A329213 Decimal expansion of the fundamental frequency of the note F#4/Gb4 in hertz.

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

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 F#4/Gb4 (3 semitones below A4) is 440*2^(-3/12) Hz = 370.0 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 4

Formula

Equals 220 * 2^(3/4).

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...  (A329212)
  |           +---------------------------------------
   >----------| F#4/Gb4  369.9944227116...  (this seq)
  |           +---------------------------------------
  |  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[8, 4], 10, 120][[1]] (* Harvey P. Dale, May 05 2023 *)

Prog

(PARI) default(realprecision, 100); 440 * 2^(-3/12)

Crossrefs

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

Sequence in context: A160178 A011383 A329513 * A007844 A224523 A159785

Adjacent sequences: A329210 A329211 A329212 * A329214 A329215 A329216

Keyword

nonn,easy,cons

Author

Jianing Song, Nov 08 2019

Status

approved