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

Author

Jianing Song, Nov 08 2019

Keywords

• nonn
• easy
• cons

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.

Examples

			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]
		

Links

• Wikipedia, Piano key frequencies
• Index entries for sequences based on music
• Index entries for algebraic numbers, degree 12

Crossrefs

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

Programs

Mathematica

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

PARI

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

Formula

Equals 220 * 2^(11/12).