A329212 Decimal expansion of the fundamental frequency of the note F4 in hertz.

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

Offset

3,1

Comments

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.

Links

Table of n, a(n) for n=3..93.

Wikipedia, Piano key frequencies

Index entries for sequences based on music

Index entries for algebraic numbers, degree 3

Formula

Equals 220 * 2^(2/3).

Example

Frequencies of notes in an octave (Hz):
   >--------------------------------------------------
  |
  |  C4                  261.6255653005...  (A329207)
  |           +---------------------------------------
   >----------| C#4/Db4  277.1826309768...  (A329208)
  |           +---------------------------------------
  |  D4                  293.6647679174...  (A329209)
  |           +---------------------------------------
   >----------| D#4/Eb4  311.1269837220...  (A329210)
  |           +---------------------------------------
  |  E4                  329.6275569128...  (A329211)
  |
   >--------------------------------------------------
  |
  |  F4                  349.2282314330...  (this seq)
  |           +---------------------------------------
   >----------| F#4/Gb4  369.9944227116...  (A329213)
  |           +---------------------------------------
  |  G4                  391.9954359817...  (A329214)
  |           +---------------------------------------
   >----------| G#4/Ab4  415.3046975799...  (A329215)
  |           +---------------------------------------
  |  A4                  440.0000000000
  |           +---------------------------------------
   >----------| A#4/Bb4  466.1637615180...  (A329217)
  |           +---------------------------------------
  |  B4                  493.8833012561...  (A329218)
  |
   >--------------------------------------------------
[New layout from Jon E. Schoenfield, Nov 08 2019]

Mathematica

RealDigits[220 Surd[4, 3], 10, 120][[1]] (* Harvey P. Dale, Jul 31 2021 *)

Prog

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

Crossrefs

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

Sequence in context: A019676 A246726 A019900 * A290373 A122791 A011429

Adjacent sequences: A329209 A329210 A329211 * A329213 A329214 A329215

Keyword

nonn,easy,cons

Author

Jianing Song, Nov 08 2019

Status

approved