, Explaining the Equal Temperament, Nov, Yuval, www.yuvalnov.org, live,web.archive.org/web/20190526025417/https://www.yuvalnov.org/temperament, 2019-05-26, 2019-12-26, 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 Hz and the sixth A is 880 Hz). The frequency of a pitch is derived by multiplying (ascending) or dividing (descending) the frequency of the previous pitch by the twelfth root of two (approximately 1.059463). For example, to get the frequency one semitone up from A4 (A{{music|#}}4), multiply 440 Hz by the twelfth root of two. To go from A4 up two semitones (one whole tone) to B4, multiply 440 twice by the twelfth root of two (or once by the sixth root of two, approximately 1.122462). To go from A4 up three semitones to C5 (a minor third), multiply 440 Hz 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.WEB,www.pianotechnician.com/tuning.html, Information on Piano Tuning, Citak, Ray, www.pianotechnician.com, live,www.pianotechnician.com/tuning.html," title="web.archive.org/web/20190226033129www.pianotechnician.com/tuning.html,">web.archive.org/web/20190226033129www.pianotechnician.com/tuning.html, 2019-02-26, 2019-12-26, This deviation from equal temperament is called the Railsback curve.The following equation gives the frequency {{mvar|f}} (Hz) of the {{mvar|n}}th key on the idealized standard piano with the 49th key tuned to A4 at 440 Hz: f(n) = left(sqrt[12]{2},right)^{n-49} times 440 ,text{Hz}, = 2^{frac{n-49}{12}} times 440 ,text{Hz},where {{mvar|n}} is shown in the table below.Conversely, the key number of a pitch with a frequency {{mvar|f}} (Hz) on the idealized standard piano is: n = 12 , log_2left({frac{f}{440 ,text{Hz}}}right) + 49

List

File:Piano Frequencies.svg|frame|alt=Piano Keyboard|An 88-key piano, with the octaves numbered and Middle C (cyan) and A440 (yellow) highlighted]] (File:Piano key frequencies.png|thumb|left|50px|A printable version of the standard key frequencies (only including the 88 keys on a standard piano)){{clear}}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.WEB,www.abc.net.au/news/2018-09-15/worlds-first-108-key-concert-grand-piano-built-by-australian/10246340, Australian behind world’s grandest piano, Wills, Oscar, King, Rosie, 2018-09-15, ABC News, en-AU, Australia, live,web.archive.org/web/20190611190146/https://www.abc.net.au/news/2018-09-15/worlds-first-108-key-concert-grand-piano-built-by-australian/10246340, 2019-06-11, 2019-12-26, (Note: these piano key numbers 1-108 are not the {{mvar|n}} keys in the equations or the table.){| class=“wikitable sortable” style="text-align:center;“! rowspan=“2” width=“30px” |Piano key number! rowspan=“2” width=“30px” |MIDI note number! rowspan=“2” width=“150px” |Helmholtz nameWEB,www.flutopedia.com/octave_notation.htm, Octave Notation, Goss, Clint, 2019-02-18, Flutopedia, live,flutopedia.com/octave_notation.htm," title="web.archive.org/web/20190512205909flutopedia.com/octave_notation.htm,">web.archive.org/web/20190512205909flutopedia.com/octave_notation.htm, 2019-05-12, 2019-12-26, ! rowspan=“2” width=“140px” |Scientific pitch name! rowspan=“2” width=“20px” |{{mvar|n}}! rowspan=“2” width=“138px” |Frequency {{mvar|f}}({{mvar|n}}) (Hz) (Equal temperament) WEB,pages.mtu.edu/~suits/notefreqs.html, Frequencies of Musical Notes, A4 = 440 Hz, Suits, Bryan, 1998, Physics of Music — Notes, Michigan Tech University, live,web.archive.org/web/20191216163453/https://pages.mtu.edu/~suits/notefreqs.html, 2019-12-16, 2019-12-26, ! colspan=“6” | Corresponding open strings on other instruments-!width=“5%” | Violin!width=“6%” | Viola!width=“7%” | Cello!width=“7%” | Bass!width=“9%” | Guitar!width=“5%” | Ukulele| bgcolor=“lightgray” |

108|119				| |||||

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107	118	a{{music	b}}′′′′′	A{{music	b}}8	98	7458.620

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106	117	a′′′′′	A8	97	7040.000

105	116	g{{music	b}}′′′′′	G{{music	b}}8	96	6644.875

104	115	g′′′′′	G8	95	6271.927

103	114	f{{music	b}}′′′′′	F{{music	b}}8	94	5919.911

102	113	f′′′′′	F8	93	5587.652

101	112	e′′′′′	E8	92	5274.041

99	110	d′′′′′	D8	90	4698.636

octave	Eighth octave C>C8 Eighth octave|88|4186.009||||||

octave|C7 Double high C|76|2093.005||||||

octave|C6 Soprano C (High C)|64|1046.502||||||

octave|C5 Tenor C|52|523.2511||||||

A4 A440	440.0000|A|A| || High A (Optional)| A

octave	Middle C	40	261.6256|||||| C

octave|C3|28|130.8128|C (5 String)|C||C (6 string)||

octave|C2 Deep C|16|65.40639|||C|||

octave|C1 Pedal C|4|32.70320||||C (Upright Extension)||

96	19	G͵͵	G0	-1	24.49971

94	17	F͵͵	F0	-3	21.82676

93	16	E͵͵	E0	-4	20.60172

91	14	D͵͵	D0	-6	18.35405

89	12	C͵͵ sub-contra-octave	C0 Double Pedal C	-8	16.35160

See also

• Piano tuning
• Scientific pitch notation
• Music and mathematics

References

{{Musical keyboards}}{{Pitch (music)}}