A329215 - OEIS

%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