A329209 Decimal expansion of the fundamental frequency of the note D4 in hertz.

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

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 D4 (7 semitones below A4) is 440*2^(-7/12) Hz = 293.7 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 12

Formula

Equals 220 * 2^(5/12).

Example

Frequencies of notes in an octave (Hz):
   >--------------------------------------------------
  |
  |  C4                  261.6255653005...  (A329207)
  |           +---------------------------------------
   >----------| C#4/Db4  277.1826309768...  (A329208)
  |           +---------------------------------------
  |  D4                  293.6647679174...  (this seq)
  |           +---------------------------------------
   >----------| D#4/Eb4  311.1269837220...  (A329210)
  |           +---------------------------------------
  |  E4                  329.6275569128...  (A329211)
  |
   >--------------------------------------------------
  |
  |  F4                  349.2282314330...  (A329212)
  |           +---------------------------------------
   >----------| 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[440 1/Surd[2^7, 12], 10, 120][[1]] (* Harvey P. Dale, Aug 01 2021 *)

Prog

(PARI) default(realprecision, 100); 440 * 2^(-7/12)

Crossrefs

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

Sequence in context: A275838 A323720 A021777 * A095802 A334472 A243448

Adjacent sequences: A329206 A329207 A329208 * A329210 A329211 A329212

Keyword

nonn,easy,cons

Author

Jianing Song, Nov 08 2019

Status

approved