cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-3 of 3 results.

A010774 Decimal expansion of 12th root of 2.

Original entry on oeis.org

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

Views

Author

N. J. A. Sloane

Keywords

Comments

This number figures in our standard 12-tone tuning of music today.
It represents the frequency ratio of a semitone in equal temperament. The equal-tempered chromatic scale divides the octave, which has a ratio of 2:1, into twelve parts of equal ratio: [2^(n/12), 2^((n+1)/12)), 0 <= n <= 11. - Daniel Forgues, Feb 28 2013

Examples

			2^(1/12) = 1.059463094359295264561825294946341700779204317494...

References

  • D. Coulter, Digital Audio Processing. Berkeley, California: Focal Press (2000) p. 30
  • Ian Stewart, Professor Stewart's Incredible Numbers, London, Profile Books, 2015, pp. 217-228.

Links

Crossrefs

Cf. A103922, A010768.
Cf. A214832, A254531.

Programs

Formula

Equals Product_{k>=0} (1 + (-1)^k/(12*k + 11)). - Amiram Eldar, Jul 29 2020
Equals sqrt(A010768). - Hugo Pfoertner, May 31 2024

A214832 Integer part of A440 piano key frequencies, start with A0 = the 1st key.

Original entry on oeis.org

27, 29, 30, 32, 34, 36, 38, 41, 43, 46, 48, 51, 55, 58, 61, 65, 69, 73, 77, 82, 87, 92, 97, 103, 110, 116, 123, 130, 138, 146, 155, 164, 174, 184, 195, 207, 220, 233, 246, 261, 277, 293, 311, 329, 349, 369, 391, 415, 440, 466, 493, 523, 554, 587, 622, 659, 698, 739, 783, 830, 880, 932, 987, 1046, 1108, 1174, 1244, 1318, 1396, 1479, 1567, 1661, 1760, 1864, 1975, 2093, 2217, 2349, 2489, 2637, 2793, 2959, 3135, 3322, 3520, 3729, 3951, 4186
Offset: 1

Views

Author

Jon Perry, Mar 07 2013

Keywords

Comments

A254531(a(k)) = k, k = 1..88. - Reinhard Zumkeller, Feb 04 2015

Examples

			Middle C is 261.626 Hz so a(40) = 261.

Links

Crossrefs

Cf. A059620, A079731, A131062, A101285, A131071.
Cf. A254531, A010774.

Programs

  • Haskell
    a214832 = floor . (* 440) . (2 **) . (/ 12) . fromIntegral . subtract 49
-- Reinhard Zumkeller, Nov 23 2014
  • JavaScript
    for (i=1;i<=88;i++) document.write(Math.floor(Math.pow(2,(i-49)/12)*440)+", ");
  • PARI
    a(n)=floor(440*2^((n-49)/12));

Formula

a(n) = floor[2^((n-49)/12)*440] (Hz) for 1 <= n <= 88.

A079731 Fundamental piano frequencies in Hertz rounded to nearest integer.

Original entry on oeis.org

28, 55, 110, 220, 440, 880, 1760, 3520
Offset: 0

Views

Author

Ralf Stephan, Feb 18 2003

Keywords

Links

Crossrefs

Cf. A214832, A254531.

Formula

a(n)=round(27.5*2^n), n=0...7.
Showing 1-3 of 3 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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