A329215 Decimal expansion of the fundamental frequency of the note G#4/Ab4 in hertz.

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, 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, 6, 0, 5, 4, 6, 0, 5, 0, 3, 0, 9, 4, 9, 3, 3, 9, 8, 8, 7, 3, 2, 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 G#4/Ab4 (1 semitone below A4) is 440*2^(-1/12) Hz = 415.3 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^(11/12).

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...  (A329213)
  |           +---------------------------------------
  |  G4                  391.9954359817...  (A329214)
  |           +---------------------------------------
   >----------| G#4/Ab4  415.3046975799...  (this seq)
  |           +---------------------------------------
  |  A4                  440.0000000000
  |           +---------------------------------------
   >----------| A#4/Bb4  466.1637615180...  (A329217)
  |           +---------------------------------------
  |  B4                  493.8833012561...  (A329218)
  |
   >--------------------------------------------------
[New layout from Jon E. Schoenfield, Nov 08 2019]

Mathematica

First[RealDigits[220*2^(11/12), 10, 100]] (* Paolo Xausa, Jun 18 2024 *)

Prog

(PARI) default(realprecision, 100); 440 * 2^(-1/12)

Crossrefs

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

Sequence in context: A067061 A115210 A199150 * A214892 A030352 A212643

Adjacent sequences: A329212 A329213 A329214 * A329216 A329217 A329218

Keyword

nonn,easy,cons

Author

Jianing Song, Nov 08 2019

Status

approved