Piano key frequencies: Difference between revisions
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{{Short description| |
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{{More citations needed|date=December 2019}} |
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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 [[Equal temperament#Twelve-tone equal temperament|twelve-tone equal temperament]], with the 49th key, the fifth A (called A<sub>4</sub>), tuned to 440 Hz (referred to as [[A440 (pitch standard)|A440]]).<ref name=":0">{{Cite web|url=http://www.ericweisstein.com/encyclopedias/music/EqualTemperament.html|title=Equal Temperament -- from Eric Weisstein's Treasure Trove of Music|last=Weisstein|first=Eric|website=Eric Weisstein's Treasure Trove of Music|url-status=live|archive-url=https://web.archive.org/web/20190614131343/http://www.ericweisstein.com/encyclopedias/music/EqualTemperament.html|archive-date=2019-06-14|access-date=2019-12-26}}</ref><ref name=":1">{{Cite web|url=https://www.yuvalnov.org/temperament/|title=Explaining the Equal Temperament|last=Nov|first=Yuval|website=www.yuvalnov.org|url-status=live|archive-url=https://web.archive.org/web/20190526025417/https://www.yuvalnov.org/temperament|archive-date=2019-05-26|access-date=2019-12-26}}</ref> |
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 [[Equal temperament#Twelve-tone equal temperament|twelve-tone equal temperament]], with the 49th key, the fifth A (called A<sub>4</sub>), tuned to 440 Hz (referred to as [[A440 (pitch standard)|A440]]).<ref name=":0">{{Cite web|url=http://www.ericweisstein.com/encyclopedias/music/EqualTemperament.html|title=Equal Temperament -- from Eric Weisstein's Treasure Trove of Music|last=Weisstein|first=Eric|website=Eric Weisstein's Treasure Trove of Music|url-status=live|archive-url=https://web.archive.org/web/20190614131343/http://www.ericweisstein.com/encyclopedias/music/EqualTemperament.html|archive-date=2019-06-14|access-date=2019-12-26}}</ref><ref name=":1">{{Cite web|url=https://www.yuvalnov.org/temperament/|title=Explaining the Equal Temperament|last=Nov|first=Yuval|website=www.yuvalnov.org|url-status=live|archive-url=https://web.archive.org/web/20190526025417/https://www.yuvalnov.org/temperament|archive-date=2019-05-26|access-date=2019-12-26}}</ref> 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).<ref name=":0" /><ref name=":1" /> For example, to get the frequency one semitone up from A<sub>4</sub> (A{{music|#}}<sub>4</sub>), multiply 440 Hz by the twelfth root of two. To go from A<sub>4</sub> up two semitones (one [[whole tone]]) to B<sub>4</sub>, multiply 440 twice by the twelfth root of two (or once by the sixth root of two, approximately 1.122462). To go from A<sub>4</sub> up three semitones to C<sub>5</sub> (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]]. |
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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 (music)|sharp]]. To compensate for this, octaves are tuned slightly wide, [[stretched octave|stretched]] according to the inharmonic characteristics of each instrument.<ref>{{Cite web|url=https://www.pianotechnician.com/tuning.html|title=Information on Piano Tuning|last=Citak|first=Ray|website=www.pianotechnician.com|url-status=live|archive-url=https://web.archive.org/web/20190226033129/http://www.pianotechnician.com/tuning.html|archive-date=2019-02-26|access-date=2019-12-26}}</ref> This deviation from equal temperament is called the [[Railsback curve]]. |
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 (music)|sharp]]. To compensate for this, octaves are tuned slightly wide, [[stretched octave|stretched]] according to the inharmonic characteristics of each instrument.<ref>{{Cite web|url=https://www.pianotechnician.com/tuning.html|title=Information on Piano Tuning|last=Citak|first=Ray|website=www.pianotechnician.com|url-status=live|archive-url=https://web.archive.org/web/20190226033129/http://www.pianotechnician.com/tuning.html|archive-date=2019-02-26|access-date=2019-12-26}}</ref> This deviation from equal temperament is called the [[Railsback curve]]. |
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The following equation gives the frequency {{mvar|f}} of the {{mvar|n}}<sup>th</sup> key, as shown in the table:<ref name=":0" /> |
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The following equation gives the frequency {{mvar|f}} (Hz) of the {{mvar|n}}<sup>th</sup> key on the idealized standard piano with the 49th key tuned to A<sub>4</sub> at 440 Hz: |
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:<math> |
:<math> |
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f(n) = \left(\sqrt[12]{2}\,\right)^{n-49} \times 440 \,\text{Hz}\, |
f(n) = \left(\sqrt[12]{2}\,\right)^{n-49} \times 440 \,\text{Hz}\, = 2^{\frac{n-49}{12}} \times 440 \,\text{Hz}\, |
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</math> |
</math> |
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where {{mvar|n}} is shown in the table below.<ref name=":0" /> |
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(a' = A<sub>4</sub> = A440 is the 49th key on the idealized standard piano) |
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Conversely, the key number of a pitch with a frequency {{mvar|f}} (Hz) on the idealized standard piano is: |
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Alternatively, this can be written as: |
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:<math> |
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f(n) = 2^{\frac{n-49}{12}} \times 440 \,\text{Hz}\, |
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</math> |
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Conversely, starting from a frequency on the idealized standard piano tuned to A440, one obtains the key number by: |
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:<math> |
:<math> |
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n = 12 \, \log_2\left({\frac{f}{440 \,\text{Hz}}}\right) + 49 |
n = 12 \, \log_2\left({\frac{f}{440 \,\text{Hz}}}\right) + 49 |
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[[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)]] |
[[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)]] |
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{{clear}} |
{{clear}} |
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Values in '''bold''' are exact on an |
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 C<sub>0</sub> to B<sub>8</sub> was first built in 2018 by [[Stuart & Sons]].<ref>{{Cite web|url=https://www.abc.net.au/news/2018-09-15/worlds-first-108-key-concert-grand-piano-built-by-australian/10246340|title=Australian behind world's grandest piano|last=Wills|first=Oscar|last2=King|first2=Rosie|date=2018-09-15|website=ABC News|language=en-AU|publication-place=Australia|url-status=live|archive-url=https://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|archive-date=2019-06-11|access-date=2019-12-26}}</ref> (Note: these piano key numbers 1-108 are not the {{mvar|n}} keys in the equations or the table.) |
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<!--PLEASE DO NOT "CORRECT" THE KEY NUMBERS; KEYS 89 THROUGH 97 ARE AT THE BOTTOM--> |
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<!--PLEASE DO NOT CORRECT THE PIANO KEY NUMBERS; KEYS 89 THROUGH 97 ARE AT THE BOTTOM OF TABLE--> |
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{| class="wikitable sortable" style="text-align:center;" |
{| class="wikitable sortable" style="text-align:center;" |
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! rowspan="2" width="30px" | |
! rowspan="2" width="30px" |Piano key number |
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! rowspan="2" width="30px" |MIDI note |
! rowspan="2" width="30px" |MIDI note number |
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! rowspan="2" width="150px" |[[Helmholtz pitch notation|Helmholtz]] name<ref name=":2">{{Cite web|url=http://www.flutopedia.com/octave_notation.htm|title=Octave Notation|last=Goss|first=Clint|date=2019-02-18|website=Flutopedia|url-status=live|archive-url=https://web.archive.org/web/20190512205909/http://flutopedia.com/octave_notation.htm|archive-date=2019-05-12|access-date=2019-12-26}}</ref> |
! rowspan="2" width="150px" |[[Helmholtz pitch notation|Helmholtz]] name<ref name=":2">{{Cite web|url=http://www.flutopedia.com/octave_notation.htm|title=Octave Notation|last=Goss|first=Clint|date=2019-02-18|website=Flutopedia|url-status=live|archive-url=https://web.archive.org/web/20190512205909/http://flutopedia.com/octave_notation.htm|archive-date=2019-05-12|access-date=2019-12-26}}</ref> |
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! rowspan="2" width="140px" |[[Scientific pitch notation|Scientific]] name<ref name=":2" /> |
! rowspan="2" width="140px" |[[Scientific pitch notation|Scientific pitch]] name<ref name=":2" /> |
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! rowspan="2" width="20px" |{{mvar|n}} |
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! rowspan="2" width="138px" |Frequency ([[Hertz|Hz]]) (Equal temperament) <ref>{{Cite web|url=https://pages.mtu.edu/~suits/notefreqs.html|title=Frequencies of Musical Notes, A4 = 440 Hz|last=Suits|first=Bryan|year=1998|website=Physics of Music — Notes|publisher=[[Michigan Tech University]]|url-status=live|archive-url=https://web.archive.org/web/20191216163453/https://pages.mtu.edu/~suits/notefreqs.html|archive-date=2019-12-16|access-date=2019-12-26}}</ref> |
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! rowspan="2" width="138px" |Frequency {{mvar|f}}({{mvar|n}}) ([[Hertz|Hz]]) (Equal temperament) <ref>{{Cite web|url=https://pages.mtu.edu/~suits/notefreqs.html|title=Frequencies of Musical Notes, A4 = 440 Hz|last=Suits|first=Bryan|year=1998|website=Physics of Music — Notes|publisher=[[Michigan Tech University]]|url-status=live|archive-url=https://web.archive.org/web/20191216163453/https://pages.mtu.edu/~suits/notefreqs.html|archive-date=2019-12-16|access-date=2019-12-26}}</ref> |
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! colspan="6" | Corresponding open strings |
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! colspan="6" | Corresponding open strings on other instruments |
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|-- |
|-- |
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!width="5%" | [[Violin#Tuning|Violin]] |
!width="5%" | [[Violin#Tuning|Violin]] |
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||108 |
||108 |
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|119 |
|119 |
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| b′′′′′ || B<sub>8</sub>|| 7902.133 || |
| b′′′′′ || B<sub>8</sub>||99|| 7902.133 || |
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| bgcolor="lightgray" | a{{music|#}}′′′′′/b{{music|b}}′′′′′ |
| bgcolor="lightgray" | a{{music|#}}′′′′′/b{{music|b}}′′′′′ |
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| bgcolor="lightgray" | A{{music|#}}<sub>8</sub>/B{{music|b}}<sub>8</sub> |
| bgcolor="lightgray" | A{{music|#}}<sub>8</sub>/B{{music|b}}<sub>8</sub> |
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| bgcolor="lightgray" | 98 |
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| bgcolor="lightgray" | 7458.620 |
| bgcolor="lightgray" | 7458.620 |
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| bgcolor="lightgray" | |
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| bgcolor="lightgray" | a′′′′′ |
| bgcolor="lightgray" | a′′′′′ |
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| bgcolor="lightgray" | A<sub>8</sub> |
| bgcolor="lightgray" | A<sub>8</sub> |
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| bgcolor="lightgray" | 97 |
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| bgcolor="lightgray" |'''7040.000''' |
| bgcolor="lightgray" |'''7040.000''' |
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| bgcolor="lightgray" | g{{music|#}}′′′′′/a{{music|b}}′′′′′ |
| bgcolor="lightgray" | g{{music|#}}′′′′′/a{{music|b}}′′′′′ |
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| bgcolor="lightgray" | G{{music|#}}<sub>8</sub>/A{{music|b}}<sub>8</sub> |
| bgcolor="lightgray" | G{{music|#}}<sub>8</sub>/A{{music|b}}<sub>8</sub> |
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| bgcolor="lightgray" | 96 |
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| bgcolor="lightgray" |6644.875 |
| bgcolor="lightgray" |6644.875 |
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| bgcolor="lightgray" | g′′′′′ |
| bgcolor="lightgray" | g′′′′′ |
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| bgcolor="lightgray" | G<sub>8</sub> |
| bgcolor="lightgray" | G<sub>8</sub> |
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| bgcolor="lightgray" | 95 |
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| bgcolor="lightgray" |6271.927 |
| bgcolor="lightgray" |6271.927 |
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| bgcolor="lightgray" | f{{music|#}}′′′′′/g{{music|b}}′′′′′ |
| bgcolor="lightgray" | f{{music|#}}′′′′′/g{{music|b}}′′′′′ |
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| bgcolor="lightgray" | F{{music|#}}<sub>8</sub>/G{{music|b}}<sub>8</sub> |
| bgcolor="lightgray" | F{{music|#}}<sub>8</sub>/G{{music|b}}<sub>8</sub> |
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| bgcolor="lightgray" | 94 |
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| bgcolor="lightgray" | 5919.911 |
| bgcolor="lightgray" | 5919.911 |
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| bgcolor="lightgray" | f′′′′′ |
| bgcolor="lightgray" | f′′′′′ |
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| bgcolor="lightgray" | F<sub>8</sub> |
| bgcolor="lightgray" | F<sub>8</sub> |
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| bgcolor="lightgray" | 93 |
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| bgcolor="lightgray" | 5587.652 |
| bgcolor="lightgray" | 5587.652 |
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| bgcolor="lightgray" | e′′′′′ |
| bgcolor="lightgray" | e′′′′′ |
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| bgcolor="lightgray" | E<sub>8</sub> |
| bgcolor="lightgray" | E<sub>8</sub> |
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| bgcolor="lightgray" | 92 |
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| bgcolor="lightgray" | 5274.041 |
| bgcolor="lightgray" | 5274.041 |
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| bgcolor="lightgray" | d{{music|#}}′′′′′/e{{music|b}}′′′′′ |
| bgcolor="lightgray" | d{{music|#}}′′′′′/e{{music|b}}′′′′′ |
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| bgcolor="lightgray" | D{{music|#}}<sub>8</sub>/E{{music|b}}<sub>8</sub> |
| bgcolor="lightgray" | D{{music|#}}<sub>8</sub>/E{{music|b}}<sub>8</sub> |
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| bgcolor="lightgray" | 91 |
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| bgcolor="lightgray" | 4978.032 |
| bgcolor="lightgray" | 4978.032 |
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| bgcolor="lightgray" | d′′′′′ |
| bgcolor="lightgray" | d′′′′′ |
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| bgcolor="lightgray" | D<sub>8</sub> |
| bgcolor="lightgray" | D<sub>8</sub> |
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| bgcolor="lightgray" | 90 |
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| bgcolor="lightgray" | 4698.636 |
| bgcolor="lightgray" | 4698.636 |
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| bgcolor="lightgray" | c{{music|#}}′′′′′/d{{music|b}}′′′′′ |
| bgcolor="lightgray" | c{{music|#}}′′′′′/d{{music|b}}′′′′′ |
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| bgcolor="lightgray" | C{{music|#}}<sub>8</sub>/D{{music|b}}<sub>8</sub> |
| bgcolor="lightgray" | C{{music|#}}<sub>8</sub>/D{{music|b}}<sub>8</sub> |
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| bgcolor="lightgray" | 89 |
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| bgcolor="lightgray" | 4434.922 |
| bgcolor="lightgray" | 4434.922 |
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|c′′′′′ 5-line [[octave]] |
|c′′′′′ 5-line [[octave]] |
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|[[Eighth octave C|C<sub>8</sub>]] Eighth octave |
|[[Eighth octave C|C<sub>8</sub>]] Eighth octave |
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|88 |
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|4186.009 |
|4186.009 |
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|b′′′′ |
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|B<sub>7</sub> |
|B<sub>7</sub> |
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|87 |
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|a{{music|#}}′′′′/b{{music|b}}′′′′ |
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|A{{music|#}}<sub>7</sub>/B{{music|b}}<sub>7</sub> |
|A{{music|#}}<sub>7</sub>/B{{music|b}}<sub>7</sub> |
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|86 |
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|a′′′′ |
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|A<sub>7</sub> |
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|85 |
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|'''3520.000''' |
|'''3520.000''' |
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|g{{music|#}}′′′′/a{{music|b}}′′′′ |
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|G{{music|#}}<sub>7</sub>/A{{music|b}}<sub>7</sub> |
|G{{music|#}}<sub>7</sub>/A{{music|b}}<sub>7</sub> |
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|84 |
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|g′′′′ |
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|G<sub>7</sub> |
|G<sub>7</sub> |
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|83 |
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|f{{music|#}}′′′′/g{{music|b}}′′′′ |
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|F{{music|#}}<sub>7</sub>/G{{music|b}}<sub>7</sub> |
|F{{music|#}}<sub>7</sub>/G{{music|b}}<sub>7</sub> |
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|f′′′′ |
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|F<sub>7</sub> |
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|e′′′′ |
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|E<sub>7</sub> |
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|D{{music|#}}<sub>7</sub>/E{{music|b}}<sub>7</sub> |
|D{{music|#}}<sub>7</sub>/E{{music|b}}<sub>7</sub> |
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|79 |
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|d′′′′ |
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|D<sub>7</sub> |
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|c{{music|#}}′′′′/d{{music|b}}′′′′ |
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|C{{music|#}}<sub>7</sub>/D{{music|b}}<sub>7</sub> |
|C{{music|#}}<sub>7</sub>/D{{music|b}}<sub>7</sub> |
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|77 |
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|2217.461 |
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|c′′′′ 4-line [[octave]] |
|c′′′′ 4-line [[octave]] |
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|C<sub>7</sub> [[Double high C]] |
|C<sub>7</sub> [[Double high C]] |
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|76 |
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|b′′′ |
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|B<sub>6</sub> |
|B<sub>6</sub> |
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|75 |
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|1975.533 |
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|a{{music|#}}′′′/b{{music|b}}′′′ |
|a{{music|#}}′′′/b{{music|b}}′′′ |
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|A{{music|#}}<sub>6</sub>/B{{music|b}}<sub>6</sub> |
|A{{music|#}}<sub>6</sub>/B{{music|b}}<sub>6</sub> |
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|74 |
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|a′′′ |
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|A<sub>6</sub> |
|A<sub>6</sub> |
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|73 |
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|'''1760.000''' |
|'''1760.000''' |
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|g{{music|#}}′′′/a{{music|b}}′′′ |
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|G{{music|#}}<sub>6</sub>/A{{music|b}}<sub>6</sub> |
|G{{music|#}}<sub>6</sub>/A{{music|b}}<sub>6</sub> |
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|72 |
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|g′′′ |
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|G<sub>6</sub> |
|G<sub>6</sub> |
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|71 |
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|1567.982 |
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|f{{music|#}}′′′/g{{music|b}}′′′ |
|f{{music|#}}′′′/g{{music|b}}′′′ |
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|F{{music|#}}<sub>6</sub>/G{{music|b}}<sub>6</sub> |
|F{{music|#}}<sub>6</sub>/G{{music|b}}<sub>6</sub> |
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|70 |
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|1479.978 |
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Line 405: | Line 430: | ||
|f′′′ |
|f′′′ |
||
|F<sub>6</sub> |
|F<sub>6</sub> |
||
|69 |
|||
|1396.913 |
|1396.913 |
||
| |
| |
||
Line 417: | Line 443: | ||
|e′′′ |
|e′′′ |
||
|E<sub>6</sub> |
|E<sub>6</sub> |
||
|68 |
|||
|1318.510 |
|1318.510 |
||
| |
| |
||
Line 429: | Line 456: | ||
|d{{music|#}}′′′/e{{music|b}}′′′ |
|d{{music|#}}′′′/e{{music|b}}′′′ |
||
|D{{music|#}}<sub>6</sub>/E{{music|b}}<sub>6</sub> |
|D{{music|#}}<sub>6</sub>/E{{music|b}}<sub>6</sub> |
||
|67 |
|||
|1244.508 |
|1244.508 |
||
| |
| |
||
Line 441: | Line 469: | ||
|d′′′ |
|d′′′ |
||
|D<sub>6</sub> |
|D<sub>6</sub> |
||
|66 |
|||
|1174.659 |
|1174.659 |
||
| |
| |
||
Line 453: | Line 482: | ||
|c{{music|#}}′′′/d{{music|b}}′′′ |
|c{{music|#}}′′′/d{{music|b}}′′′ |
||
|C{{music|#}}<sub>6</sub>/D{{music|b}}<sub>6</sub> |
|C{{music|#}}<sub>6</sub>/D{{music|b}}<sub>6</sub> |
||
|65 |
|||
|1108.731 |
|1108.731 |
||
| |
| |
||
Line 465: | Line 495: | ||
|c′′′ 3-line [[octave]] |
|c′′′ 3-line [[octave]] |
||
|C<sub>6</sub> [[Soprano C]] (High C) |
|C<sub>6</sub> [[Soprano C]] (High C) |
||
|64 |
|||
|1046.502 |
|1046.502 |
||
| |
| |
||
Line 477: | Line 508: | ||
|b′′ |
|b′′ |
||
|B<sub>5</sub> |
|B<sub>5</sub> |
||
|63 |
|||
|987.7666 |
|987.7666 |
||
| |
| |
||
Line 489: | Line 521: | ||
|a{{music|#}}′′/b{{music|b}}′′ |
|a{{music|#}}′′/b{{music|b}}′′ |
||
|A{{music|#}}<sub>5</sub>/B{{music|b}}<sub>5</sub> |
|A{{music|#}}<sub>5</sub>/B{{music|b}}<sub>5</sub> |
||
|62 |
|||
|932.3275 |
|932.3275 |
||
| |
| |
||
Line 501: | Line 534: | ||
|a′′ |
|a′′ |
||
|A<sub>5</sub> |
|A<sub>5</sub> |
||
|61 |
|||
|'''880.0000''' |
|'''880.0000''' |
||
| |
| |
||
Line 513: | Line 547: | ||
|g{{music|#}}′′/a{{music|b}}′′ |
|g{{music|#}}′′/a{{music|b}}′′ |
||
|G{{music|#}}<sub>5</sub>/A{{music|b}}<sub>5</sub> |
|G{{music|#}}<sub>5</sub>/A{{music|b}}<sub>5</sub> |
||
|60 |
|||
|830.6094 |
|830.6094 |
||
| |
| |
||
Line 525: | Line 560: | ||
|g′′ |
|g′′ |
||
|G<sub>5</sub> |
|G<sub>5</sub> |
||
|59 |
|||
|783.9909 |
|783.9909 |
||
| |
| |
||
Line 537: | Line 573: | ||
|f{{music|#}}′′/g{{music|b}}′′ |
|f{{music|#}}′′/g{{music|b}}′′ |
||
|F{{music|#}}<sub>5</sub>/G{{music|b}}<sub>5</sub> |
|F{{music|#}}<sub>5</sub>/G{{music|b}}<sub>5</sub> |
||
|58 |
|||
|739.9888 |
|739.9888 |
||
| |
| |
||
Line 549: | Line 586: | ||
|f′′ |
|f′′ |
||
|F<sub>5</sub> |
|F<sub>5</sub> |
||
|57 |
|||
|698.4565 |
|698.4565 |
||
| |
| |
||
Line 561: | Line 599: | ||
|e′′ |
|e′′ |
||
|E<sub>5</sub> |
|E<sub>5</sub> |
||
|56 |
|||
|659.2551 |
|659.2551 |
||
|E |
|E |
||
Line 573: | Line 612: | ||
|d{{music|#}}′′/e{{music|b}}′′ |
|d{{music|#}}′′/e{{music|b}}′′ |
||
|D{{music|#}}<sub>5</sub>/E{{music|b}}<sub>5</sub> |
|D{{music|#}}<sub>5</sub>/E{{music|b}}<sub>5</sub> |
||
|55 |
|||
|622.2540 |
|622.2540 |
||
| |
| |
||
Line 585: | Line 625: | ||
|d′′ |
|d′′ |
||
|D<sub>5</sub> |
|D<sub>5</sub> |
||
|54 |
|||
|587.3295 |
|587.3295 |
||
| |
| |
||
Line 597: | Line 638: | ||
|c{{music|#}}′′/d{{music|b}}′′ |
|c{{music|#}}′′/d{{music|b}}′′ |
||
|C{{music|#}}<sub>5</sub>/D{{music|b}}<sub>5</sub> |
|C{{music|#}}<sub>5</sub>/D{{music|b}}<sub>5</sub> |
||
|53 |
|||
|554.3653 |
|554.3653 |
||
| |
| |
||
Line 609: | Line 651: | ||
|c′′ 2-line [[octave]] |
|c′′ 2-line [[octave]] |
||
|C<sub>5</sub> [[Tenor C]] |
|C<sub>5</sub> [[Tenor C]] |
||
|52 |
|||
|523.2511 |
|523.2511 |
||
| |
| |
||
Line 621: | Line 664: | ||
|b′ |
|b′ |
||
|B<sub>4</sub> |
|B<sub>4</sub> |
||
|51 |
|||
|493.8833 |
|493.8833 |
||
| |
| |
||
Line 633: | Line 677: | ||
|a{{music|#}}′/b{{music|b}}′ |
|a{{music|#}}′/b{{music|b}}′ |
||
|A{{music|#}}<sub>4</sub>/B{{music|b}}<sub>4</sub> |
|A{{music|#}}<sub>4</sub>/B{{music|b}}<sub>4</sub> |
||
|50 |
|||
|466.1638 |
|466.1638 |
||
| |
| |
||
Line 641: | Line 686: | ||
| |
| |
||
|- |
|- |
||
| bgcolor="white" style="color:black" | 49 |
| bgcolor="white" style="color:black" | 49 |
||
|69 |
|69 |
||
|a′ |
|a′ |
||
|A<sub>4</sub> [[A440 (pitch standard)|A440]] |
| bgcolor="yellow" style="color:black" |A<sub>4</sub> [[A440 (pitch standard) | A440]] |
||
| bgcolor="yellow" style="color:black" |49 |
|||
| bgcolor="yellow" style="color:black" |'''440.0000''' |
| bgcolor="yellow" style="color:black" |'''440.0000''' |
||
|A |
|A |
||
Line 657: | Line 703: | ||
|g{{music|#}}′/a{{music|b}}′ |
|g{{music|#}}′/a{{music|b}}′ |
||
|G{{music|#}}<sub>4</sub>/A{{music|b}}<sub>4</sub> |
|G{{music|#}}<sub>4</sub>/A{{music|b}}<sub>4</sub> |
||
|48 |
|||
|415.3047 |
|415.3047 |
||
| |
| |
||
Line 669: | Line 716: | ||
|g′ |
|g′ |
||
|G<sub>4</sub> |
|G<sub>4</sub> |
||
|47 |
|||
|391.9954 |
|391.9954 |
||
| |
| |
||
Line 681: | Line 729: | ||
|f{{music|#}}′/g{{music|b}}′ |
|f{{music|#}}′/g{{music|b}}′ |
||
|F{{music|#}}<sub>4</sub>/G{{music|b}}<sub>4</sub> |
|F{{music|#}}<sub>4</sub>/G{{music|b}}<sub>4</sub> |
||
|46 |
|||
|369.9944 |
|369.9944 |
||
| |
| |
||
Line 693: | Line 742: | ||
|f′ |
|f′ |
||
|F<sub>4</sub> |
|F<sub>4</sub> |
||
|45 |
|||
|349.2282 |
|349.2282 |
||
| |
| |
||
Line 705: | Line 755: | ||
|e′ |
|e′ |
||
|E<sub>4</sub> |
|E<sub>4</sub> |
||
|44 |
|||
|329.6276 |
|329.6276 |
||
| |
| |
||
Line 717: | Line 768: | ||
|d{{music|#}}′/e{{music|b}}′ |
|d{{music|#}}′/e{{music|b}}′ |
||
|D{{music|#}}<sub>4</sub>/E{{music|b}}<sub>4</sub> |
|D{{music|#}}<sub>4</sub>/E{{music|b}}<sub>4</sub> |
||
|43 |
|||
|311.1270 |
|311.1270 |
||
| |
| |
||
Line 729: | Line 781: | ||
|d′ |
|d′ |
||
|D<sub>4</sub> |
|D<sub>4</sub> |
||
|42 |
|||
|293.6648 |
|293.6648 |
||
|D |
|D |
||
Line 741: | Line 794: | ||
|c{{music|#}}′/d{{music|b}}′ |
|c{{music|#}}′/d{{music|b}}′ |
||
|C{{music|#}}<sub>4</sub>/D{{music|b}}<sub>4</sub> |
|C{{music|#}}<sub>4</sub>/D{{music|b}}<sub>4</sub> |
||
|41 |
|||
|277.1826 |
|277.1826 |
||
| |
| |
||
Line 752: | Line 806: | ||
|60 |
|60 |
||
|c′ 1-line [[octave]] |
|c′ 1-line [[octave]] |
||
|C<sub>4</sub> [[C (musical note)#Middle C|Middle C]] |
| bgcolor="skyblue" style="color:black" |C<sub>4</sub> [[C (musical note)#Middle C|Middle C]] |
||
| bgcolor="skyblue |
| bgcolor="skyblue" |40 |
||
| bgcolor="skyblue" |261.6256 |
|||
| |
| |
||
| |
| |
||
Line 765: | Line 820: | ||
|b |
|b |
||
|B<sub>3</sub> |
|B<sub>3</sub> |
||
|39 |
|||
|246.9417 |
|246.9417 |
||
| |
| |
||
Line 777: | Line 833: | ||
|a{{music|#}}/b{{music|b}} |
|a{{music|#}}/b{{music|b}} |
||
|A{{music|#}}<sub>3</sub>/B{{music|b}}<sub>3</sub> |
|A{{music|#}}<sub>3</sub>/B{{music|b}}<sub>3</sub> |
||
|38 |
|||
|233.0819 |
|233.0819 |
||
| |
| |
||
Line 789: | Line 846: | ||
|a |
|a |
||
|A<sub>3</sub> |
|A<sub>3</sub> |
||
|37 |
|||
|'''220.0000''' |
|'''220.0000''' |
||
| |
| |
||
Line 801: | Line 859: | ||
|g{{music|#}}/a{{music|b}} |
|g{{music|#}}/a{{music|b}} |
||
|G{{music|#}}<sub>3</sub>/A{{music|b}}<sub>3</sub> |
|G{{music|#}}<sub>3</sub>/A{{music|b}}<sub>3</sub> |
||
|36 |
|||
|207.6523 |
|207.6523 |
||
| |
| |
||
Line 813: | Line 872: | ||
|g |
|g |
||
|G<sub>3</sub> |
|G<sub>3</sub> |
||
|35 |
|||
|195.9977 |
|195.9977 |
||
|G |
|G |
||
Line 825: | Line 885: | ||
|f{{music|#}}/g{{music|b}} |
|f{{music|#}}/g{{music|b}} |
||
|F{{music|#}}<sub>3</sub>/G{{music|b}}<sub>3</sub> |
|F{{music|#}}<sub>3</sub>/G{{music|b}}<sub>3</sub> |
||
|34 |
|||
|184.9972 |
|184.9972 |
||
| |
| |
||
| |
| |
||
| |
| |
||
| |
|||
| High F (7 String) |
|||
| |
| |
||
| |
| |
||
Line 837: | Line 898: | ||
|f |
|f |
||
|F<sub>3</sub> |
|F<sub>3</sub> |
||
|33 |
|||
|174.6141 |
|174.6141 |
||
| |
| |
||
| |
| |
||
| |
| |
||
|High F (7 String) |
|||
| |
|||
| |
| |
||
| |
| |
||
Line 849: | Line 911: | ||
|e |
|e |
||
|E<sub>3</sub> |
|E<sub>3</sub> |
||
|32 |
|||
|164.8138 |
|164.8138 |
||
| |
| |
||
| |
| |
||
| |
| |
||
|High E (5th tunig, 5 String Bass) |
|||
| |
|||
| |
| |
||
| |
| |
||
Line 861: | Line 924: | ||
|d{{music|#}}/e{{music|b}} |
|d{{music|#}}/e{{music|b}} |
||
|D{{music|#}}<sub>3</sub>/E{{music|b}}<sub>3</sub> |
|D{{music|#}}<sub>3</sub>/E{{music|b}}<sub>3</sub> |
||
|31 |
|||
|155.5635 |
|155.5635 |
||
| |
| |
||
Line 873: | Line 937: | ||
|d |
|d |
||
|D<sub>3</sub> |
|D<sub>3</sub> |
||
|30 |
|||
|146.8324 |
|146.8324 |
||
| |
| |
||
Line 885: | Line 950: | ||
|c{{music|#}}/d{{music|b}} |
|c{{music|#}}/d{{music|b}} |
||
|C{{music|#}}<sub>3</sub>/D{{music|b}}<sub>3</sub> |
|C{{music|#}}<sub>3</sub>/D{{music|b}}<sub>3</sub> |
||
|29 |
|||
|138.5913 |
|138.5913 |
||
| |
| |
||
Line 897: | Line 963: | ||
|c small [[octave]] |
|c small [[octave]] |
||
|C<sub>3</sub> |
|C<sub>3</sub> |
||
|28 |
|||
|130.8128 |
|130.8128 |
||
|C (5 String) |
|C (5 String) |
||
Line 909: | Line 976: | ||
|B |
|B |
||
|B<sub>2</sub> |
|B<sub>2</sub> |
||
|27 |
|||
|123.4708 |
|123.4708 |
||
| |
| |
||
Line 921: | Line 989: | ||
|A{{music|#}}/B{{music|b}} |
|A{{music|#}}/B{{music|b}} |
||
|A{{music|#}}<sub>2</sub>/B{{music|b}}<sub>2</sub> |
|A{{music|#}}<sub>2</sub>/B{{music|b}}<sub>2</sub> |
||
|26 |
|||
|116.5409 |
|116.5409 |
||
| |
| |
||
Line 933: | Line 1,002: | ||
|A |
|A |
||
|A<sub>2</sub> |
|A<sub>2</sub> |
||
|25 |
|||
|'''110.0000''' |
|'''110.0000''' |
||
| |
| |
||
| |
| |
||
| |
| |
||
|A (5th tuning Upright) |
|||
| |
|||
|A |
|A |
||
| |
| |
||
Line 945: | Line 1,015: | ||
|G{{music|#}}/A{{music|b}} |
|G{{music|#}}/A{{music|b}} |
||
|G{{music|#}}<sub>2</sub>/A{{music|b}}<sub>2</sub> |
|G{{music|#}}<sub>2</sub>/A{{music|b}}<sub>2</sub> |
||
|24 |
|||
|103.8262 |
|103.8262 |
||
| |
| |
||
Line 957: | Line 1,028: | ||
|G |
|G |
||
|G<sub>2</sub> |
|G<sub>2</sub> |
||
|23 |
|||
|97.99886 |
|97.99886 |
||
| |
| |
||
Line 969: | Line 1,041: | ||
|F{{music|#}}/G{{music|b}} |
|F{{music|#}}/G{{music|b}} |
||
|F{{music|#}}<sub>2</sub>/G{{music|b}}<sub>2</sub> |
|F{{music|#}}<sub>2</sub>/G{{music|b}}<sub>2</sub> |
||
|22 |
|||
|92.49861 |
|92.49861 |
||
| |
| |
||
Line 981: | Line 1,054: | ||
|F |
|F |
||
|F<sub>2</sub> |
|F<sub>2</sub> |
||
|21 |
|||
|87.30706 |
|87.30706 |
||
| F (6 String) |
| Low F (6 String) |
||
| F (6 String) |
| Low F (6 String) |
||
| |
| |
||
| |
| |
||
Line 993: | Line 1,067: | ||
|E |
|E |
||
|E<sub>2</sub> |
|E<sub>2</sub> |
||
|20 |
|||
|82.40689 |
|82.40689 |
||
| |
| |
||
Line 1,005: | Line 1,080: | ||
|D{{music|#}}/E{{music|b}} |
|D{{music|#}}/E{{music|b}} |
||
|D{{music|#}}<sub>2</sub>/E{{music|b}}<sub>2</sub> |
|D{{music|#}}<sub>2</sub>/E{{music|b}}<sub>2</sub> |
||
|19 |
|||
|77.78175 |
|77.78175 |
||
| |
| |
||
Line 1,017: | Line 1,093: | ||
|D |
|D |
||
|D<sub>2</sub> |
|D<sub>2</sub> |
||
|18 |
|||
|73.41619 |
|73.41619 |
||
| |
| |
||
Line 1,029: | Line 1,106: | ||
|C{{music|#}}/D{{music|b}} |
|C{{music|#}}/D{{music|b}} |
||
|C{{music|#}}<sub>2</sub>/D{{music|b}}<sub>2</sub> |
|C{{music|#}}<sub>2</sub>/D{{music|b}}<sub>2</sub> |
||
|17 |
|||
|69.29566 |
|69.29566 |
||
| |
| |
||
Line 1,041: | Line 1,119: | ||
|C great [[octave]] |
|C great [[octave]] |
||
|C<sub>2</sub> [[Deep C]] |
|C<sub>2</sub> [[Deep C]] |
||
|16 |
|||
|65.40639 |
|65.40639 |
||
| |
| |
||
Line 1,053: | Line 1,132: | ||
|B͵ |
|B͵ |
||
|B<sub>1</sub> |
|B<sub>1</sub> |
||
|15 |
|||
|61.73541 |
|61.73541 |
||
| |
| |
||
Line 1,065: | Line 1,145: | ||
|A{{music|#}}͵/B{{music|b}}͵ |
|A{{music|#}}͵/B{{music|b}}͵ |
||
|A{{music|#}}<sub>1</sub>/B{{music|b}}<sub>1</sub> |
|A{{music|#}}<sub>1</sub>/B{{music|b}}<sub>1</sub> |
||
|14 |
|||
|58.27047 |
|58.27047 |
||
| |
| |
||
Line 1,077: | Line 1,158: | ||
|A͵ |
|A͵ |
||
|A<sub>1</sub> |
|A<sub>1</sub> |
||
|13 |
|||
|'''55.00000''' |
|'''55.00000''' |
||
| |
| |
||
Line 1,089: | Line 1,171: | ||
|G{{music|#}}͵/A{{music|b}}͵ |
|G{{music|#}}͵/A{{music|b}}͵ |
||
|G{{music|#}}<sub>1</sub>/A{{music|b}}<sub>1</sub> |
|G{{music|#}}<sub>1</sub>/A{{music|b}}<sub>1</sub> |
||
|12 |
|||
|51.91309 |
|51.91309 |
||
| |
| |
||
Line 1,101: | Line 1,184: | ||
|G͵ |
|G͵ |
||
|G<sub>1</sub> |
|G<sub>1</sub> |
||
|11 |
|||
|48.99943 |
|48.99943 |
||
| |
| |
||
| |
| |
||
| |
| |
||
|G (5th tuning Upright) |
|||
| |
|||
| |
| |
||
| |
| |
||
Line 1,113: | Line 1,197: | ||
|F{{music|#}}͵/G{{music|b}}͵ |
|F{{music|#}}͵/G{{music|b}}͵ |
||
|F{{music|#}}<sub>1</sub>/G{{music|b}}<sub>1</sub> |
|F{{music|#}}<sub>1</sub>/G{{music|b}}<sub>1</sub> |
||
|10 |
|||
|46.24930 |
|46.24930 |
||
| |
| |
||
Line 1,125: | Line 1,210: | ||
|F͵ |
|F͵ |
||
|F<sub>1</sub> |
|F<sub>1</sub> |
||
|9 |
|||
|43.65353 |
|43.65353 |
||
| |
| |
||
| |
| |
||
|Low F (6 String) |
|||
| |
|||
| |
| |
||
| |
| |
||
Line 1,137: | Line 1,223: | ||
|E͵ |
|E͵ |
||
|E<sub>1</sub> |
|E<sub>1</sub> |
||
|8 |
|||
|41.20344 |
|41.20344 |
||
| |
| |
||
Line 1,149: | Line 1,236: | ||
|D{{music|#}}͵/E{{music|b}}͵ |
|D{{music|#}}͵/E{{music|b}}͵ |
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|D{{music|#}}<sub>1</sub>/E{{music|b}}<sub>1</sub> |
|D{{music|#}}<sub>1</sub>/E{{music|b}}<sub>1</sub> |
||
|7 |
|||
|38.89087 |
|38.89087 |
||
| |
| |
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|D͵ |
|D͵ |
||
|D<sub>1</sub> |
|D<sub>1</sub> |
||
|6 |
|||
|36.70810 |
|36.70810 |
||
| |
| |
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|C{{music|#}}͵/D{{music|b}}͵ |
|C{{music|#}}͵/D{{music|b}}͵ |
||
|C{{music|#}}<sub>1</sub>/D{{music|b}}<sub>1</sub> |
|C{{music|#}}<sub>1</sub>/D{{music|b}}<sub>1</sub> |
||
|5 |
|||
|34.64783 |
|34.64783 |
||
| |
| |
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Line 1,185: | Line 1,275: | ||
|C͵ contra-[[octave]] |
|C͵ contra-[[octave]] |
||
|C<sub>1</sub> Pedal C |
|C<sub>1</sub> Pedal C |
||
|4 |
|||
|32.70320 |
|32.70320 |
||
| |
| |
||
| |
| |
||
| |
| |
||
|C (Upright Extension or 5th tuning) |
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| |
|||
| |
| |
||
| |
| |
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Line 1,197: | Line 1,288: | ||
|B͵͵ |
|B͵͵ |
||
|B<sub>0</sub> |
|B<sub>0</sub> |
||
|3 |
|||
|30.86771 |
|30.86771 |
||
| |
| |
||
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|A{{music|#}}͵͵/B{{music|b}}͵͵ |
|A{{music|#}}͵͵/B{{music|b}}͵͵ |
||
|A{{music|#}}<sub>0</sub>/B{{music|b}}<sub>0</sub> |
|A{{music|#}}<sub>0</sub>/B{{music|b}}<sub>0</sub> |
||
|2 |
|||
|29.13524 |
|29.13524 |
||
| |
| |
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|A͵͵ |
|A͵͵ |
||
|A<sub>0</sub> |
|A<sub>0</sub> |
||
|1 |
|||
|'''27.50000''' |
|'''27.50000''' |
||
| |
| |
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| bgcolor="lightgray" | G{{music|#}}͵͵/A{{music|b}}͵͵ |
| bgcolor="lightgray" | G{{music|#}}͵͵/A{{music|b}}͵͵ |
||
| bgcolor="lightgray" | G{{music|#}}<sub>0</sub>/A{{music|b}}<sub>0</sub> |
| bgcolor="lightgray" | G{{music|#}}<sub>0</sub>/A{{music|b}}<sub>0</sub> |
||
| bgcolor="lightgray" |0 |
|||
| bgcolor="lightgray" | 25.95654 |
| bgcolor="lightgray" | 25.95654 |
||
| bgcolor="lightgray" | |
| bgcolor="lightgray" | |
||
Line 1,245: | Line 1,340: | ||
| bgcolor="lightgray" | G͵͵ |
| bgcolor="lightgray" | G͵͵ |
||
| bgcolor="lightgray" | G<sub>0</sub> |
| bgcolor="lightgray" | G<sub>0</sub> |
||
| bgcolor="lightgray" | -1 |
|||
| bgcolor="lightgray" | 24.49971 |
| bgcolor="lightgray" | 24.49971 |
||
| bgcolor="lightgray" | |
| bgcolor="lightgray" | |
||
Line 1,257: | Line 1,353: | ||
| bgcolor="lightgray" | F{{music|#}}͵͵/G{{music|b}}͵͵ |
| bgcolor="lightgray" | F{{music|#}}͵͵/G{{music|b}}͵͵ |
||
| bgcolor="lightgray" | F{{music|#}}<sub>0</sub>/G{{music|b}}<sub>0</sub> |
| bgcolor="lightgray" | F{{music|#}}<sub>0</sub>/G{{music|b}}<sub>0</sub> |
||
| bgcolor="lightgray" | -2 |
|||
| bgcolor="lightgray" | 23.12465 |
| bgcolor="lightgray" | 23.12465 |
||
| bgcolor="lightgray" | |
| bgcolor="lightgray" | |
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| bgcolor="lightgray" | F͵͵ |
| bgcolor="lightgray" | F͵͵ |
||
| bgcolor="lightgray" | F<sub>0</sub> |
| bgcolor="lightgray" | F<sub>0</sub> |
||
| bgcolor="lightgray" | -3 |
|||
| bgcolor="lightgray" | 21.82676 |
| bgcolor="lightgray" | 21.82676 |
||
| bgcolor="lightgray" | |
| bgcolor="lightgray" | |
||
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| bgcolor="lightgray" | E͵͵ |
| bgcolor="lightgray" | E͵͵ |
||
| bgcolor="lightgray" | E<sub>0</sub> |
| bgcolor="lightgray" | E<sub>0</sub> |
||
| bgcolor="lightgray" | -4 |
|||
| bgcolor="lightgray" | 20.60172 |
| bgcolor="lightgray" | 20.60172 |
||
| bgcolor="lightgray" | |
| bgcolor="lightgray" | |
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| bgcolor="lightgray" | D{{music|#}}͵͵/E{{music|b}}͵͵ |
| bgcolor="lightgray" | D{{music|#}}͵͵/E{{music|b}}͵͵ |
||
| bgcolor="lightgray" | D{{music|#}}<sub>0</sub>/E{{music|b}}<sub>0</sub> |
| bgcolor="lightgray" | D{{music|#}}<sub>0</sub>/E{{music|b}}<sub>0</sub> |
||
| bgcolor="lightgray" | -5 |
|||
| bgcolor="lightgray" | 19.44544 |
| bgcolor="lightgray" | 19.44544 |
||
| bgcolor="lightgray" | |
| bgcolor="lightgray" | |
||
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| bgcolor="lightgray" | D͵͵ |
| bgcolor="lightgray" | D͵͵ |
||
| bgcolor="lightgray" | D<sub>0</sub> |
| bgcolor="lightgray" | D<sub>0</sub> |
||
| bgcolor="lightgray" | -6 |
|||
| bgcolor="lightgray" | 18.35405 |
| bgcolor="lightgray" | 18.35405 |
||
| bgcolor="lightgray" | |
| bgcolor="lightgray" | |
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Line 1,317: | Line 1,418: | ||
| bgcolor="lightgray" | C{{music|#}}͵͵/D{{music|b}}͵͵ |
| bgcolor="lightgray" | C{{music|#}}͵͵/D{{music|b}}͵͵ |
||
| bgcolor="lightgray" | C{{music|#}}<sub>0</sub>/D{{music|b}}<sub>0</sub> |
| bgcolor="lightgray" | C{{music|#}}<sub>0</sub>/D{{music|b}}<sub>0</sub> |
||
| bgcolor="lightgray" | -7 |
|||
| bgcolor="lightgray" | 17.32391 |
| bgcolor="lightgray" | 17.32391 |
||
| bgcolor="lightgray" | |
| bgcolor="lightgray" | |
||
Line 1,329: | Line 1,431: | ||
| bgcolor="lightgray" | C͵͵ sub-contra-[[octave]] |
| bgcolor="lightgray" | C͵͵ sub-contra-[[octave]] |
||
| bgcolor="lightgray" | C<sub>0</sub> Double Pedal C |
| bgcolor="lightgray" | C<sub>0</sub> Double Pedal C |
||
| bgcolor="lightgray" | -8 |
|||
| bgcolor="lightgray" | 16.35160 |
| bgcolor="lightgray" | 16.35160 |
||
| bgcolor="lightgray" | |
| bgcolor="lightgray" | |
||
Line 1,342: | Line 1,445: | ||
* [[Scientific pitch notation]] |
* [[Scientific pitch notation]] |
||
* [[Music and mathematics]] |
* [[Music and mathematics]] |
||
==External links== |
|||
* [http://shakahara.com/pianopitch2.php interactive piano frequency table] – A PHP script allowing the reference pitch of A4 to be altered from 440 Hz. |
|||
* [https://web.archive.org/web/20190510200224/https://mdoege.github.io/PySynth/ PySynth] – A simple [[Python (programming language)|Python]]-based [[software synthesizer]] that prints the key frequencies table and then creates a few demo songs based on that table. |
|||
* "[http://www.sengpielaudio.com/calculator-notenames.htm Keyboard and frequencies]", ''SengpielAudio.com''. |
|||
* [http://www.deimos.ca/notefreqs 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. |
|||
==References== |
==References== |
||
<references /> |
|||
<references /> |
|||
{{Musical keyboards}} |
{{Musical keyboards}} |
||
{{Pitch (music)}} |
{{Pitch (music)}} |
||
[[Category:Piano |
[[Category:Piano]] |
||
[[Category:Musical tuning]] |
[[Category:Musical tuning]] |
Latest revision as of 15:50, 1 July 2024
This article needs additional citations for verification. (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).[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 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).[1][2] For example, to get the frequency one semitone up from A4 (A♯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.[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 Hz:
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[edit]
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.[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 | |||||
---|---|---|---|---|---|---|---|---|---|---|---|
Violin | Viola | Cello | Bass | Guitar | Ukulele | ||||||
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[edit]
References[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.