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Decimal expansion of the fundamental frequency of the note F4 in hertz.
10

%I #12 Aug 21 2023 11:14:40

%S 3,4,9,2,2,8,2,3,1,4,3,3,0,0,3,8,8,4,4,4,5,3,7,5,2,4,0,6,3,9,9,0,7,8,

%T 1,7,2,8,6,1,2,8,5,3,2,1,3,7,9,6,7,6,6,2,1,5,7,8,2,2,8,6,7,6,0,1,5,4,

%U 7,6,3,1,2,3,7,3,2,8,2,1,8,1,2,0,1,7,9,7,2,6,9

%N Decimal expansion of the fundamental frequency of the note F4 in hertz.

%C In 12-tone equal temperament, when A4 (the fifth A on the Piano keyboard) is tuned to 440 Hz, the frequency of the note F4 (4 semitones below A4) is 440*2^(-4/12) Hz = 349.2 Hz.

%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Piano_key_frequencies">Piano key frequencies</a>

%H <a href="/index/Mu#music">Index entries for sequences based on music</a>

%H <a href="/index/Al#algebraic_03">Index entries for algebraic numbers, degree 3</a>

%F Equals 220 * 2^(2/3).

%e Frequencies of notes in an octave (Hz):

%e >--------------------------------------------------

%e |

%e | C4 261.6255653005... (A329207)

%e | +---------------------------------------

%e >----------| C#4/Db4 277.1826309768... (A329208)

%e | +---------------------------------------

%e | D4 293.6647679174... (A329209)

%e | +---------------------------------------

%e >----------| D#4/Eb4 311.1269837220... (A329210)

%e | +---------------------------------------

%e | E4 329.6275569128... (A329211)

%e |

%e >--------------------------------------------------

%e |

%e | F4 349.2282314330... (this seq)

%e | +---------------------------------------

%e >----------| F#4/Gb4 369.9944227116... (A329213)

%e | +---------------------------------------

%e | G4 391.9954359817... (A329214)

%e | +---------------------------------------

%e >----------| G#4/Ab4 415.3046975799... (A329215)

%e | +---------------------------------------

%e | A4 440.0000000000

%e | +---------------------------------------

%e >----------| A#4/Bb4 466.1637615180... (A329217)

%e | +---------------------------------------

%e | B4 493.8833012561... (A329218)

%e |

%e >--------------------------------------------------

%e [New layout from _Jon E. Schoenfield_, Nov 08 2019]

%t RealDigits[220 Surd[4,3],10,120][[1]] (* _Harvey P. Dale_, Jul 31 2021 *)

%o (PARI) default(realprecision, 100); 440 * 2^(-4/12)

%Y See the Example section above for the fundamental frequency of some other notes.

%K nonn,easy,cons

%O 3,1

%A _Jianing Song_, Nov 08 2019