login
Decimal expansion of the fundamental frequency of the note D#4/Eb4 in hertz.
10

%I #14 Jun 18 2024 11:08:31

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

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

%U 1,1,4,5,2,6,1,6,6,3,5,4,8,5,4,7,0,8,5,2,5,7,5

%N Decimal expansion of the fundamental frequency of the note D#4/Eb4 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 D#4/Eb4 (6 semitones below A4) is 440*2^(-6/12) Hz = 311.1 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_02">Index entries for algebraic numbers, degree 2</a>

%F Equals 220 * sqrt(2).

%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... (this seq)

%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... (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 First[RealDigits[220*Sqrt[2], 10, 100]] (* _Paolo Xausa_, Jun 18 2024 *)

%o (PARI) default(realprecision, 100); 440 * 2^(-6/12)

%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