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%I #15 Jun 19 2024 03:05:23
%S 4,1,5,3,0,4,6,9,7,5,7,9,9,4,5,1,3,8,5,2,2,4,4,1,7,8,8,9,3,3,7,1,5,1,
%T 2,5,4,4,3,3,3,0,0,5,3,4,6,9,0,4,6,8,3,8,0,4,6,5,3,5,0,6,2,6,2,0,0,4,
%U 6,0,5,4,6,0,5,0,3,0,9,4,9,3,3,9,8,8,7,3,2,0,0
%N Decimal expansion of the fundamental frequency of the note G#4/Ab4 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 G#4/Ab4 (1 semitone below A4) is 440*2^(-1/12) Hz = 415.3 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_12">Index entries for algebraic numbers, degree 12</a>
%F Equals 220 * 2^(11/12).
%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... (A329212)
%e | +---------------------------------------
%e >----------| F#4/Gb4 369.9944227116... (A329213)
%e | +---------------------------------------
%e | G4 391.9954359817... (A329214)
%e | +---------------------------------------
%e >----------| G#4/Ab4 415.3046975799... (this seq)
%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 First[RealDigits[220*2^(11/12), 10, 100]] (* _Paolo Xausa_, Jun 18 2024 *)
%o (PARI) default(realprecision, 100); 440 * 2^(-1/12)
%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